(Lukas Schreiber, Jörg Schönherr) Water and Solutions
(Lukas Schreiber, Jörg Schönherr) Water and Solutions
(Lukas Schreiber, Jörg Schönherr) Water and Solutions
Lukas Schreiber
Jrg Schnherr
123
ISBN 978-3-540-68944-7
e-ISBN 978-3-540-68945-4
Preface
Transport properties of plant cuticles are important for different fields of modern
plant sciences. Ecologists and physiologists are interested in water losses to the
environment via the cuticle. Penetration of plant protecting agents and nutrients
into leaves and fruits is relevant for research in agriculture and plant protection.
Ecotoxicologists need to know the amounts of environmental xenobiotics which
accumulate in leaves and other primary plant organs from the environment. For all
of these studies suitable methods should be used, and a sound theoretical basis helps
to formulate testable hypotheses and to interpret experimental data. Unnecessary
experiments and experiments which yield ambiguous results can be avoided.
In this monograph, we have analysed on a molecular basis the movement of
molecules across plant cuticles. Based on current knowledge of chemistry and structure of cuticles, we have characterised the aqueous and lipophilic pathways, the
nature and mechanisms of mass transport and the factors controlling the rate of
movement. We have focused on structureproperty relationships for penetrant transport, which can explain why water and solute permeabilities of cuticles differ widely
among plant species. Based on this knowledge, mechanisms of adaptation to environmental factors can be better understood, and rates of cuticular penetration can be
optimised by plant physiologists and pesticide chemists.
This monograph is a mechanistic analysis of foliar penetration. We have made no
attempt to review and summarise data on foliar penetration of specific solutes into
leaves of specific plant species under a specific set of environmental conditions. A
number of reviews can be consulted if this is of interest (Cottrell 1987; Cutler et al.
1982; Holloway et al. 1994; Kerstiens 1996a; Riederer and Mller 2006). A wealth
of additional literature is cited in these books.
Once synthesised, the plant cuticle is a purely extra-cellular membrane, and
metabolism or active transport which greatly affect transport across cytoplasmic
membranes are not involved in cuticular penetration. For this reason, a number of
books on sorption and diffusion in man-made polymeric membranes were sources
of inspiration in writing this monograph. We drew heavily on the classical books by
Crank (1975), Crank and Park (1968), Israelachvili (1991) and Vieth (1991).
vi
Preface
This is not a review about foliar penetration. We aimed at writing a general textbook on sorption and diffusion in cuticles. Based on characteristic and representative
examples we show (1) how problems related to water and solute transport across
cuticles can experimentally be approached using suitable methods developed in the
past, (2) the way in which these data can be analysed, and what we can learn from
these results about structure and functioning of cuticles, and finally (3) the limitations and problems in data interpretation. At the end of each chapter, problems and
solutions can be found. Some of them summarise the highlights of the text, some
illustrate implications and others are intended as exercises of calculations.
The idea of analysing permeability of cuticles based on structureproperty relationships was born during a stay (19671972) by one of us (JS) as a doctoral
student in Bukovacs laboratory at Michigan State University, USA. Later, the concepts developed in the two volumes by Hartley and Graham-Bryce (1980) were of
immense help to us in formulating testable hypotheses. In writing, we have relied
greatly on our own work conducted at the Botany departments of the Universities
of Mnchen, Bonn and Hannover, but the book could not have been written without the collaborative research in the last decades with M. Riederer (University of
Wrzburg), K. Lendzian (Technische Universitt Mnchen), B.T. Grayson (Shell,
Sittingbourne, England), P. Baur (now Bayer Crop Science) and Anke Buchholz
(now Syngenta, Switzerland).
It was one of our aims to provide a better understanding of cuticular penetration,
and to formulate some basic rules for predicting and optimising rates of cuticular
penetration. This requires some elementary mathematics, but we have kept equations simple and calculus is not required to follow our arguments or to solve the
problems. Some basic knowledge of chemistry and physics are helpful but not
mandatory. We hope this book will be useful to Master and doctoral students working in different fields of plant sciences (ecology, physiology, molecular biology,
ecotoxicology, plant nutrition, horticulture, pesticide science and plant protection)
when faced for the first time with problems related to permeability of plant cuticles
to water and solutes. Researchers at universities, applied research institutions and
those in the agrochemical industry working on transport across cuticles will find
numerous useful hints. This book was written as a text book and can be used for
teaching, since in each chapter (1) we state the problem, (2) we describe an experimental solution, (3) we present a critical analysis of the experimental data, and (4) at
the end of each chapter we add problems intended to help the student in verifying
understanding of concepts and calculations.
Germany
November 2008
Lukas Schreiber
Jrg Schnherr
Acknowledgements
vii
Contents
1
2
3
8
8
10
11
14
15
15
15
18
20
26
27
27
28
31
32
33
35
37
37
38
39
40
43
ix
Contents
45
46
48
49
51
51
51
53
53
55
58
58
60
60
Water Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1 Water Permeability of Synthetic Polymer Membranes and Polymer
Matrix Membranes: A Comparison of Barrier Properties . . . . . . . . . . 61
4.2 Isoelectric Points of Polymer Matrix Membranes . . . . . . . . . . . . . . . . 65
4.3 Ion Exchange Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.1 Cation Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Water Vapour Sorption and Permeability as Affected by pH,
Cations and Vapour Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.5 Diffusion and Viscous Transport of Water: Evidence for Aqueous
Pores in Polymer Matrix Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5.1 Lipophilic and Hydrophilic Pathways in the
Polymer Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.2 Permeability of the Pore and Cutin Pathways . . . . . . . . . . . . . 89
4.5.3 Effect of Partial Pressure of Water Vapour on Permeances
of the Pore and Cutin Pathways . . . . . . . . . . . . . . . . . . . . . . . . 92
4.6 Water Permeability of Isolated Astomatous Cuticular Membranes . . 93
4.6.1 Comparing Water Permeability of CM with that of MX . . . . 93
4.6.2 Water Permeability of CM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.6.2.1 Chemical Composition of Wax and Its
Relationship to Water Permeability . . . . . . . . . . . . . 96
4.6.2.2 Water Permeability of CM and Diffusion
of Stearic Acid in Wax . . . . . . . . . . . . . . . . . . . . . . . . 98
4.6.2.3 Co-Permeation of Water and Lipophilic Solutes . . . 101
4.6.2.4 Effect of Partial Vapour Pressure (Humidity)
on Permeability of CM . . . . . . . . . . . . . . . . . . . . . . . 104
4.6.2.5 Effect of AgCl Precipitates on Water Permeance . . 105
Contents
xi
4.6.3
xii
Contents
6.1.6.3
Contents
xiii
7.4.2
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
Chapter 1
From the very beginning of life on earth, all living organisms established protective
interfaces between themselves and the aqueous or gaseous environment. In all cases
these interfaces are of lipid nature. The first unicellular organisms developed cell
membranes of phospholipids separating the cytoplasm from the surrounding aqueous environment. Phospholipids are major constituents of cytoplasmic membranes
of contemporary organisms. Later in evolution, multicellular organism with specialised tissues and organs appeared, and the mainland was conquered successfully
by plants and animals. Since the water potential of the atmosphere is always strongly
negative, there is a constant loss of water from living organisms to the atmosphere.
In order to survive and avoid desiccation, land-living animals and plants had to cope
with this situation. With terrestrial higher plants, the evolutionary answer to this
challenge was the development of a cuticle about 500 million years ago. Insects and
mammals are also protected by cuticles or skins. Their cuticles have similar functions, but they differ in chemistry and structure from the plant cuticle (Andersen
1979; Rawlings 1995).
The plant cuticle is an extracellular polymer membrane which covers all primary organs such as stems, leaves, flowers and fruits. In contrast to most synthetic
polymer membranes, which are mostly homogeneous in structure and composition,
plant cuticles are polymer membranes characterised by a pronounced heterogeneity in both chemical composition as well as fine structure. A functional analysis of
barrier properties of plant cuticles requires detailed information on chemistry and
structure. It is one of our major objectives to relate chemistry and structure of cuticles to water and solute permeability. We have evaluated the literature in an attempt
to find the information necessary for relating permeability of cuticles to chemistry
and structure.
Using the terminology of engineering, cuticles can be classified as composite
membranes. They are composed of two chemically distinct fractions, the polymer
matrix membrane (MX) and soluble cuticular lipids (SCL), often called cuticular
waxes. For unambiguous chemical analysis and for measuring permeability, cuticles are isolated either chemically or enzymatically (Schnherr and Riederer 1986).
The method of choice is enzymatic isolation at room temperature using pectinase
Fig. 1.1 Scanning electron micrograph of the morphological surface of a cuticle isolated with
pectinase from an inner Clivia miniata leaf. Cuticular pegs, protruding between anticlinal cell
walls, reveal the pattern of the epidermal cells
(Sect. 9.1). This avoids heat and treatment with chemicals which might cause
hydrolysis or other chemical reactions. Pectinase digests the pectin layer interposed
between cuticles and the cellulose wall of the epidermis. Occasionally a pectinase/cellulase mixture has been used, but the benefit of including cellulose has never
been clearly demonstrated. Even when isolated using pectinase alone, the inner surfaces of the cuticular membrane look clean and cellulose residues are not detectable
(Fig. 1.1).
We shall refer to isolated cuticles as cuticular membranes (CM), while the term
cuticle is reserved to cuticles still attached to epidermis and/or organs. Cuticles
cannot be isolated from leaves or fruits of all plant species. CM which can be
obtained by enzymatic isolation have been preferentially used for chemical analysis, because this avoids ambiguities concerning the origin of the materials (waxes,
cutin acids) obtained by extraction and depolymerisation. If enzymatic isolation of
cuticles is not possible, air-dried leaves must be used. In these cases, there is a risk
that some of the products obtained by solvent extraction or depolymerisation may
have originated from other parts of the leaf.
Leaf CM {Citrus aurantium (bitter orange), Hedera helix (ivy), Prunus laurocerasus (cherry laurel)} preferentially used in transport experiments have an average
mass of 250400 g cm2 (Schreiber and Schnherr 1996a), although CM thickness can vary between 30 nm (Arabidopsis thaliana (mouse-ear-cress)) and 30 m
(fruit CM of Malus domestica (apple)). Specific gravity of CM is around 1.1 g cm3
(Schreiber and Schnherr 1990), and using this factor the average thickness of these
leaf CM can be calculated to range from about 2.3 to 3.7 m.
If the MX is subjected to hydrolysis in 6 N HCl at 120C, an insoluble polymer
is obtained. This polymer has the consistency of chewing gum, and an elemental composition very similar to a polyester of hydroxyfatty acids (Schnherr and
Bukovac 1973). It is considered to be pure cutin. The aqueous HCl supernatant contains a complex mixture of carbohydrates, amino acids and phenols, but only amino
acids have been determined quantitatively (Schnherr and Bukovac 1973; Schnherr
and Huber 1977). Some cuticular carbohydrates and phenolic substances have also
been characterised (Marga et al. 2001; Hunt and Baker 1980). Polarised light (Sitte
and Rennier 1963) and thermal expansion (Schreiber and Schnherr 1990) indicate
the presence of crystalline cellulose. It is not known if polar solutes obtained by acid
hydrolysis are simply trapped in the cutin as polysaccharides or polypeptides, or if
they are covalently attached to cutin. Phenolic acids contained in the MX of ripe
tomato fruits are released by ester hydrolysis, but it is uncertain if they were linked
to cutin or to other constituents of the MX (Hunt and Baker 1980). Riederer and
Schnherr (1984) have fractionated CM of leaves and fruits from various species
(Table 1.1).
The mass of the CM per unit area varies widely among species between
262 g cm2 (Cucumis (cucumber) fruit CM) and 2,173 g cm2 (Lycopersicon
(tomato) fruit CM). The wax fraction varies even more and is smallest with Citrus
leaves (5%) and largest with Pyrus (pear) cv. Bartlett abaxial leaf CM (45%). The
average weight fraction of the MX is 76%, with cutin and polar polymers amounting
to 55% and 21% respectively. Variation among species in the fraction of polar polymers and cutin is much smaller than in mass per area of CM or in weight fraction of
waxes (Table 1.1).
Table 1.1 Mass per area and composition of selected cuticular membranes (data from Riederer
and Schnherr 1984)
Species
CM
(g cm2 )
SCL
(% of CM)
MX
(% of CM)
CU
(% of MX)
HY
(% of MX)
Fruit CM
Capsicum
Cucumis
Lycopersicon
Solanum
1,971
262
2,173
599
10
20
7
8
90
80
93
92
61
55
69
62
29
25
24
30
Leaf CM
Citrus ab
Clivia ad
Clivia ab
Ficus ad
Ficus ab
Hedera ad
Hedera ab
Nerium ad
Nerium ab
Olea ad
Pyrus cv. Conf. ad
Pyrus cv. Conf. ad
Pyrus cv. Bartlett ad
Pyrus cv. Bartlett ab
318
530
466
458
493
450
430
1,318
1,633
836
353
324
350
421
5
20
18
25
37
19
17
39
37
29
31
32
38
45
95
80
82
75
63
81
83
61
63
71
69
68
62
55
73
64
66
56
52
60
61
45
46
50
46
47
43
37
22
16
16
19
11
21
22
16
17
21
23
21
19
18
744 (602)
24 (12)
76 (12)
55 (10)
21 (4.7)
Mean (sd)
CM, cuticular membrane; SCL, soluble cuticular lipids (waxes); CU, cutin; HY, fraction
hydrolysable with HCl (polar polymers); ab, abaxial; ad, adaxial; sd, standard deviation
Table 1.2 Common C16 - and C18 -monomers occurring in the polymer matrix of several plant
species
Compound
Chemical Structure
C16 -monomers
Palmitic acid
CH3
Palmitic alcohol
CH3
16-Hydroxypalmitic acid
OHCH2
1,16-Palmitic diacid
COOH
9,16-Dihydroxypalmitic acid
OHCH2
COOH
CH2OH
COOH
COOH
COOH
OH
OH
10,16-Dihydroxypalmitic acid
OHCH2
COOH
C18 -monomers
Stearic acid
CH3
Stearic alcohol
CH3
18-Hydroxystearic acid
OHCH2
COOH
CH2OH
COOH
OH
9,10,18-Trihydroxystearic acid
OHCH2
COOH
OH
18-Hydroxy-9,10-epoxystearic acid
COOH
OHCH2
O
C18 unsaturated dicarboxylic acids (Nawrath 2006), which does not fit the picture of cutin composition derived from all previous investigations (Table 1.2).
Unfortunately, barrier properties of this type of atypical cutin have not yet been
characterised. Thus, one should be cautious before generalising cutin composition
obtained by transesterification of MX of plant species from which CM can be
isolated. This may represent a specific set of cutins characteristic of isolable cuticles.
We are searching for the relationship between chemistry and structure of cuticles
and their permeability to water and solutes. Permeability of a membrane is related to
structure, which in turn depends on chemical composition. Unfortunately, we could
not find any study relating the above cutin classification to water or solute permeability. Number, type and distribution of polar functional groups in the polymer,
crystallinity, and the prevalence of the glassy and rubbery states at physiological
temperatures are important properties. In composite polymers, the mutual arrangement of the various polymers is also important. Simply looking at the products
obtained by transesterification or acid hydrolysis reveals little about the structure
and function of the polymer.
The monomer composition does not tell us much about the original composition
of the polymer and the way the monomers were cross-linked and arranged in the
MX. The cutin models which are based on type and predominance of cutin acids
are guesswork, and are as good as the underlying assumptions (Kolattukudy 2004).
A new approach is non-destructive NMR spectroscopy (Fang et al. 2001), directly
mapping the intact polymer and the intermolecular cross-linking of the monomers
without prior degradation of the MX. This approach allows the identification of
ester linkages in cutin in vivo, and it shows that sugar moieties can be linked to
cutin monomers, although the exact type of bond has not yet been identified. In
spite of these numerous attempts, we must admit that we are still far away from a
complete picture of the molecular architecture of cutin or the MX.
Another complication often overlooked is the fact that cuticles containing epoxyfatty acids (Holloway et al. 1981) are only partially degraded by transesterification,
and the chemical analysis of these MX is incomplete. A significant if not major fraction of the MX resists degradation, indicating the existence of bonds other than ester
linkages in the cutin polymer. This non-ester cutin is also called cutan, whereas
that fraction of the MX cross linked by ester bonds is called cutin. There is evidence that intermolecular cross-linking in cutan is mainly by ether bonds (Villena
et al. 1999). This non-degradable fraction of the cuticle is still poorly characterised,
because of major methodological limitations.
Clivia miniata plants are monocots, and leaves grow at their base. The age of
leaf segments increases with distance from leaf base. Adaxial cuticles have been
isolated from leaf strips, and the MX has been fractionated into ester cutin and cutan
(Riederer and Schnherr 1988). Fractionation of total cutin into ester cutin and nonester cutin (cutan) was possible only starting with position 34 cm from base. Most
of the young cuticle is made up of ester cutin (Fig. 1.2), which increases rapidly with
age, and in the study above its amount doubled at position 56 cm when epidermal
350
300
total cutin
250
ester cutin
200
150
100
cutan
50
0
10
15
20
cells had obtained their maximum area. Initially, cutan mass increased slowly up
to 89 cm, but later its mass increased more rapidly and at 1920 cm it was higher
than the mass of ester-cutin. Ester cutin reached its maximum mass at 1113 cm;
thereafter it decreased, showing that ester cutin was converted in part to cutan.
Following transesterification the lipophilic cutin monomers are recovered with
organic solvents like chloroform. Polar compounds released by transesterification
are lost, since they remain in the reaction residue, which is discarded. Due to this
experimental approach, it was overlooked in all previous analyses of cutin composition that glycerol, a small and highly polar organic molecule, is also released and
forms an important cross-linker in the MX (Graca et al. 2002).
Polypeptides (Schnherr and Huber 1977), aromatic compounds (Hunt and Baker
1980) and carbohydrates (Wattendorff and Holloway 1980; Dominguez and Heredia
1999; Marga et al. 2001) are significant although minor constituents of the MX. The
question arises as to whether they have any specific functions in the MX or if their
presence is accidental. Nothing is known about the nature and the origin of the proteins. Their presence in amounts of about 1% has only been shown by amino acid
analysis (Schnherr and Huber 1977) or CHN analysis (Schreiber et al. 1994) of
isolated cuticles. It is not known whether proteins in the MX are structural proteins
with functional stabilising properties like extensins in plant cell walls. Alternatively,
it can be suggested that enzymes involved in the polymerisation of the MX (cutin
esterases) were trapped during polymer formation in the MX.
More rational explanations are available for the presence in the MX of about
2040% of carbohydrates, mainly pectin and cellulose. The outer epidermal cell
wall and the cuticle on top of it must be connected to each other in some way. There
is evidence that this connection can be by direct covalent links of sugar molecules
to cutin molecules (Fang et al. 2001), and in addition cellulose fibrils extending
into the MX network may contribute to this connection. It is obvious that a significant amount of polar functional groups on the inner physiological side of the
MX is protected from enzymatic digestion by the cutin polymer. This can easily be
demonstrated by testing the wettability with water of the physiological outer and
inner surfaces of the MX. Contact angles on the physiological outer side are around
90 , indicating a surface chemistry of methyl and methylene groups, as should
be the case with a polymer mainly composed of aliphatic monomers (Holloway
1970). Quite different from the outer side, the physiological inner side of the MX is
wet by water, and droplets spread. This indicates a highly polar surface chemistry,
presumably composed of hydroxyl and carboxyl groups from cellulose and pectin
fibrils.
It is also evident that crystalline cellulose has a fundamental function within
the amorphous cutin polymer, acting as a stabiliser which strongly affects the
biomechanical properties of cuticles. Volume expansion of pure cutin, obtained by
hydrolysis of carbohydrates, is much higher than expansion of the MX (Schreiber
and Schnherr 1990). Unfortunately, immunological techniques with antibodies
directed versus specific epitopes of cell wall carbohydrates have not yet been carried out. This type of study should allow mapping with high precision the chemical
nature and the spatial arrangement of carbohydrates in cross sections of the MX,
using immunogold labelling and transmission electron microscopy.
Despite the fact that the MX is a biopolymer composed of lipophilic monomers,
it is also evident that significant amounts of polar functionalities (hydroxyl, carboxyl
and amino groups) are present. The degree of polarity of ionisable groups depends
on pH. Therefore, the amounts and the local distribution of these polar groups within
the MX are important with respect to diffusion of polar molecules like water and
ions, simply because water is sorbed to polar groups in the MX. Sorption of water,
effect of pH on ionisation of functional groups, ion exchange capacities of cuticles
and effects on transport properties are a major topic of Chap. 4. The fact that water
sorbed to the MX acts as a plasticiser in the membrane is evident from investigations
of the biomechanical properties of cuticles. Rheological properties like extensibility
and plasticity of isolated cuticles have been shown to strongly increase upon hydration (Edelmann et al. 2005; Round et al. 2000), indicating interaction of water with
polar domains within the MX.
Fig. 1.3 Scanning electron micrographs of the leaf surface of (a) Quercus robur (oak) and
(b) Vinca major (periwinkle). A delicate pattern of epicuticular wax crystallites is visible on the
oak surface, whereas the periwinkle surface is characterised by a pronounced pattern of cuticular
folding
epi- and intracuticular waxes. Dipping or rinsing leaves with chloroform at room
temperature often results in partial extraction of waxes (Riederer and Schneider
1989) especially when cuticles are thick. By varying solvents and duration of extraction it has been attempted to selectively extract epicuticular waxes (Silva Fernandes
et al. 1964; Holloway 1974; Baker et al. 1975; Baker and Procopiou 1975). Jetter
et al. (2006) have argued that selective extraction of surface waxes with solvents is
not possible, and they favour various stripping techniques (Ensikat et al. 2000; Jetter
et al. 2000; Riederer and Markstdter 1996). Following stripping, cuticle surfaces
appeared smooth and clean, showing that stripping removes wax bloom completely.
However, there is no direct evidence that smooth continuous wax films covering the
cutin are also removed. These uncertainties affect the validity of conclusions concerning amounts of surface waxes and effects of surface waxes on permeability of
cuticles. We shall return to this problem in later chapters.
10
Table 1.3 Most common substance classes of cuticular waxes identified by gas chromatography
and mass spectrometry
Substance
class
Chemical formula
Range of
chain lengths
Major
homologues
Acids
Aldehydes
Alcohols
Alkanes
Secondary alcohols
Esters
C16 C32
C22 C32
C22 C32
C21 C35
C23 C33
C36 C70
11
COOH
OH
b-amyrin
OH
oleanolic acid
Fig. 1.4 Chemical structures of the triterpenoic alcohol -amyrin and the triterpenoic acid
oleanolic acid occurring in cuticular wax of various species
Triterpenoids are derived from the terpenoid metabolism (Guhling et al. 2006).
Very common triterpenoids (Fig. 1.4) are pentacyclic triterpenoic alcohols (e.g.,
-amyrin and -amyrin) and acids (e.g., oleanolic acid and ursolic acid). Triterpenoids occur only in some species, whereas long-chain aliphatic compounds
represent typical components of all waxes analysed so far. Occurrence of triterpenoids in larger amounts is generally limited to certain taxonomically related
species. Waxes of many species of the Rosaceae, for example, are characterised by
the predominance of triterpenoids amounting to 50% and more of the total wax coverage of the MX, as is the case with Prunus laurocerasus (Jetter et al. 2000), whereas
in other species (e.g., Hedera helix, Arabidospsis thaliana) triterpenoids are present
in wax extracts only in traces. Pentacyclic triterpenoids are planar molecules with
very high melting points, and it is difficult to imagine how they could form homogeneous mixtures with linear long-chain aliphatic wax molecules. It is not known
whether they are partially crystalline in and on the CM, as is the case with the linear
long-chain aliphatic molecules.
12
different chain lengths within each substance class. A representative wax sample
can be composed of 50 individual compounds and more. Often, the most prominent
wax compounds are identified, whereas compounds present only in traces remain
unidentified. Identification of 9095% of the compounds occurring in a specific
wax sample is considered a successful analysis, and this can take a fairly long time,
when time needed for identifying unknown mass spectra is included.
Quantification is normally carried out adding an internal standard (e.g., an
alkane) of known amount to the wax samples. Ideally, for each individual wax compound, varying in chain length and functionalization, the best standard would of
course be the identical compound. However, most wax compounds are not commercially available as standards. Furthermore, in view of the large number of
wax molecules which are normally present in a typical wax sample, it would be
unrealistic running a separate standard for each wax molecule, even if it was available. Therefore, in most cases an alkane, representing a linear long-chain aliphatic
molecule as they are typically found in wax samples, is used as internal standard.
Alkanes of even chain lengths (e.g., C24 ) are preferred, since alkanes of uneven
chain length are dominant in plant waxes.
In addition to these limitations in quantitative wax analysis, there is another problem which has rarely been addressed in the past. The total amount of cuticular
wax determined gravimetrically is generally larger than wax amounts determined by
GCMS. Various reasons might contribute to this observation. Weighing does not
discriminate between wax compounds and non-wax compounds, which may contribute to total weight loss. On the other hand, analysis by GC is highly specific, and
permits exact identification of compounds. Wax and other compounds (e.g., sugars)
can be distinguished. Esters with very high molecular weight can present formidable
problems in GC due to their very long retention times (Santos et al. 2007) and the
tendency to produce broad and blurred peaks. Esters with high molecular weight
(>700800) also approach the detection limit of the MS. This could lead to an
underestimation of wax amounts, especially in wax samples with high amounts of
esters.
Compounds with very high molecular weights have been detected in wax from
Hedera helix leaves (Hauke and Schreiber 1998). The large difference between wax
amounts determined gravimetrically and by GCMS was mainly due to a limited
resolution of the analytical approach. The difference in wax amounts depended on
leaf age and season (Fig. 1.5a). When wax extracts from ivy CM were separated on
a column packed with silica gel using solvents of different polarity and subjected
to GSMS, two distinct wax fractions were obtained. The long-chain aliphatics as
described above were eluted from the column with the apolar solvent (diethylether),
and this could be analysed directly by gas chromatography. This fraction yielded
alkanes, alcohols, aldehydes, acids and esters. The eluate of the polar solvent (chloroform/methanol/water in ratios of 60:25:5) resulted in an additional wax fraction,
which could not be analysed directly by gas chromatography but only after transesterification (Fig. 1.5b). Analysis of this transesterified polar wax fraction revealed
that it was composed of di- and presumably trimers of -hydroxy fatty acids in the
chain lengths C12 C16 , which were linked by ester bonds to linear long-chain alco-
13
a
800
600
400
200
0
b
800
600
400
200
0
c
800
600
400
200
0
0
30
60
90
120
150
180
hols with chain lengths from C22 to C32 . Compounds of similar oligomeric structure
have also been found in gymnosperms, and they are called estolides (Bianchi 1995).
Molecular weights and polarity of these compounds are too high for direct GC analysis. They do not move on the column, and are overlooked if not transesterified.
When apolar and polar wax fractions are combined, total amounts of wax are close
to the wax amounts determined gravimetrically (Fig. 1.5c). Based on these results,
it appears that gravimetric determination of wax amounts is more reliable. We dont
know if the problem occurs with waxes of all species, but we suggest that wax
amounts determined by GC should always be compared to those determined gravimetrically. If a significant difference is observed, fractionation of waxes by column
chromatography is indicated. Deterioration of the ability of a column to separate
homologues, broadening of peaks and discolouration of the column entrance could
also indicate the presence of estolides in the sample which failed to move on the
column. As a corollary, it should be realised that it is not a good practice to analyse waxes from leaves of unspecified age and to use only one sampling time. There
simply exists no typical wax composition of leaves and fruits.
14
15
structure and permeability. From the 372 studies reviewed, only two explicitly dealt
with diffusion. Wattendorff and Holloway (1984) used potassium permanganate as
tracer. Schmidt et al. (1981) attempted to find a correlation between water permeability and fine structure of Clivia CM at different stages of development. All
other workers rationalised their work by alluding to the barrier function of cuticles,
but they simply used standard procedures to generate pictures, while permeability
was not estimated. Nevertheless, some useful terminology and information about
structurepermeability relationships may be obtained from some of these studies.
Extracting waxes increases permeability by 13 orders of magnitude (Chap. 4
and 6). This shows that cuticular waxes play a decisive role in water and solute
permeability, and both localisation and structure of waxes are important in understanding structureproperty relationships. The presence of polar paths in lipophilic
cuticles is another topic of importance, because it is a prerequisite for penetration of
hydrated ionic solutes but not necessarily of water (Schnherr 2006).
1.4.1 Nomenclature
We adopt the definitions and nomenclature of Jeffree (2006), which is also used
by most of the workers in the field. The cuticle is a polymeric membrane located
on the epidermal wall of primary organs. It has a layered structure. The outermost
layer is called cuticle proper (CP), and the layer underneath is the cuticular layer
(CL). In many species, an external cuticular layer (ECL) located under the CP and
an internal cuticular layer (ICL) facing the epidermal wall can be distinguished.
Soluble cuticular lipids or waxes occur as epicuticular waxes and as embedded or
intracuticular waxes. CP, CL and waxes constitute the cuticle (CM), which in some
species can be isolated enzymatically. Due to its layered structure, the cuticle is a
heterogeneous membrane. We distinguish transversal heterogeneity which is apparent in cross-sections, and lateral heterogeneity which arises due to the presence of
trichomes and stomata.
16
the cell wall. If cuticles are stained with toluidine blue at pH 9, the cutin also binds
toluidine blue due to the presence of carboxyl groups (unpublished results). Cationexchange capacity of cuticles will be dealt with later (Sect. 4.3). Resolution of the
light microscope is of the order of 0.5 m, and this prevents the study of transversal
heterogeneity of very thin cuticles.
With polarised light, location and orientation of crystalline waxes have been
studied. All CM investigated with polarised light exhibited birefringence or double refraction. Birefringence is evidence for the presence of crystalline structures.
In cross-sections of cuticles, waxes give negative and cellulose gives a positive
birefringence (Meyer 1938; Roelofsen 1952; Sitte and Rennier 1963). There are
a few examples of positive birefringence due to waxes in cuticles (Sitte and
Rennier 1963). Extracting or melting waxes eliminates wax birefringence. On
cooling, birefringence reappears, showing re-crystallisation from the melt.
Extracted CM exhibit form double refraction, indicating the presence of lamellar voids. Form birefringence disappears when the polymer matrix is imbibed with
solvents having the same refractive index as cutin, which is 1.5. In periclinal positions the lamellar voids are oriented parallel to the surface of the cuticle, and in vivo
they are filled with wax platelets in which the long axes of the paraffinic chains are
oriented perpendicular to the surface of the CM. If viewed from the top, the waxes
of Clivia cuticles appear isotropic, but near the anticlinal walls lamellae bend down
towards the anticlinal walls, and in these positions waxes appear birefringent when
viewed from the top (Meyer 1938). This shows an oblique orientation of the wax
molecules in anticlinal pegs.
The presence of cellulose in cuticles has been a subject of controversy among
microscopists, because it does not exhibit the typical histochemical reactions when
embedded in cutin. Crystalline cellulose exhibits positive birefringence, and the
outer epidermal walls are always positive birefringent (Fig. 1.6). The CL of most
cross-sections of cuticles did not show positive birefringence. Extracting or melting
waxes to eliminate possible interference of negative birefringence of waxes did not
change this picture. It appears that the CL of most plant cuticles contains little if
any crystalline cellulose. Most researchers agree that the CP is free of crystalline
cellulose. Polarised light does not detect amorphous polysaccharides, but with the
transmission electron microscope (TEM) polysaccharides can be demonstrated in
the CM. They are amorphous, since they are not birefringent (see below).
Using Ficus elastica leaves, Sitte and Rennier (1963) observed form double
refraction in the outer regions of the CM very early, when it was only about
2.5 m thick and the leaf was still unfurling. Incorporation of wax into these preformed voids occurred early, but reached its maximum only when the leaf was fully
expanded. At the same time, the thickness of the CM increased by interposition
of cutin between the CL and the epidermal wall, and the layered structure shown
in Fig. 1.6 was formed. The mature leaf had a lamellated CP of 12 m, the ICL
measured about 2.5 m and the ECL was about 3 m thick.
The formation of voids in cutin prior to deposition of crystalline intracuticular waxes is an astounding phenomenon, yet a necessity because crystallisation
of wax in a dense polymer network is improbable. Cutin monomers are likely to
17
Fig. 1.6 Staining of cross-sections of cuticles from selected species and birefringence. The cuticle
stained red with Sudan III and the cellulose wall stained blue with methylene blue. The signs
of birefringence and of intensity () are shown on the left and the right side of each species
respectively. (Redrawn from Sitte and Rennier 1963)
18
interfere with crystallisation and prevent it. An aliphatic hydrocarbon with n carbon
(C) atoms has a length of 0.154 nC (Barrow 1961). A layer of a C20 fatty acid or
alcohol would be 3.1 nm thick, and paraffin with 31 carbon atoms would need a
lamellar void of 4.8 nm thickness.
Wax birefringence is generally restricted to CP and CL, that is to the cuticle
which stains with Sudan III. However, birefringence of the CP is difficult to assess
with certainty, as it is less than 1 m thick and close to or below the limit of resolution of the light microscope. Intensity of birefringence of thick CM as shown in
Fig. 1.6 was not uniform, indicating that crystalline waxes do not occur in equal
amounts at all positions. Intensity and occurrence of anisotropy differed among
species. Prunus laurocerasus had two layers of negative birefringence and a narrow
isotropic zone close to the cell wall. Olea europaea exhibited very little wax birefringence, and in Ficus CL a layer having positive wax birefringence can be seen.
Positive birefringence of the ECL and negative birefringence of the ICL of Ficus
disappeared on extraction, which indicates that they are both caused by crystalline
waxes, but their orientation differs.
It should be remembered that only crystalline waxes are anisotropic, while individual wax molecules sorbed in cutin are not detected. Studies with polarised light
give no information if all waxes are crystalline or if portions of the wax are amorphous and are sorbed as individual molecules within amorphous cutin. At room
temperature, about 80% of the wax of Citrus aurantium is amorphous (Reynhardt
and Riederer 1991). In leaves of Fagus sylvatica and Hordeum vulgare, about 72%
and 48% of the waxes are amorphous, respectively (Reynhardt and Riederer 1994).
Thus, a large fraction of the total wax is amorphous and must be somewhere on or
in the cutin, but it cannot be localised with polarised light.
There is no hint in Fig. 1.6 that epicuticular waxes contributed to birefringence
of cuticle cross-sections. This is amazing, since epicuticular waxes occur in many
species in substantial amounts (Sect. 1.3). Epicuticular waxes are definitely crystalline, at least a fraction of them (Jeffree 2006; Jetter at al. 2006). They were not
seen with polarised light, and this may be a problem of resolution, or they may go
unnoticed because their orientation is not uniform. This is unfortunate, because the
contribution of epicuticular waxes to barrier properties of cuticles is an important
and controversial issue.
19
and glaucous. Bright, green and glossy leaves have a smooth layer of epicuticular
wax that reflects light effectively. Thickness and structure of this wax layer cannot
be investigated with the SEM, because wax-free cutin and a smooth wax layer look
very similar.
Microcrystalline wax blooms have two obvious functions. Light reflection can
reduce heat damage to leaves, and it renders their surfaces difficult to wet. This
prevents leaching of solutes from the apoplast during rain. The function of epicuticular waxes as a barrier to solutes is a matter of debate and conjecture, because
it has not been investigated or at least not published. Foliar application of chemicals requires that leaves are wet, and this is realised by adding surfactants. This
assures that aqueous spray droplets are retained, but this is only an indirect effect,
and it is not known whether permeability of cuticles is affected by the wax bloom.
If epicuticular waxes occur as a continuous wax layer on top of the CP, this would
have a substantial effect on water and solute permeability (Chap. 4). In glossy leaves
which have little microcrystalline wax bloom, wax crusts can be seen with the SEM.
Is there such a continuous wax film under the wax bloom? Haas and Rentschler
(1984) painted the adaxial leaf surface of blackberry leaves (Rubus fruticosus) with
cellulose nitrate dissolved in amyl acetate (6% w/v). After evaporation of the solvent, it was possible to strip off the cellulose nitrate film. The surface of the cuticle
looked perfectly smooth after stripping, and the wax bloom was entrapped in the
film. It is possible that a smooth wax layer remained on the cuticle after stripping,
because it did not adhere to polar cellulose nitrate. Transpiration of leaves before
and after stripping was not measured, but surface wax entrapped in the cellulose
nitrate and total wax obtained by washing of adaxial leaf surfaces with chloroform
were analysed. Total wax amounted to 14.4 g cm2 , most of which was located
on the surface (12.9 g cm2 ). Epicuticular wax contained mainly alcohol acetates
(36%) n-alcohols (30%) and n-alkyl esters (25%), while major components of intracuticular waxes were fatty acids (20%), alcohols (44%) and alcohol acetates (28%).
Triterpenoid acids were detected only in the intracuticular wax.
Jetter et al. (2006) have criticised this approach, because partial extraction of
intracuticular waxes by amyl alcohol cannot be precluded. Jetter et al. (2000)
used cryo-adhesive sampling to obtain epicuticular wax from adaxial surfaces of
Prunus laurocerasus leaves. Total cuticular wax was 28 g cm2 , and epicuticular wax amounted to 13 g cm2 . The epicuticular wax consisted exclusively of
aliphatic constituents, while intracuticular wax contained large amounts of triterpenoids and small amounts of aliphatics. The effect of removal of epicuticular waxes
on water permeability was not investigated, and it is not clear whether cryo-adhesive
sampling also removes the background wax film completely.
A recent study using the atomic force microscope (AFM) and vital leaves of
Euphorbia latyrus, Galanthus nivalis and Ipheion uniflorum revealed that progressively the surface of the cuticle is covered completely with monomolecular and then
bimolecular layers (Koch et al. 2004). The surface of the cuticle was first cleaned
from surface wax with an epoxy resin glue. Parallel to the formation of wax layers,
rod-like crystals arose that grew at their tips. This is a fascinating study, because
it demonstrates within 80 min the presence of highly ordered mono- and bilayers
20
21
22
7000
6000
12
5000
Thickness (m)
8000
4000
3000
2000
10
8
cell wall
cuticular layer
4
2
cuticle proper
0
0
1000
5
10
15
20
Distance from leaf base (cm)
0
0
10
15
20
25
The adaxial cuticle of Clivia miniata leaves has a laminated CP, and is ideally
suited to study cuticle development. Clivia is a monocot, and leaves grow at their
base such that cuticle age increases in direction to the leaf tip. Size of epidermal
cells, thickness of cuticles and cell wall, cutin composition, cutin biosynthesis and
fine structure have been investigated as a function of position, that is of age (Mrida
et al. 1981; Schmidt and Schnherr 1982; Lendzian and Schnherr 1983; Riederer
and Schnherr 1988).
Between position 1 cm and 5 cm, the projected area of epidermal cells increased
about ninefold from 800 m2 to 7,000 m2 . Afterwards, cell area no longer changed.
At the same positions, cell length increased from 50 to 250 m (Riederer and Schnherr 1988); that is, epidermis cells increased both in length and width up to position
5 cm (Fig. 1.7).
The CP was synthesised first and its thickness increased up to 3 cm from leaf
base. Fine structure also changed. Maximum thickness of CP was about 200
250 nm, and it increased no further between 3 and 20 cm (Figs. 1.7 and 1.8 inset).
Starting at position 3 cm the cuticular layer developed, and it increased in thickness up to position 20 cm from leaf base. Fine structure of the CL (Fig. 1.8) and
chemistry (Riederer and Schnherr 1988) changed significantly.
Lamellation of the CP is best seen at 3 cm from base. At higher positions (>4 cm)
the central part of the CM has little contrast, probably because OsO4 does not penetrate because the CP is incrusted with waxes. The cuticular layer starts to develop at
position 3 cm and increases in thickness at higher (older) positions. The CL is initially reticulate, but in old and mature positions fine structure has disappeared. It is
23
Fig. 1.8 Transmission electron micrographs of transverse sections of adaxial cuticles from Clivia
miniata at different stages of development. Numbers at the lower left corners refer to distance from
leaf base. Fixed en bloc with OsO4 , and sections were stained with uranyl acetate and lead citrate.
(Taken from Riederer and Schnherr 1988)
not known if incrustation with waxes prevents penetration of OsO4 or if polar reactive functional groups have disappeared or are covered up. At position 20 cm cutan
occurs in very large amounts (Fig. 1.2), and during transformation of ester cutin to
cutan epoxy groups and double bonds are most likely consumed. It is believed that
the dark fibrillar network (5 cm) marks the location of polar polymers embedded in
cutin, but it is not known why it is no longer visible in old cuticles.
24
The chemical nature of the CP is a matter of debate (Jeffree 2006). Some workers
believe that electron-lucent lamellae are waxes, while the more dense lamellae are
made of cutin. This is pure speculation, because it has not been established that
typical ester cutin is present in the CP at all. The mass of the CP is very small relative
to the total mass of the CM, and constituents that occur only in traces might be lost
during processing. After transesterification of cutin from positions 23 cm where
the CP contributes most of the mass of the CM (Fig. 1.8), only nine n-fatty acid
(C12 , C14 , C16 and C18 ) homologues have been identified which amounted to 52%
of the total mass of cutin. The most frequent cutin acid (11%) was 9,10-epoxy-18hydroxyoctadecanoic acid (Riederer and Schnherr 1988). It is difficult to envision
a polymer composed of 50% of simple fatty acids.
The CP of Clivia cuticle survived extraction of CM with chloroform (Fig. 1.9)
and exhibited heavy contrast. Electron-lucent lamellae were preserved, and this is
unlikely to happen if they were made of waxes. The CL was differentiated into an
external (ECL) and internal (ICL) layer, with large differences in contrast. Since
the specimen was extracted, penetration by KMnO4 was not hindered by waxes,
and failure of the ECL to develop contrast indicates that reactive groups had been
eliminated during cutan formation.
Fig. 1.9 Transverse section of a polymer matrix membrane obtained from the adaxial surface of
a young Clivia miniata leaf. The MX was stained with KMnO4 prior to embedding, and sections
were stained with uranyl acetate and lead citrate. (Taken from Schmidt and Schnherr 1982)
25
Fig. 1.10 Transverse sections of Clivia polymer matrix treated with BF3 MeOH. Sections were
stained with lead citrate. (Taken from Schmidt and Schnherr 1982)
The presence of cutan in the ECL is clearly seen in a specimen extracted with
chloroform and depolymerised with BF3 MeOH (Fig. 1.10). This treatment eliminated ester cutin and left cutan and the polar polymers behind. These polar polymers
strongly reacted with lead citrate applied as section stain. Cutan did not exhibit any
fine structure, and it is not known if this is due to failure of uranyl acetate to penetrate
cutan and/or the embedding medium.
Periclinal penetration of KMnO4 during en block staining was considerably
faster in electron dense lamellae than in electron-lucent lamellae of Agave and
Clivia cuticles (Wattendorff and Holloway 1984), but the contribution of the lamellated CP to water or solute permeability of CM has not been studied and is not
known. Schmidt et al. (1981) studied water permeability of isolated Clivia CM and
MX. Water permeability of young and mature CM was the same, but extracting
26
waxes increased permeance by factors of 438 and 216 in young and mature CM
respectively. This demonstrates that water permeance of MX decreased during leaf
development, when MX mass increased from 0.4 to 0.7 mg cm2 . The lower permeance of MX from mature leaves indicates that cutan has a lower permeability than
cutin (Figs. 1.8, 1.9 and 1.10).
Fig. 1.11 Autoradiograph of the adaxial surface of young Clivia miniata leaf of 17 cm length.
Droplets containing 3 H-hexadecanoic acid were placed on the cuticle, and incubated for 24 h in the
dark at 100% humidity. Before applying the X-ray film, the leaf was extracted exhaustively with
chloroform/methanol to remove all soluble radioactivity. (Taken from Lendzian and Schnherr
1983)
Problems
27
Problems
1. What is the average thickness of a cuticle, and what are the upper and lower
values of very thick and very thin cuticles?
28
Solutions
1. Most cuticles are about 23 m thick (Citrus aurantium, Hedera helix, Prunus
laurocerasus); however, depending on the species thickness of cuticles can vary
between 30 nm (leaf cuticle of Arabidopsis) and 30 m (fruit cuticle of apple).
2. This statement is partially correct. Plant cuticles are composed only to a certain
degree of hydroxylated fatty acids which are cross-linked via ester bonds. Many
cuticles contain cutan, which is less well characterised and cross-linked by other
bonds (ether bonds and probably direct CC-bonds) than ester bonds. Therefore, it cannot be degraded by transesterification reactions. Furthermore, there
are polar compounds (carbohydrates, proteins and phenols) forming a small but
important fraction of the cuticle mass.
3. On average, the cuticle contains about 100 g cm2 . However, depending on
the species, wax coverage can vary tremendously between 10 (leaf cuticle of
Citrus aurantium) and 400 (leaf cuticle of Nerium oleander (oleander)) to
3,000 g cm2 (fruit cuticle of Malus domestica).
4. Cuticular waxes are in most cases composed of linear long-chain aliphatic compounds and cyclic terpenoids. Linear long-chain aliphatics are composed of
different substance classes (e.g., acids, aldehydes, alcohols, alkanes, secondary
alcohols and esters) with chain length ranging from C20 to C36 . Esters composed
of primary fatty acids (C16 C36 ) and alcohols (C20 C36 ) have chain lengths
between C36 and C70 .
5. A major problem often encountered in wax analysis is the fact that gravimetrically determined amounts are often higher than wax amounts determined by
gas chromatography. The reasons for this observation are variable and not fully
understood. Gravimetric determination of wax amounts could lead to an overestimation, whereas determination by GC could lead to an underestimation of wax
amounts.
6. Different approaches (e.g., varying extraction times and mechanical removal of
waxes) have been suggested, but most of these procedures can be questioned.
Solutions
29
Even if there is no epicuticular wax film visible with the SEM, it is not clear
whether there is still a thin mono- or bimolecular layer of wax on the outer
surface of the cuticle.
7. Treating cuticles with chemicals before looking at them with the TEM is necessary to increase their contrast. OsO4 is lipophilic and thus is sorbed to lipophilic
cutin domains. In addition, it oxidises double bonds. KMnO4 is a strong oxidising agent breaking double bounds and converting alcoholic OH-groups to
carboxyl groups. In cuticles, OH-groups of carbohydrates are probably oxidised
by KMnO4 . However, no systematic studies concerning how OsO4 and KMnO4
exactly react with cuticles have been carried out.
8. Cuticles are heterogeneous membranes because they are composed of cutin,
cuticular waxes and polar polymers. The cutin polymer itself is composed of
a lipophilic and polar fraction. Cuticles are characterised by transversal heterogeneity. A thin outer layer called cuticle proper (CP) of unknown composition is
succeeded by a much thicker inner layer called cuticular layer (CL) composed of
cutin and polar polymers. Lateral heterogeneity arises because, besides normal
epidermal cells, stomata and trichomes occur in most leaf epidermises.
Chapter 2
Plant cuticles are thin membranes. Thickness typically ranges from 1 to 15 m. The
inner surface of the cuticle faces the apoplastic fluid, which is an aqueous solution
of mineral ions and small organic molecules. Most of the time, the morphological
outer surface of the cuticle of terrestrial plants is in contact with air having humidity
ranging from 20% to 90% or higher. During fog or rain, the outer surface of the
cuticle can be wet by water.
Water and solutes can cross the cuticle in both directions. Normally humidity is
below 100%, and water flows towards the outer surface where it evaporates. This
is called cuticular transpiration. During rain and fog, with humidity close to 100%
and wet leaf surfaces, the flow in the opposite direction can also happen. In addition, leaching of solutes from the apoplast to the leaf surface occurs (Tuckey 1970).
Cuticles are permeable to many solutes such as nutrients, growth regulators, insecticides, fungicides and environmental chemicals. The importance of these transport
processes for survival of plants, plant production and environmental pollution is
obvious. Hence, plant scientists have studied them extensively for more than five
decades. In spite of these efforts, mass transport across cuticles is still not wellunderstood. Rates of cuticular penetration differ greatly among plants species and
solutes, but the reasons are still obscure.
Once synthesised, the cuticle represents a purely physical system. It does not
actively interact with water and solutes. Penetration is a physical process. For this
reason the term cuticular uptake is inappropriate, as it insinuates active participation in mass transfer by plants, cuticles or parts of them. Unfortunately, foliar
uptake or cuticular uptake have often been used in the literature.
In the majority of cases, water and solutes cross cuticles by diffusion, which is
based on random molecular motions over small molecular distances. Quantitative
description of diffusion involves a mathematic model based on fundamental physical properties. This kind of approach is not very popular with many biologists,
who when confronted to Ficks law of diffusion are tempted to change the subject.
However, Fick, one of the pioneers in diffusion, was a biologist, more precisely a
physiologist, who among other things worked on astigmatism of the eye, functioning
of muscles and thermal functioning of the human body (quoted from Cussler 1984).
31
32
33
Fig. 2.1 Schematic drawing of a typical transport apparatus. Donor and receiver solutions are
separated by a membrane
Water is added to both compartments. Solutions are stirred for mixing. The apparatus is maintained at constant temperature, and at time zero we add to one of the
compartments a small amount of urea. This compartment is called donor. The other
compartment is the receiver from which samples are withdrawn periodically. Alternatively, the total volume of the receiver is withdrawn for chemical analysis and an
equal amount of water is returned to the receiver. Urea concentration in the receiver
is measured by a suitable method, and the total amount of urea that penetrated is
calculated. Sampling intervals are so short that the concentration in the donor practically remains constant, while at the same time sufficient urea must penetrate into
the receiver to allow chemical analysis. These data can be analysed using three
different models.
2.1.1 Model 1
We first plot the amount of urea (mol) that penetrates against time (h) and observe
that after some time the amount (M) increases linearly with time (t) (Fig. 2.2).
The slope of the linear portion of the plot is the flow (M/t), and the intersection
with the x-axis is the extrapolated hold-up time (te ). It takes some time before the
first molecules penetrate the membrane and appear in the receiver solution. Some
additional time passes before the transport becomes steady. The sum of both is the
hold-up time. To make the result more general we divide the flow by the area (A) of
the membrane exposed to urea (10 cm2 ) and we obtain the flux (J), which amounts
34
8e-9
6e-9
te = 0.3 h
4e-9
0
0
Time (h)
Fig. 2.2 Steady state penetration of urea showing the hold-up time (te ) and a linear increase in
amount diffused per time. Donor concentration was 1 103 mol m3
F
M 1
= .
t
A A
(2.1)
Increasing the membrane area by a factor of 2 increases the flow of urea by the same
factor. J is the normalised flow also called flow density and is independent of membrane area. J is useful to compare results of experiments with different membrane
areas.
Next we want to find out what happens when we vary concentration differences.
In our experiment, the urea concentration in the receiver remained practically zero
and the donor concentration was constant. Now we conduct a number of experiments using the same membrane but different donor concentrations, determine the
urea flux and plot it against the concentration of the donor using SI units (Fig. 2.3).
In this particular case we obtain a linear plot (but this must not always be the
case), which tells us that the flux is proportional to concentration in the donor or
more precisely to the difference in urea concentration between donor and receiver.
The slope of the plot is the coefficient of proportionality (P)
J = P (Cdonor Creceiver ) .
(2.2)
This mass transfer coefficient is often called permeability coefficient (P), and in our
example it has the dimension of a velocity (4.16 107 m s1 ). If flux measurements
are conducted at only one concentration, P can still be calculated from data given
in Fig. 2.2, but in this case we would not know if P is constant or if it depends on
concentration. In this model, the thickness of the membrane need not be known.
35
2.5e-9
2.0e-9
1.5e-9
1.0e-9
slope: 4.16 x 107 m/s
5.0e-10
0.0
2
3
4
Donor concentration (103 mol/m3)
Fig. 2.3 The effect of donor concentration on steady state flux of urea
Hence, model 1 is suitable in all cases when membrane thickness is not known or
difficult to estimate accurately.
2.1.2 Model 2
We next want to find out how the flux varies when we change membrane thickness
(). With biological membranes thickness cannot be manipulated, but for the present
purpose we use a gelatine membrane which can be prepared at different thicknesses
by casting 10% hot aqueous gelatine between two glass plates separated by spacers.
After cooling to room temperature, stable membranes are obtained that can be used
in experiments. As above, we determine the flux of urea at a given urea concentration
of the donor, but we use membranes of different thicknesses (). When we plot J
vs , we find that the flux is inversely related to membrane thickness. The flux is
reduced by one half when the membrane thickness is doubled (Fig. 2.4). At a given
donor concentration, the product of flux and membrane thickness is constant
J = D (Cdonor Creceiver ) .
(2.3)
Equation (2.3) is a form of Ficks law of diffusion, and the new proportionality
coefficient is the well-known diffusion coefficient (D) having the dimension m2 s1 .
D may not be constant, and it often depends on concentration. However, this is
easy to find out by conducting experiments using a membrane with constant thickness but different donor concentrations. In our example, the plot J vs 1/ is linear
and has the slope of 1.25 1012 molm1 s1 (Fig. 2.4 inset). D is obtained by
dividing this slope by the concentration difference between donor and receiver (here
1 103 molm3 ). In our example, this leads to a D of 1.25 109 m2 s1 .
36
1.4e-9
1.2e-9
1.0e-9
8.0e-10
6.0e-10
200
400
600
800
1000
4.0e-10
2.0e-10
0.001
0.002
0.003
0.004
Membrane thickness (m)
0.005
0.006
Fig. 2.4 The effect of membrane thickness on steady state flux of urea and calculation of the
diffusion coefficient (inset). Donor concentration was 1 103 mol m3
Multiplying P (2.2) by the membrane thickness in meters yields the permeability coefficient of a membrane having 1 m thickness (P) which has the dimension
m2 s1 and is numerically equal to D since the membrane is aqueous
P = D = P.
(2.4)
Using the data of Fig. 2.3, which were generated using a membrane having 3 mm
thickness, we obtain P = 1.25 109 m2 s1 . P is very useful for comparing
permeability of homogeneous membranes to various solutes and to water.
The diffusion coefficient may also be calculated from the extrapolated hold-up
time (te ) and the square of the membrane thickness (2 ):
D=
2
.
6te
(2.5)
The derivation of (2.5) can be found in Crank (1975). Using the hold-up time given
in Fig. 2.2 and a membrane thickness of 3 mm, we obtain (3 103 m2 )/(6
1,200 s) = 1.25 109 m2 s1 . Since we worked with an aqueous membrane,
P = D.
37
2.1.3 Model 3
Mass transfer across a membrane may also be analysed in analogy to a first order
chemical reaction. In this case, the change in urea concentration in the receiver with
time (molm3 s1 ) is taken to be proportional to donor concentration:
Creceiver
= kCdonor .
t
(2.6)
(2.7)
(2.8)
These equations are of the same type as (2.2) and (2.3), which state that mass flux
(2.2) or mass flux times membrane thickness (2.3) are proportional to concentration difference. This analogy may ease the apprehension some biologists experience
when dealing with Ficks law.
The reciprocal of conductance is the electrical resistance, and 1/conductivity is
called resistivity. This convention can also be used with mass conduction. For a
perfect analogy, we rename the permeability coefficient (P) from (2.2) and call it
38
permeance (P) and its reciprocal value (mass) resistance (R). The reciprocal value
of P (permeability coefficient) from (2.4) then becomes resistivity. This terminology was suggested by Hartley and Graham-Bryce (1980), and we shall be using it
throughout this book.
To further illustrate the use and the usefulness of the above models and calculations, we will add a few examples related to problems in the plant sciences.
Initially, steady state transport is considered. Later we deal with situations when
concentrations change with time.
D
(Cdonor Creceiver ) .
(2.9)
D for urea in water at 25 C can be looked up in tables (Cussler 1984). At a concentration of 103 mol l1 it amounts to 1.38 109 m2 s1 . Lets assume a thickness
of the epidermal wall of 10 m for calculating D/ = 1.38 104 m s1 , and
with Cdon = 103 moll1 the steady state flux of urea is 1.38 107 mol m2 s1 .
According to (2.2) and (2.3) D/ equals P, which means that the permeance of the
epidermal wall is 1.38 104 m s1 . This is a very interesting and useful result,
because we can use it to prove that solutes applied to the outer surface of the cuticle
will not accumulate in the cell wall. Diffusion coefficients in cuticles of solutes are
always smaller than 1015 m2 s1 (Chap. 6), and with a cuticle thickness of 5 m we
obtain a permeance of 2 1010 m s1 . This is more than six orders of magnitude
2.3 Steady State Diffusion Across a Stagnant Water Film Obstructed by Cellulose and Pectin 39
Fig. 2.5 Schematic drawing (not to scale) of a water film having the thickness and separating
plasmalemma and cuticle
smaller than permeance of cell walls, and accumulation of solutes in the cell wall
is a highly unlikely event. This can be shown to be true in a more formal way by
considering the cuticle and the cell wall as two resistances in series.
40
J=
Awater
D
(Cdonor Creceiver ) .
Acell wall
(2.11)
The flux of urea will be reduced by a factor of 0.9 if the solids of the cell wall add
up to 10% of the total volume. We have implicitly assumed that these small amounts
of pectins and cellulose do not affect D.
Fig. 2.6 Photomicrograph of a thin cross-section of an adaxial Clivia leaf epidermis. The lipophilic
cuticle is stained orange with Sudan III, and the acidic cell wall is blue after staining with Toluidine
blue at pH 4.0
41
(2.12)
42
Fig. 2.7 Concentration profiles across a lipophilic membrane. (a) Linear profile obtained with a
lipophilic solute having a partition coefficient K > 1. The concentration in the membrane at the
solution/membrane interface is higher by the factor K than concentration of donor and receiver
respectively. (b) Linear profile with a solute having K < 1. (c) Profile of the chemical potential ( ) across a membrane. The profile is not linear, and there are no discontinuities at the
solution/membrane interface on either side
j = j + RT lnC j .
(2.14)
43
< water
.
cuticle
J
2.78 108 mol m2 s1
=
= 2.78 108 m s1 .
Cdonor Creceiver
1 molm3
(2.15)
44
6e-8
5e-8
4e-8
3e-8
t e = 0.8 h
2e-8
1e-8
0
0
Time (h)
Fig. 2.8 Steady state diffusion of 2,4-D across a pepper fruit CM. Membrane area was 1 cm2 and
donor concentration was 1 mol m3
the real driving force was much greater than assumed in our calculation. This could
be accounted for by including the partition coefficient K in (2.2):
J = P (KCdonor KCreceiver ) = PK (Cdonor Creceiver ) .
(2.16)
If we decide to use model 2 for analysing the data, (2.3) assumes the form
J=
DK
(Cdonor Creceiver ) ,
(2.17)
which shows that permeance P is a mixed parameter which includes the diffusion
and partition coefficient and membrane thickness:
P=
DK
.
(2.18)
45
(2.19)
C0Vdonor
.
Vdonor + Vreceiver
(2.20)
As long as Cdonor Creceiver , we can write for the mean flow rate (F)
F=
(2.21)
where numerical suffixes denote times (t). For experiments allowing major change
of C to occur, we must use the differential form of (2.21)
Vreceiver
dCreceiver
dCdonor
= Vdonor
= F = PA (Cdonor Creceiver ) .
dt
dt
(2.22)
(2.23)
Equation (2.23) assumes more convenient forms under the following situations. If
Cdonor is held constant by having Vdonor Vreceiver or by other means, Vdonor becomes
unimportant and we can write
PAt
C0 Creceiver
= ln
.
Vreceiver
C0
(2.24)
(2.25)
46
When working with weak electrolytes, Creceiver may be maintained at zero by using
a buffer as receiver in which the solute is fully ionised. Lipophilic solutes may be
scavenged and trapped in phospholipid vesicles, which maintains the concentration
of the aqueous phase of the receiver at practically zero. Rearranging (2.25) leads to
ln (Cdonor /C0 )
PA
=
= k.
t
Vdonor
(2.26)
When ln (Cdonor /C0 ) is plotted vs time, a straight line is obtained with slope k.
Equations (2.4)(2.26) treat mass transfer as a first-order process (model 3), and k
is the first-order rate constant. Permeance (P) can be calculated when k, A and Vdonor
are known. Equation (2.26) states that Cdonor /C0 decays exponentially with time
Cdonor
= ekt ,
C0
(2.27)
and once k has been determined experimentally, the donor concentration can be
calculated for any time interval. The time required for the donor concentration to
decrease to one half is
ln 0.5 = kt
(2.28)
and the half time (t1/2 ) is 0.693/k. A simple experiment will help to demonstrate
the use of the above equations.
47
a
1.0
Solute fraction
0.8
Mt / M0 left in donor
0.6
0.4
0.2
0.0
2
10
Time (days)
0.0
1.00
-0.5
0.61
-1.0
0.37
0.22
-1.5
-2.0
ln (Cdonor / C0)
0.08
-2.5
0
10
Time (days)
Fig. 2.9 Non-steady penetration of 2,4-D across a pepper fruit CM. The fraction of 2,4-D left in
the donor decreases with time (pink squares), and the fraction of 2,4-D which was sampled from
the receiver (cyan dots) increases (a). Both fractions add up to 1.0 at all times. The dotted line
marks the point at which Mt /M0 is 0.5. Plotting ln (Cdonor /C0 ) vs time results in a linear plot (b).
The slope represents the rate constant k
48
An estimate of P may also be obtained from the raw data in Fig. 2.9a. During the
first day Cdonor decreased from C0 (1 molm3 ) by a factor of 0.221. These data can
be used to calculate the flow of 2,4-D from (2.21)
1 106 m3 0.221molm3
Vdonor Cdonor
=
= 2.56 1012 mols1 .
F=
t
86,400 s
(2.30)
This figure must be divided by membrane area and driving force. Using the initial
concentration of the donor of 1 molm3 , we obtain
P=
F
2.56 1012 mols1
= 2.56 108 m s1 ,
=
ACdonor
1 104 m2 (1 molm3 )
(2.31)
which is a little smaller than that calculated using (2.29). The donor concentration
decreased during the first day from 1 molm3 to 0.779 molm3 , and this decrease
in driving force with time is responsible for the non-linearity seen in Fig. 2.9a. If we
want to calculate P assuming steady state conditions, we could use the mean donor
concentration (2.21) during the first day, which is the concentration after 12 h of
0.89 molm3 . With this driving force we obtain a P of 2.88 107 m s1 , and this is
identical to that calculated from the first-order rate constant (2.29). This calculation
nicely shows that the error in P is not really large when we assume constant driving
force, while in fact Cdonor decreased significantly. However, it is essential to use the
average donor concentration and not the initial one.
.
(2.32)
= 2 ln
2 1/2
D
16 9 16
49
The quantity in square brackets contains only the constant , and can be evaluated.
After rearranging we have
0.049
D=
.
(2.33)
(t/2 )1/2
This equation is applicable to all temperatures, but D should not depend on concentration. If the latter restriction is abandoned, the appropriate equation is
Mt
Dt
4
=
(2.34)
M0
2
and D can be obtained from the slope of a plot Mt /M0 vs t. This equation can be
used to calculate D from sorption or desorption kinetics.
line. Plotting data as Mt /M0 vs the square root of time t. resulted in a straight line
up to about Mt /M0 = 0.7 (Fig. 2.10b).
D can be calculated from the slope of the linear portion of the plot using (2.34),
which after rearrangement results in
D=
(slope)2 2
.
16
(2.35)
50
1.1
desorption
1.0
0.9
sorption
0.8
Mt / M0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
200
400
600
800
1000
1200
1400
Time (s)
1.1
1.0
0.9
0.8
Mt / M0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
10
20
Square root of time (in
30
40
s1/2 )
Fig. 2.10 Water vapour sorption (pink circles) and desorption (cyan triangles) at 35 C in a polymethacrylate membrane having a thickness of 183 m plotted vs time (a) or vs the square root of
time (b). (Redrawn from data of Kishimoto et al. 1960)
If diffusion coefficients are identical when calculated from sorption and desorption experiments, this is good evidence that D does not depend on concentration.
This was the case in our example, since sorption and desorption plots were superimposed up to Mt /M0 = 1 (Fig. 2.10a). This is not too surprising, since water content
was only 1%, even at the highest vapour pressure.
Solutions
51
2.7 Summary
In this chapter we have presented three basic transport models, and we have shown
how permeance (P), diffusion coefficients (D) and first-order rate constants (k) can
be calculated from measurements of mass flux and membrane thickness. We have
pointed out that it is not a good practice to compare data on mass transfer across
cuticles from different species and various solutes when data are given as percent
penetrated during a single arbitrary time interval. Such data can not be related to
properties of cuticles or solutes.
Most problems can be handled by analogy to the above models and equations.
In the chapters to follow, some additional equations are presented for analysing flux
data. If new problems should arise which have not been treated here, the readers
will find assistance in the books by Crank (1975), Crank and Park (1968), Cussler
(1984), Hartley and Graham-Bryce (1980) and Vieth (1991).
Problems
1. What are the numerical values of the resistance in cell wall (P = 1.38
104 m s1 ) and cuticle (P = 1.46 107 m s1 ), and what is the total resistance?
2. What are the steady state fluxes of urea and sucrose across a cell wall with
= 1 m when the concentration difference between donor and receiver is
1 103 mol l1 ? The diffusion coefficient of sucrose in water is 5.23 1010
m2 s1 .
3. In calculations (2.15), we assumed that 2,4-D was either in the donor or in the
receiver solutions. Since K is 600, some of the 2,4-D must have been in the
cuticle. How much was it, and did this omission significantly affect permeance?
Use a specific weight of the cuticle of 1,000 kgm3 .
4. If the experiment shown in Fig. 2.9 had been terminated after 2 or 3 days, which
permeance would have resulted using the steady state assumption, and how much
would it differ from the true value?
5. Diffusion of lipophilic solutes in cuticular waxes is a very slow process, and
diffusion coefficients in the range of 1018 to 1021 m2 s1 have been measured.
How long would it take to reach Mt /M0 = 0.5 if the wax layer is 2 m thick?
Solutions
1. The resistance of the cell wall is 7,246 s m1 , and the resistance of the cuticle
is 6.849 106 s m1 . The sum of the two resistances is 6.857 106 s m1 , and
this is not significantly different from the resistance of the cuticle. Hence, the
resistance of the cell wall is negligible.
52
2. We use (2.9) and obtain the steady state fluxes of urea and sucrose across the cell
wall as 1.38 103 and 5.23 104 mol m2 s1 respectively.
3. We solve this problem in four steps. (1) The amount of non-ionised 2,4-D in
the donor is the product of mass (0.1 l = 0.1 kg) and concentration of donor
(1 103 mol l1 ), which is 1 104 mol. (2) The concentration of 2,4-D in the
cuticle can be calculated using (2.12). The concentration of 2,4-D in the cuticle
is the product of the donor concentration (1 103 mol kg1 ) and partition coefficient (600), which is 0.6 mol kg1 . (3) The area of cuticle exposed to the donor
was 1 cm2 and the thickness was 10 m, which results in a volume of cuticle of
1 109 m3 . With a specific weight of cuticle of 1,000 kgm3 , the mass of the
cuticle exposed to the donor is 1 106 kg. The amount of 2,4-D in the cuticle is the product of mass of cuticle times 2,4-D concentration in cuticle, which
amounts to 6 107 mol. (4) According to Fig. 2.7 the solute concentration in
the cuticle during steady state is only half the maximum concentration. Hence,
in the steady state 1 104 mol 2,4-D are in the donor, while only 3 107 mol
are sorbed in the cuticle. This is a negligible amount, and we can safely use the
donor concentration of 1 103 mol l1 in calculating permeance. However, it
should be clear from the calculation that sorption in the cuticle would not have
been negligible if the donor volume had been only 1 ml or less.
4. From Fig. 2.9a we read the fractions of 2,4-D that would have been collected
from the receiver, had we taken only one sample after the second (0.39) or the
third day (0.53) respectively. Using (2.30) and these figures, we calculate the flow
(F) in 2 days or 3 days as 2.25 1011 and 2.04 1011 mol s1 respectively.
Before we can calculate P using (2.31), we must decide which donor concentration to use. We are ignorant, and use the initial concentration of 1 molm3 and
obtain a P of 2.25 107 m s1 if we terminated the experiment after 2 days, and
2.04 107 m s1 if the experiment lasted 3 days. The true P calculated from the
rate constant k is 2.89 107 m s1 ; hence, we underestimated P by factors of
1.28 and 1.42 respectively. This may not seem a lot, but we must remember that
the 2,4-D concentration of the receiver was zero throughout, because we used a
pH of 9.2 and all 2,4-D molecules reaching the receiver were ionised. Without
this trick, C across the membrane would have been much smaller and the error
in P much larger, the magnitude depending on the volume of the receiver.
5. We use (2.34) to solve this problem, and obtain 55 h and 2,273 days respectively.
Chapter 3
Since 1960, units of measurement have been based on the SI (Systme International)
system, and we shall be using it in this book. Basic units in this system are (among
others) metre (m), kilogram (kg), mol, seconds (s), Pascal (Pa) and Kelvin (K).
This has not always been the case, and before 1960 the CGS system (cm, g, s) was
common in the natural sciences. In engineering, a great variety of non-metric units
(i.e., inch, pound, fluid ounce, and horse-power) are still in use, particularly in the
Anglo-Saxon countries.
In Chap. 2, mass transfer across membranes was characterised by permeance,
diffusion coefficients and first-order rate constants. We shall use these parameters to
explain why permeability of cuticles from different plant species to various solutes
differs greatly. Permeability depends on chemistry and structure of membranes, and
we shall relate chemistry and structure of cuticles to their permeability. To this end,
we have incorporated studies by physical scientists, engineers and biologists on permeability of natural and synthetic membranes published during the last 7 decades.
This necessitates converting older units into SI units.
53
54
0.4
0.3
0.2
te
0.1
0.0
0
50
100
150
200
250
300
Time (min)
Fig. 3.1 Water vapour transport across an ethyl cellulose (EC) membrane at 25 C. The pressure
increase in the receiver compartment was plotted vs time. (Redrawn from Yasuda and Stannett
1962)
an increase in pressure of the receiver, and this was used to calculate the flux. The
steady state flux was obtained by keeping the pressure difference between donor and
receiver practically constant (steady state). Gas or vapour pressures were measured
in cm mercury (cmHg). Vapour pressure greatly depends on temperature, which
necessitates rigorous temperature control. In this book, we shall deal with permeability of membranes to water and water vapour. Penetration of permanent gases
(O2 , N2 , CO2 ) has been reviewed by Lendzian and Kerstiens (1991). While the following conversions also apply to permanent gases, we shall simply use the term
vapour. A typical example is steady state diffusion of water vapour at 25 C across
an ethyl cellulose (EC) membrane, as shown in Fig. 3.1.
After some time the flux becomes steady, and from these data the extrapolated
hold-up time (te ) and the steady state flux (amount per unit area and time) can
be calculated. Volumes of gases or vapours greatly depend on temperature, and
fluxes were expressed as volume at standard temperature (273.15 K) and pressure
(101,325 Pa), abbreviated as STP. For calculating permeability (PHg ), the volume
of gas or vapour at STP (Jv ) was multiplied by membrane thickness ( in cm) and
divided by the pressure in the donor (pdonor in cmHg)
PHg =
cm3 (STP)cm2 s1 cm
Jv
.
=
pdonor
cmHg
(3.1)
55
3.1.1 Example
Diffusion of water vapour across a polyethylene terephthalate (PET) membrane of
0.1 cm thickness was measured at 25 C. The vapour pressure in the donor chamber
was 2.375 cmHg, which is the saturation vapour pressure of water at 25 C. Jv was
4.2 107 cm3 vapour (STP) per cm2 and s. From these data PHg can be calculated
using (3.1):
PHg =
3
4.2 107cm3 (STP) 0.1 cm
8 cm (STP) cm
=
1.77
10
.
cm2 s 2.375 cmHg
cm2 s cmHg
(3.2)
One might be tempted to simplify this dimension of PHg and write cm2 s1 , because
in writing PHg driving force was 1 cmHg. This was never done, and we shall stick
to the extended unit found in the literature, which does not use the suffix Hg to
characterise this type of permeability coefficient.
In biology, it is not customary to use fluxes based on vapour volume. Instead,
mass fluxes (mol or kg) are used. Hence, we must convert the volume flux of gases
or vapours (Jv ) into mass fluxes (J). The volume of water vapour at STP can be converted to gram water by considering the vapour as an ideal gas, and this was always
assumed when calculating Jv from experimental flux data expressed in pressure units
(Fig. 3.1). The volume (V ) of 1 mol of an ideal gas at STP can be calculated from
the ideal gas law:
V=
nRT
1 mol 8.3143 m3 Pa 273.15K
=
= 0.022414 m3,
p
mol K 101,325 Pa
(3.3)
where R is the gas constant. One mol of water has a mass of 18 g, and the density of
water vapour (wv ) at STP is
wv =
18 g
mass
=
= 8.03 104 g cm3
volume 22.414 103 cm3
(3.4)
(3.5)
56
0.95
1.43
1.90
2.375
4.0
4e-7
2.4
3e-7
3.2
2e-7
1.6
slope: 4.2 x 107 cm3 (STP)/ c m2 s
1e-7
JW X1010 g cm2 s1
0
5e-7
0.8
0
0.0
0.2
0.4
0.6
0.8
1.0
other driving forces in more detail later. Since water activity of the vapour is equal
to partial or fractional vapour pressure (p/p0), that is awv = p/p0, we can convert
driving force in cmHg to partial pressure simply by dividing actual vapour pressure
by saturation vapour pressure. With water at 25 C, saturation vapour pressure is
2.375 cmHg.
Based on the CGS system of the original literature, permeability (Pw ) of a 1 cm
thick membrane is
Pw =
(3.6)
57
identical for vapour and liquid water as long as temperature is the same (aw = awv ).
Hence, permeability coefficients are numerically identical when driving force is
expressed as water activity of vapour or liquid. However, ecologists prefer to use
the water vapour concentration (Cwv ) over leaves as driving force of transpiration.
At 100% humidity (p/p0 = awv = 1) and at 25 C, 1 m3 of air contains 23.05 g water
in the vapour phase (Nobel 1983), and the permeability coefficient now becomes
Pwv =
= 1.46 10
2 1
cm s
= 1.46 10
10
(3.7)
2 1
m s .
Pw and Pwv have identical dimensions, but they differ by a factor equal to the ratio
of density of liquid water and water vapour concentration. At 25 C we have
w
1,000 kgm3
=
= 43,384.
Cwv
23.05 103 kg m3
(3.8)
This has caused considerable confusion among workers in different fields, and for
this reason it is absolutely necessary to specify which type of driving force was used
in calculating permeance or permeability coefficients for diffusion of water.
Using the above derivations and definitions, the various permeability coefficients
can be easily converted. The numbers given as examples refer to a temperature
of 25 C
Pwv
wv (STP) cmHgsaturation
=
PHg
Cwv
(3.9)
4
(8.03 10 g cm3 ) (2.375 cmHg)
=
= 82.7.
23.05 106 g cm3
Note that only wv (STP) is constant, while the saturation vapour pressure
(cmHgsaturation ) and concentration of water vapour in air (Cwv ) vary with temperature
and must be looked up in tables (i.e., Nobel 1983)
Pw
= wv (STP) cmHgsaturation
PHg
(3.10)
(3.11)
58
PHg
.
D
(3.12)
For the PETP membrane shown in Fig. 3.2, PHg was 1.77 108 cm3 (STP) cm per
cm2 s cmHg, and D amounted to 3.94 109 cm2 s1 (Yasuda and Stannett 1962).
With these data we obtain
S =
PHg
1.77 108 cm3 (STP) cm
=
D
cm2 s cmHg (3.94 109 cm2 s1 )
= 4.49
(3.13)
(3.14)
Multiplying KHg by the density of water vapour at STP results in a new partition
coefficient Kw which is on the basis mass per volume:
Kw = KHg wv (STP)
cm3 vapor(STP)
4 g water
8.03
10
= 10.66
cm3 polymer
cm3 vapour
g water
.
= 8.56 103 3
cm polymer
(3.15)
59
The density of PETP at 25 C is 1.39 g cm3 , and dividing the above figure by density of the polymer we finally arrive at a partition coefficient of 6.16 103 on a
mass basis (g g1 or kg kg1 ). This lengthy calculation can be shortened by using
permeability coefficients other than PHg . With Pw , which can be obtained from PHg
using (3.10), we obtain Kw directly:
Kw =
3
3.37 1011 cm2 s1
Pw
3 cm water
=
=
8.56
10
D
cm3 polymer
3.94 109 cm2 s1
(3.16)
(3.17)
In calculating the ratios P/D, we must use the same units. Above, we used the CGS
system. If SI units are used for P and D the numerical values are the same, and the
dimensions of the partition coefficients would be m3 vapour per m3 polymer.
The concentration of water in the polymer can be obtained by multiplying the
partition coefficient by the appropriate driving force, which is the driving force used
in calculating the permeability coefficient (P). For instance:
Cwpolymer = Kw aw = (8.56 103) (1.0)
= 8.56 103 cm3 water/cm3 polymer.
(3.18)
(3.19)
The results are numerically identical only at 4 C when density of water is 1 g cm3 .
At higher and lower temperatures water activity is always 1.0, but concentration
of water is lower or higher. However, at physiological temperatures density of liquid water varies little with temperature, and is practically 1 g cm3 . With Kwv , the
concentration of water vapour (Cwv ) must be used
Cwpolymer = Kwv Cwv
= 370.6 (23.05 106 g cm3 ) = 8.54 103 g cm3 .
(3.20)
All of these partition coefficients can be found in the literature, but often without
the super- and subscripts used here. One should be sure to understand how they
were derived, since all are dimensionless. This also applies to KHg when (STP) is
omitted. We have added the same suffixes to the partition coefficients which were
used in calculating permeability coefficients, to make it clear how they are defined
and calculated. This was not always the case in the literature.
60
This complexity observed with water in polymers usually does not exist with
solutes. As long as the same molal dimensions are used for polymer and solution,
they cancel in calculating partition coefficients.
Problems
1. At 25 C, the concentration of water vapour in air at 100% humidity is
23.05 g m3, while in vacuum it is 803 g m3 (3.4) when p/p0 = 1. What is the
reason for this difference?
2. The units of pressure have changed. It is useful to remember that 1 Torr =
133.32 Pa 1 mmHg; 1 atm = 760 Torr, 1 bar 750 Torr. Normal pressure is
defined as 760 mmHg = 101,325 Pa = 1.01325 bar. What would be the steady
state slope in Fig. 3.1 in Pa s1 ?
3. If the EC-membrane (Fig. 3.1) had a thickness of 1 mm, what would be the
diffusion coefficient?
4. Using the data given in Fig. 3.1, calculate the steady state flux (Jv ) of water
vapour in cm3 (STP) cm2 s1 by using the equation
Jv =
273
Vreceiver
preceiver
.
t A
273 + 25 760 mmHg
(3.21)
The volume of the receiver was 100 cm3 , A was 1 cm2 and temperature was 25C.
5. With the result obtained in problem 4, calculate PHg of the membrane. Membrane
thickness was 1 cm, and the pressure in the donor was 2.375 cmHg.
6. Assuming a linear sorption isotherm, what is the equilibrium concentration
(g g1 ) of water in EC (density 1.13 g cm3 ) at 25 C at 50% humidity?
Solutions
1. In air at normal pressure, the total pressure is the sum of the partial pressures of
O2 , N2 and water vapour. In the absence of O2 and N2 , much more water vapour
is soluble per unit volume.
2. We obtain 0.267 Pamin1 or 4.44 103 Pa s1
3. We use D = 2 /6te and obtain D = 2.78 1011 m2 s1 or 2.78 107 cm2 s1 .
4. The steady state flux is 4.02 106 cm3 (STP) cm2 s1 .
5. Using (3.1) we obtain PHg = 1.96 106 cm3 (STP) cm2 s1 per cmHg.
6. We solve this problem in four steps. We already calculated PHg and D and (i) we
now calculate Pw using (3.10) and obtain 3.74 109 cm2 s1 . (ii) Dividing this
number by D (3.16) we obtain Kw = 1.35 102 cm3 water per cm3 polymer.
(iii) From (3.18) with p/p0 = aw = 0.5, we calculate the water content at 50%
humidity of 6.73 103 cm3 water per cm3 polymer. (iv) Dividing this figure by
1.13 g cm3 and assuming a density of liquid water of 1 g cm3 , we obtain the
water content of 5.95 g water per g polymer.
Chapter 4
Water Permeability
All terrestrial organisms have a problem in common; they must minimise water
loss to the atmosphere and prevent desiccation. The driving force of transpiration at
25 C and 50% humidity is 95 MPa, and at lower humidity it is even greater. Water
supply is often short. Higher plants, insects and mammals use similar strategies to
save water. They have generated membranes of very low water permeability at their
interface with the dry air surrounding them most of the time. Synthetic polymers
used for membranes, tubing, containers and other packaging materials also have
low permeability to gases, water and other solvents to protect goods. Before we turn
to permeability of cuticles and to strategies of plants to built effective barriers for
protection against adverse influences from the environment, we will briefly compare
water permeability of synthetic membranes with permeance of plant polymer matrix
membranes. Synthetic polymer membranes have been studied extensively during
the last decades, and structurepermeability relationships have been established.
What can we learn from homogeneous synthetic membranes to better understand
permeability of heterogeneous plant cuticles?
61
62
4 Water Permeability
dihydroxyfatty acids. Composition of ivy leaf cuticles is 65% C, 25% O, 9.3% H and
0.8% N (Schreiber et al. 1994). Polar functional groups are permanent dipoles which
are involved in hydrogen bonding and they affect sorption of water and water permeability of a polymer (Schnherr 2006). Electron microscopy suggests that cutin
and polar polymers do not form a homogeneously mixed phase (copolymers). In
TEM polar polymers are seen as a network of anastomosing fibrils embedded in
cutin (Sect. 1.4.2).
In this chapter, we analyse contributions of polar polymers, cutin and waxes to
water permeability, and present evidence showing that cutin and polar polymers
form two independent parallel pathways for transport of water and highly water
soluble solutes. The effect of waxes on water permeability and their deposition in
cutin and on the surface of cuticles is another important topic.
When comparing effectiveness of cuticles as water barriers with man-made polymers, it is useful to treat water permeability of the polymer matrix and cuticular
membranes separately. There is a large number of synthetic polymers, and we
selected some which resemble cuticles structurally and chemically. Cellulose acetate
(CA), polyvinyl acetate (PVA), polyethyl methacrylate (PEMA) and polyethylene
terephthalate (PET) are polyesters. Nylon is a polyamide, and ethyl cellulose (EC) is
a cellulose ether. Depending on degree of substitution they contain 3050% oxygen
by weight. Polyethylene (PE) and polypropylene (PP) are polymers lacking functional groups. Polymers can be partially crystalline (PE, PP, PET), and depending
on temperature they occur in the glassy or the rubbery state. In the glassy state, the
polymer chains are stiffer and the polymer is more brittle than in the rubbery state
(Park 1968). All selected polymers are homogeneous, and diffusion coefficients
have been determined from sorption/desorption or from time lag (see Chap. 2).
With a few exceptions (Rust and Herrero 1969) permeability to water vapour has
been given as PHg . This can be converted to Pwv and Pwv as explained in Chap. 3.
With Pwv and D known, the partition coefficient and water content of membranes
can be calculated using (3.17) and (3.20) respectively.
Polymer matrix membranes are obtained by extracting waxes from cuticular
membranes. These MX membranes had a thickness of about 3 m, and Pw was
determined gravimetrically using the cup method (Sect. 9.7) with water inside the
chambers and humidity outside being practically zero (Schnherr and Lendzian
1981).
Water permeability of selected MX-membranes and synthetic polymer membranes is listed in Table 4.1. Some polar synthetic polymers swell, and sorption
isotherms may not be linear when partial pressure is >0.5. In these cases, values
for Pwv , D and Kwv at p/p0 < 0.5 were selected. Among the synthetic polymers,
PP is the one with the lowest and EC has the highest Pwv . They differ by a factor of 1,000, while their diffusion coefficients differ only by a factor of 39. PVA
was the polymer with the lowest diffusion coefficient, and D for the other polymers
ranged from 1011 to 1013 m2 s1 . Pwv and D are not identical, because sorption
of water vapour differs among the polymers (2.4) and (2.17). Partition coefficients
(Kwv ) were calculated as P/D, which is valid when polymers are homogeneous.
Water concentration of membranes in equilibrium with 100% humidity (Cw ) was
4.1 Water Permeability of Synthetic Polymer Membranes and Polymer Matrix Membranes
63
calculated by multiplying Kwv by 23.05 103 kg m3 , the water vapour concentration of air at 100% humidity and 25 C (3.20). Concentration of water in synthetic
polymers in equilibrium with 100% humidity (or p/p0 = 1) ranged from 0.65 to
168 kgm3 .
Pwv was obtained by multiplying Pw by 43,384 (3.11). Permeances of the selected
MX membranes ranged from 1.2 103 to 2.5 104 m s1 . In order to compare
synthetic polymers and MX membranes, both types of membranes must have the
same thickness. Permeances for the synthetic membranes were calculated as P/
for a thickness of 3 m, which is similar to thicknesses of the MX membranes in
Table 4.1. As these synthetic polymers are homogeneous, this is perfectly legitimate.
Permeances of MX membranes are similar to those calculated for the polar polymers
EC, CA, PMA, PEMA and Nylon. Permeances of PP, PE, PVA and PET membranes
are considerably lower.
Comparing diffusion coefficients meets with some difficulties (Table 4.1). Becker
et al. (1986) determined D values for Ficus and Citrus MX using the hold-up time
method (2.5), while Chamel et al. (1991) estimated D from sorption isotherms
(2.33), and their D are considerably higher than those of Becker et al. (1986).
Chamel et al. (1991) also determined water vapour sorption in CM and MX gravimetrically. Sorption in MX and CM was similar or identical because most sorption
sites (dipoles) are contributed by cutin and polar polymers, and access of water to
Table 4.1 Water permeability at 25 C of selected synthetic polymer membranes and plant polymer
matrix membranes isolated from astomatous leaf surfaces
Polymer
Pwv
D (m2 s1 )
Kwv
Cw
(kg m3 )
Pwv (m s1 )
( = 3 m)
Jwv
(g m2 h1 )
4.9 1013
1.2 1012
5.1 1015
2.7 1013
1.2 1013
1.1 1011
3.1 1012
1.9 1011
1.8 1014
4.1 1013
6.0 1015
2.6 1014
39
28
7,269
484
2,750
264
3,000
1,000
7.8 104
2,000
8.7 105
2,828
0.90
0.65
168
11.2
63
6.1
69
23
1.8 103
34
2.0 104
41
6.3 106
1.1 105
1.2 105
4.3 105
1.1 104
9.7 104
3.1 103
6.3 103
2.5 104
1.8 103
4.7 103
1.2 103
0.52
0.91
1.00
3.57
9.13
80.5
257.3
522.8
20.7
149.3
390.0
99.6
(m2 s1 )
PPa
PEa
PVAb
PETa
Nylonb
PEMAc
CAb
ECd
Ficus MXe
Ficus MXf
Citrus MXe
Citrus MXf
Pyrus MXg
Hedera MXg
a Rust
1.9 1011
3.3 1011
3.7 1011
1.3 1010
3.3 1010
2.9 109
9.3 109
1.9 108
1.4 109
5.2 109
64
4 Water Permeability
these polar functions was apparently not reduced by waxes. They reported 34 and
41 kgm3 for Ficus and Citrus MX. This is the range of Cw observed with EC,
Nylon and CA.
A further complication arises when we calculate Kwv as P/D(=Pwv /D). These
partition coefficients are larger by orders of magnitude than those obtained from
sorption experiments (Table 4.1), and as a consequence water concentrations (Cw )
are much higher than those determined gravimetrically. Precision of the sorption
experiments is very good, and no assumptions are needed to calculate water concentration in MX. Hence, these values are reliable, and values calculated as P/D must
be in error. Becker et al. (1986) calculated D from the hold-up time (te ) and membrane thickness (D = 2 /6te ). Membrane thickness also enters in calculating P (=
Pwv ). Combining the above equations we obtain Kwv = Pwv 6te /. Since water
concentration in MX obtained using the P/D ratio is larger by factors of 53 (Ficus)
and 488 (Citrus) respectively, it appears that the real diffusion paths are much longer
than thickness of the MX. This tortuosity ( ) of the MX is astounding and difficult
to explain. Later (Sect. 4.5) we shall present evidence that in MX membranes water
flows in two parallel pathways that is, in polar polymers and in the cutin polymer.
Diffusion coefficients calculated from hold-up times are some averages for the two
pathways, and no structural information can be extracted from them.
This large difference in Cw depending on method of determination is excellent
evidence that MX membranes are not homogeneous. It is not possible to characterise water transport in MX using unique values for P, D or Kwv , as is possible
with synthetic polymer membranes. The constituents of the MX (polar polymers
and cutin) form separate phases, and each phase has its own diffusion and partition coefficient. Both coefficients vary with position, and the values derived from
sorption experiments and hold-up times are some type of average, which is not very
useful for analysing water permeability of cutin and polar polymers in MX.
In homogeneous membranes, effectiveness of water barriers is characterised by
P and D. Since MX membranes are not homogeneous, this comparison is not
meaningful. Hence, we compare efficacy of membranes based on maximum water
fluxes (Jwv ). We calculated the maximum water fluxes across 3 m-thick membranes
(Table 4.1). Maximum flux occurs when driving force is maximum, that is, when
humidity on the donor side is 100% and on the receiver side 0%. The maximum flux
of water vapour (Jwv ) was obtained by multiplying Pwv by the vapour concentration
of 23.05 g m3, which at 25 C amounts to 100% humidity.
Maximum moisture flux across PP and PE is small, as would be expected for
packaging materials. Commercial household foils or bags are 310 times thicker,
and fluxes are only a third or a tenth of those shown in Table 4.1. With the more polar
polymers, Jwv ranged from 80.5 to 522.8 g m2 h1 , and with the MX-membranes
water loss amounts to 20.7390 g m2 h1 . This is of the same order as maximum
transpiration rates measured with plants when stomata are open (Larcher 1995).
Plants regulate their water household by opening or closing stomata. When stomata
are closed, transpiration rates are less than one tenth of maximum rates. This cannot be realised with water barriers having properties such as the polymer matrix.
Evolution solved this problem by incorporating waxes into cuticles (Sect. 4.6).
65
(4.1)
inside
Here R and T have the usual meaning, a is the activity of ions or salt, z is the valence
of the ions and t is the transference number of the co-ion. The transference number
66
4 Water Permeability
aoutside
RT
ln +inside
F z+ a+
(4.2)
aoutside
RT
ln inside
F (z ) a
(4.3)
67
16
14
Citrus aurantium
12
10
CM
8
6
MX
4
2
0
2
2
pH
15
Pyrus communis CM
10
Prunus armenica CM
0
5
10
15
2
6
pH
Fig. 4.1 Membrane potentials measured with cuticular membranes isolated from adaxial leaf
surfaces of Citrus aurantium, Pyrus communis (pear) and Prunus armeniaca (apricot) at 25 C
and KCl solutions of 4 103 (inner surface) and 2 103 mol l1 respectively. (Redrawn from
Schnherr and Huber 1977)
68
4 Water Permeability
potentials were highest, but did not quite reach the Nernst potential of 17.8 mV,
hence they were not perfectly permselective for cations. Under natural condition
the pH at the surfaces of the cuticles will be lower, and exclusion of anions will
be far from complete. This means that diffusion of salt can take place, and this
has been confirmed experimentally. Self-diffusion of NaBr across Citrus MX membranes was studied at pH 3 and 8.5 at 25 C, and Na+ and Br permeances were
calculated (Schnherr and Huber 1977). The concentration of NaBr and pH was the
same on both sides of the membrane (4 103 mol l1 ), which implies that there
was no net driving force. Radio-labelled ions were used (24 Na+ and 82 Br ), and
the fluxes of the ions were not coupled and both ions could diffuse independently.
At pH 3 the ratio of the permeances of Na+ /Br ranged from 0.58 to 0.69, showing that permeance for Br was higher because the membranes carried a net positive
charge and co-ion (Na+ ) diffusion was reduced by relative Donnan exclusion. At pH
8.5 the ratio of permeances ranged from 3.83 to 4.39, because the membranes were
negatively charged and now Br experienced Donnan exclusion. Thus, depending
on pH, cuticles are either cation or anion exchangers. The nature and concentration
of the fixed charges will be dealt with next.
(4.5)
69
The higher the affinity between R and the cation, the lower is the resulting pH.
For instance, the affinity of the MX for Ca2+ ions is very high, and the pH obtained
with CaCl2 is much lower as with NaCl.
The high affinity for Ca2+ can be utilised to determine cation exchange capacity
(Schnherr and Huber 1977). A known amount of isolated CM is equilibrated in
buffered solutions containing 45 CaCl2 until equilibrium is obtained. Then, the CM
pieces are washed repeatedly with deionised water to remove adhering solution and
sorbed electrolyte (CaCl2 ). With Citrus MX four washes sufficed, and radioactivity contained in cuticles no longer decreased when washing was continued. When
cuticles are dropped in 1 N HCl, the exchangeable Ca2+ is released and can be
determined by scintillation counting. This method is simple and very accurate, and
it can be used with very small amounts of CM (<1 mg) while with potentiometric
titration the batches had to be 200 mg. It is not necessary to work under a nitrogen atmosphere, since solutions are buffered. The method works only with divalent
cations. Attempts to determine exchange capacity using monovalent 137 Cs+ failed,
as radioactivity of MX continuously decreased during washing until the MX was
free of radioactivity. Cs+ was exchanged for H+ contained in equilibrium water
having a pH of 5.5 due to dissolved CO2 (Schnherr and Huber 1977).
Before isolated cuticles can be titrated, they must be conditioned by cycling
between 1 N HCl and deionised water at room temperature. This removes Ca2+ and
Mg2+ contained naturally in isolated cuticles. However, Cu2+ , Zn2+ and Fe3+ are
not completely removed, even though Schnherr and Bukovac (1973) used 6 N HCl.
After the third treatment with HCl, cuticles are washed extensively with deionised
water until free of chloride ions. This treatment eliminated 0.18 eqkg1 cations contained in isolated tomato fruit cuticles. Before conditioning, large amounts of Ca,
Mg, Ba, Fe, Cu and Zn were detected in the ash. Traces of Cu, Fe and Zn were still
left in the ash after conditioning (Schnherr and Bukovac 1973).
Cation exchange capacity increased with increasing pH (Fig. 4.2). There is a distinct plateau around pH 7 and another one around pH 9. Above pH 9, exchange
capacity of tomato fruit (cv. Traveller) MX increased by not much, while with pepper fruit and Schefflera MX exchange capacity increased further up to pH 11. Higher
pH values were not used in these experiments, to avoid hydrolysis of ester bonds in
cutin. Figure 4.2 suggests the presence of three dissociable groups in the MX differing in acid strength (pKa ). The first group is fully ionised at about pH 6, the second
at pH 9 and the third at pH 12 (Schnherr and Bukovac 1973). The exchange capacity of the first group differed among the species and ranged from 0.1 to 0.2 eq kg1 ,
while the second group had an exchange capacity of around 0.33 eqkg1 with all
three species.
Similar results were obtained with Citrus and apricot leaf cuticles, except that
the plateau around pH 6 is not so pronounced (Fig. 4.3). Using the method of paired
comparisons, exchange capacity of Citrus CM and MX was studied and no difference was detected (Schnherr and Huber 1977). Data for tomato fruit MX seen in
Fig. 4.3 were obtained with the red variety Campbell 17, and at pH 9 exchange
capacity was about 0.5 eqkg1 . If titration was continued up to pH 12 the third group
was fully ionised, and exchange capacity reached 1 eq kg1 such that the third group
70
4 Water Permeability
1.0
pepper fruit MX
0.9
0.8
0.7
0.6
0.5
tomato fruit MX
0.4
0.3
0.2
Schefflera MX
0.1
0.0
3
10
11
pH
Fig. 4.2 Exchange capacities of the MX obtained from isolated fruit cuticles of ripe pepper (Capsicum annuum) and tomato (Lycopersicon esculentum cv. Traveller) and adaxial cuticles from
Australian umbrella-tree (Schefflera actinophylla) leaves. MX was titrated at 25 C in the presence
of 0.1 N CaCl2 . (Redrawn from Schnherr and Bukovac 1973)
600
tomato MX
500
400
300
200
apricote MX
100
tomato cutin
Citrus MX /C M
0
2
pH
Fig. 4.3 Exchange capacities of MX from leaves of apricot (Prunus armeniaca) and Citrus aurantiumand tomato fruits cv. Campbell 17. Tomato fruit cutin was obtained by treating the MX (cv.
Campbell 17) with 6 N HCl for 36 h at 110 C. Exchange capacity was determined at 25 C in presence of 0.1 N CaCl2 . Data for tomato MX and cutin were obtained by potentiometric titrations
(Schnherr and Bukovac 1973). With apricot and Citrus, 45 Ca2+ in buffered solutions was used
(Schnherr and Huber 1977). (Redrawn from the original figures)
71
has an exchange capacity of 0.5 eqkg1 (data not shown). Between pH 9 and 12, the
MX changed colour from yellow/orange to red. The variety Traveller (Fig. 4.2)
does not turn red when ripe, and isolated cuticles have an opaque white appearance.
At pH 9 exchange capacity was around 0.5 eq kg1 , and above pH 9 it increased
only slightly.
Titration of MX with base results in titration curves indicative of three distinctly
different fixed groups whose acid strengths are influenced by pH, the nature of
counter ions and concentration of neutral salts. This is typical of weak acid groups
such as carboxyl and phenolic hydroxyl groups. Based on acid strengths, the first
group titrating up to pH 6 was assigned to carboxyl groups of pectins and polypeptides, the second group appeared to be donated by non-esterified carboxyl groups of
hydroxyfatty acids, and the third group most likely was phenolic in nature (Schnherr and Bukovac 1973). This picture is complicated by the presence of nitrogen in
isolated cuticles. Schnherr and Huber (1977) determined amino acids liberated by
acid hydrolysis (6 N HCl for 12 h at 110 C). Since amino acid amounts and compositions of apricot leaf MX were the same when isolated with enzyme or Zn/ZCl2 , the
polypeptides were not contaminants from the enzymatic isolation. They are located
inside the polymer, and were not removed by washing or by the recycling procedure
used to condition isolated cuticles.
Basic and acidic amino acids can contribute both acidic and basic fixed charges.
Below the isoelectric point, cuticles are positively charged because of the presence
of basic amino acids (Table 4.2). Histidine, lysine and arginine are basic amino
acids, and Kb values of their free amino groups are 6.0, 10.53 and 12.48 respectively.
Below the isoelectric points of cuticles all of them are protonated, and they lose their
charges only at pH values above 8 (histidine) or higher. Asparaginic and glutamic
acid are acidic amino acids, and the pKa of their free carboxyl groups are 3.65 and
4.25 respectively. They are ionised above the isoelectric points, and contribute to
exchange capacities of all three ionisable groups (Table 4.2).
Upon acid hydrolysis the tomato fruit MX lost 13% of its weight and all of its
nitrogen. Oxygen content decreased from 22.7% to 19.7%. Water droplets spread on
Table 4.2 Total Exchange capacity (E C ) of selected fruit and leaf MX membranes at pH 6, 8 and
9, and contribution of amino acids (AA) and pectin to E C
Species
Capsicum fruit
Lycopers. fruit
Citrus aurantium
Prunus armeniaca
Schefflera actinoph.
Pyrus communis
EC
EC
Basic AA Acidic AA
Pectin
Total AA
(meq kg1 ) (meq kg1 ) (meq kg1 ) (meq kg1 ) (meq kg1 ) (mMol kg1 )
pH 6.0
pH 89
230
200
133
120
80
580 (pH 8)
500 (pH 9)
250 (pH 8)
290 (pH 8)
400 (pH 8)
21
13
12
19
14
26
46
40
22
33
27
54
184
160
308
87
53
256
190
107
152
139
266
E C of pectins was estimated by subtracting E C of acidic amino acids from the total E C at pH 6
(data taken from Schnherr and Bukovac 1973; and Schnherr and Huber 1977)
72
4 Water Permeability
the morphological inner surface of isolated CM, but after acid hydrolysis the surface
turned hydrophobic and water droplets had contact angles around 90 . Obviously,
polar polymers were lost from the inner surface, and only cutin was left. This is
confirmed by ion exchange properties, since the first and the third ionisable groups
were eliminated. Only the second group attributed to cutin remained (Fig. 4.3). With
this background, it is clear that exchange capacity of the first group was due to
pectins and acidic amino acids, which contributed approximately 20% of the total
cation exchange capacity at pH 6. The third group was suggested to be phenolic,
because dissociation started only above pH 9. This is supported by the fact that: (1)
ripe red tomato fruits contain large amounts (4.25.6%) of bound phenolics such
as coumaric acid, naringinin and chalconaringinin (Hunt and Baker 1980), while in
mature green tomatoes flavonoids were lacking and only small amounts of coumaric
acid (0.8%) were detected, and (2) the green variety Traveller lacked the third
ionisable group (Fig. 4.2). Coumaric acid has two acidic groups, a carboxyl group
with a pKa around 4.5 and a phenolic hydroxyl group. Naringinin is a trihydroxy
flavanon. The pKa of unsubstituted phenol is 10.0 (Albert and Serjeant 1971). Substitution tends to increase acid strength, such that p-hydroxybenzoic acid has two
pKa values of 4.57 and 9.46 respectively. We could not find exact values for the
pKa values of hydroxyl groups of coumaric, naringenin and chalconaringenin, but
most likely they are >9, and this perfectly fits the titration curves seen in Figs. 4.2
and 4.3. For the varieties used in titration, we have no exact data concerning which
amounts of phenolics were actually present. If coumaric acid was present, it would
have made a contribution to the first ionisable group. Naringenin has only phenolic hydroxyl groups, and its equivalent weight is about 91 g eq1 . Since the variety
Campbell 17 had an exchange capacity of 0.5 eq kg1 between pH 9 and 12, only
45 g naringenin or 4.5% by weight could account for this. Hunt and Baker (1980)
detected 4.25.6% phenolics in three other post-climacteric tomato varieties.
73
0.5
total
0.4
0.3
Ca 2+
0.2
0.1
Na+
0.0
3
6
pH
Fig. 4.4 Simultaneous counter ion exchange of MX of Lycopersicon esculentum cv. Campbell 17
of Ca2+ and Na+ as a function of pH at 25 C. The molal concentrations of NaCl and CaCl2 were
0.1 and 5 103 mol kg1 respectively. (Redrawn from Schnherr and Bukovac 1973)
Above pH 4, more Ca2+ than Na+ was exchanged, even though Na+ concentration was 20 times higher. Most Ca2+ was exchanged by the second group (Fig. 4.4).
The apparent acid strength of dissociable fixed charges increased with increasing concentration of neutral salt, increasing valence and decreasing crystal radii
of counter ions (Schnherr and Bukovac 1973). This behaviour is typical of polyelectrolytes of the weak acid type (Helfferich 1962). The main reason for this is
the electrostatic free energy arising from the electrostatic repulsion of neighbouring
fixed charges. This repulsion causes the polymer chains to uncoil and stretch, which
lowers the configurational entropy and increases the free energy of the polymer.
As charge density and electrostatic potential increase during titration, the tendency
to form more negative charges in proximity to existing ones diminishes, and the
apparent acid strength therefore decreases as the degree of ionisation and exchange
capacity increase.
The electrostatic free energy can be reduced by association of fixed charges and
counter ions. The smaller the crystal radius of the counter ion, the greater the interaction between fixed charge and counter ions, the lower the electrostatic free energy,
and the higher the acid strength. This is exactly what was observed with tomato fruit
MX (Schnherr and Bukovac 1973). Increasing the concentration of neutral electrolyte increases the apparent acid strength because the sorbed salt tends to shield
neighbouring fixed charges, and it reduces the Donnan potential, i.e., the salt reduces
the pH difference between external solution and interstitial fluid in the polymer. The
magnitude of the combined effects of electrostatic free energy and Donnan potential can be seen from the fact that the intrinsic pKa of hydroxyfatty acids is about 5
(Albert and Serjeant 1971). In tomato fruit MX, apparent pKa was about 8 at 0.1 N
74
4 Water Permeability
CaCl2 (Fig. 4.3). At zero and 0.01 N CaCl2 , the apparent pKa of the second group
was 8.75 and 8.5 respectively (Schnherr and Bukovac 1973).
Similar arguments can explain counter ion selectivity. If two ions are available,
the polymer prefers that cation which results in the minimum electrostatic free
energy. Hence, the polymer prefers the counter ion that associates more closely with
the fixed charges (minimising the electrostatic free energy) and which results in the
smallest polymer volume (minimising the free energy of stretching and maximising
the configurational entropy). In comparison with sodium, the divalent calcium associated more closely with the fixed charges and reduced swelling, because half the
number of osmotically active particles were present. Exchangeable Ca2+ ions also
tend to have a lower osmotic coefficient than sodium (Howe and Kitchner 1955). In
epidermal cell walls there is no excess of K+ over Ca2+ , and most carboxyl groups
in cuticles will be neutralised with calcium ions.
High selectivity for Ca2+ over Na+ is evidence that in the MX negative charges
occur in close proximity. It follows that negative charges are not randomly distributed, but clustered. Likewise, a random distribution of COOH groups in a CH2
environment would be energetically unfavourable und thus improbable. This also
applies to other polar functions such as hydroxyl and amino groups. This leaves us
with the question as to the shape and location of polar clusters and their possible
role in permeability to water and ions. This will be considered next.
4.4 Water Vapour Sorption and Permeability as Affected by pH, Cations and Vapour Pressure 75
7.0e-7
Water permeance (m / s)
6.0e-7
Ethyl cellulose
5.0e-7
10 m
PMA
4.0e-7
3.0e-7
Silicon rubber
300 m
2.0e-7
150 m
1.0e-7
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Fig. 4.5 Water permeance (Pw ) at 25 C of polymer membranes as affected by partial vapour
pressure. With ethyl cellulose, water vapour in the donor was varied, and in the receiver vapour
pressure was close to zero. Membrane thickness was 1 mm, and PHg (Wellons and Stannett 1966)
was converted to Pw for a 10 m-thick membrane as described in Chap. 3. With silicon rubber and
polymethyl methacrylate (PMA) an aqueous buffer of pH 6 containing 0.1 mol l1 CaCl2 was used,
and partial pressure of the receiver was varied. Data for silicon rubber and PMA were taken from
Schnherr and Schmidt (1979) and Schnherr and Ziegler (1980) respectively
polypeptides are permanent dipoles, and their hydration is not affected by pH and
cations. Polarity and hydration of carboxyl, phenolic hydroxyl and amino groups
depend on pH and type of counter ions. From these facts, one would expect permeance to depend on pH, type of counter ion and p/p0 and in fact it does
(Fig. 4.6).
Permeance of polymer matrix membranes from Citrus aurantium increased with
increasing partial vapour pressure of the receiver. With NaCl in the donor, permeance was lowest at pH 3 and increased with pH, but dependence on p/p0 was similar
at all pH values used (Fig. 4.6). With CaCl2 in the donor, dependence on p/p0 was
similar as when MX-membranes were in the Na+ -form, but pH had no effect on
permeance. This indicates that hydration of carboxyl groups is similar when nondissociated or neutralised with Ca2+ . When the partial pressure was 0.22, permeance
was lower by a factor of 0.5 compared to pH 9. All four plots had a plateau at a
partial pressure of about 0.5.
Citrus leaf and tomato fruit cuticles have been classified as all regions reticulate. In anticlinal pegs of Citrus limon, a histochemical test (Thiry reaction)
indicated the presence of polysaccharides in the reticulum (Holloway 1982a). Most
water vapour sorbed in MX is sorbed by polar polymers (Fig. 4.7) and not by cutin.
The dependence of Pw on p/p0, pH and inorganic salts (Fig. 4.6) suggests that
76
4 Water Permeability
3.0e-7
+
Na , pH 9
2.5e-7
Na+ pH 6
2.0e-7
2+
Ca
pH 3, 6, 8
1.5e-7
+
Na pH 3
1.0e-7
5.0e-8
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Fig. 4.6 Effect of partial pressure of water vapour in the receiver on water permeance (Pw ) of Citrus
aurantium polymer matrix membranes at 25 C. Data were taken from Schnherr and Schmidt
(1979). The aqueous donor contained CaCl2 or NaCl at 0.01 mol l1 , and was buffered at pH 3, 6,
8 or 9. The same set of membranes was used with all pH values and salt solutions. Permeance was
measured using tritiated water in the donor
Fig. 4.7 Sorption of water at 25 C by ethyl cellulose, MX from Citrus aurantium leaves, tomato
(Lycopersicon esculentum) fruit and tomato cutin, as affected by partial pressure of water vapour.
Data were taken from Wellons and Stannett (1966) and Chamel et al. (1991) for EC and MX
respectively
4.4 Water Vapour Sorption and Permeability as Affected by pH, Cations and Vapour Pressure 77
in Citrus MX the reticulum contains carboxyl groups and is continuous across the
entire polymer matrix, including the cuticle proper. This is convincing evidence,
even though such a reticulum is rarely seen in TEM (Sect. 1.4). The aqueous pores
across the polymer matrix formed by the reticulum are further characterised in
Sect. 4.5. Comparable data for MX from other plant species, including those having
a lamellated cuticle proper, are not available.
Polar polymers sorb much more water than hydrophobic ones, and permeance
increases with increasing partial pressure (Fig. 4.5) because of increased sorption
of water (Barrie 1968). Sorption in the polymer matrix was measured with carboxyl groups in the hydrogen form, that is, in absence of inorganic cations (Chamel
et al. 1991). Sorption isotherms are not linear (Fig. 4.7) and resemble B.E.T. type
II isotherms. Water vapour sorption in tomato and Citrus MX was similar to that in
EC. For the MX, sorption close to 100% humidity is not available, but extrapolation
leads to figures somewhere between 70 and 80 g kg1 , which is 78% by weight.
The plateau seen in Fig. 4.6 for permeance of MX is strikingly absent in sorption
data (Fig. 4.7). This may be due to the fact that sorption in MX was measured with
carboxyl groups in the hydrogen form and in the absence of inorganic counter ions.
COOH and OH groups probably sorb similar amounts of water, because characteristic dipole moments for COOH and OH groups are similar and amount to 1.7 and
1.65 Debye respectively (Israelachvili 1991).
Sorption in tomato fruit cutin was considerably lower, and the isotherm was linear. Sorption at 100% humidity was 19 g kg1 , which is only about 25% of the
amount sorbed in the tomato MX. Cutin was generated by acid hydrolysis of tomato
fruit MX (6 N HCl, 110C, 12 h). This hydrolysis eliminates polysaccharides and
polypeptides, and probably also liberates phenolic compounds bound covalently to
the MX (Schnherr and Bukovac 1973). The bulk (75%) of the water in the MX is
sorbed by dipoles contributed by these compounds.
Polyethylene also has a linear sorption isotherm, and maximum sorption at 100%
humidity is 0.65 kgm3 (Table 4.1). With a specific gravity of 950 kgm3 maximum
sorption is 0.68 g kg1 . Hence, cutin sorbed 28 times more water than PE. Most of
this water is probably bound to free hydroxyl groups of cutin acids. When 19 g water
is sorbed in 1 kg cutin, this amounts to 1.06 molkg1 . Tomato fruit cutin is made up
mainly of C16 -dihydroxyfatty acids (Baker et al. 1982), which have a molecular
weight around 300 g mol1 . This yields a concentration of 3.33 mol hydroxy fatty
acids per kg of cutin. Hence, only a third of the mid-chain hydroxyl groups sorbed
a water molecule at 100% humidity. Those hydroxyl groups that did not sorb water
were probably engaged in intermolecular hydrogen bonds, and this indicates that
they were not distributed at random but are arranged close to each other.
At a partial pressure of 0.22, permeance was smaller by a factor of 0.5 than
at p/p0 = 1. Sorption in MX at p/p0 = 0.22 is about 10 g kg1 , while at p/p0 = 1
sorption amounted to about 7080 g kg1 . With ethyl cellulose the difference is even
larger (Fig. 4.7). It follows that permeance and water content of the membranes
were not proportional. Apparently, not all water sorbed in the MX participated in
transport.
78
4 Water Permeability
79
CTHO
,
(4.6)
where CTHO is the concentration of tritiated water (Bq m3 ), DTHO is the diffusion
coefficient (m2 s1 ) in the pore liquid, and is the thickness of the membrane. JTHO
is the flux per unit membrane area and driving force (Bq m2 s1 ). By hypothesis,
water flows exclusively in pores assumed to be circular, and the total pore area is
2
Apore = n rpore
.
(4.7)
(4.8)
Apore
Amembrane
DTHO n r2
DTHO
=
.
Amembrane
(4.9)
According to Poiseuilles law, the viscous water flux (Jviscous in m3 m2 s1 ) in capillaries is proportional to the fourth power of the radius and inversely proportional
to viscosity ( in Pa s):
4
n rpore
RT Csolute
= Pviscous Amembrane Csolute ,
(4.10)
where Vw is the partial molar volume of water (18 cm3 mol1 ). The driving force
for viscous flux is the hydrostatic pressure difference (in Pa) across the membrane.
Cuticular membranes are fragile, and an osmotic pressure difference must be used
in determining Jviscous . For this reason, the difference of hydrostatic pressure was
substituted by the difference in osmotic pressure, which according to Vant Hoff
equals RT Csolute . Hydrostatic pressure and osmotic pressure cause identical viscous fluxes if the membrane is impermeable to the solute. Dividing (4.10) by (4.9)
and solving for r2 yields
Amembrane Jviscous =
8 Vw
2
=
rpore
Pviscous
8Dw Vw
RT
Pdiffusion
(4.11)
and after substituting the literature values for the constants and taking the square
root, we have at 25 C
1 1
3
Pdiffusion
2.48 10 Pa mol K
= 0.36 (Pviscous /Pdiffusion ).
(4.12)
80
4 Water Permeability
Accounting for the diffusional component present in Pviscous , Nevis (1958) wrote the
above equation as
Pviscous Pdiffusion
rpore = 0.36
,
(4.13)
Pdiffusion
which gives the average or equivalent pore radius in nm. In deriving (4.13), the bulk
quantities for the diffusion coefficient (Dw ) and viscosity ( ) of water are used.
These equations have been employed to estimate equivalent pore radii in the
polymer matrix from Citrus leaves (Schnherr 1976a) and onion bulb scales
(Schnherr 1976b). Beyer et al. (2005) published some data from which pore radii
of pepper and tomato fruit CM can be calculated. Data for other species are not
available.
Diffusion of water across polymer matrix membranes from Citrus leaves was
measured using tritiated water. When both buffer solutions contained 0.1 N, NaCl
permeance (Pdiffusion ) was higher above pH 4 than in presence of 0.1 N CaCl2 . The
effects of pH and type of counter ions demonstrate the involvement of three different
weakly acidic groups in the MX, as was already discussed (Sect. 4.3). Above pH 9,
phenolic hydroxyl groups are responsible for the effect of pH on permeance of MX
membranes in Na+ form. Data for MX membranes in Ca2+ form above pH 8 are not
available. Under natural conditions pH in the MX will certainly be <8, and due to
high selectivity of carboxyl groups to Ca2+ ions they will be in the Ca2+ form. This
minimises swelling, and permeance is similar at all pH values, no matter if carboxyl
groups are not ionised or when neutralised with Ca2+ (Fig. 4.8).
Using (4.9) we can calculate the fractional pore area (Apore /Amembrane ), if we
assume that DTHO in the pore liquid is the same as in bulk water (2.44109 m2 s1 )
and the length of the pores is the same as the thickness of the membrane (2.66
5.0e-7
Permeance (m/s)
0.1 N NaCl
4.0e-7
2.93x104
3.0e-7
1.88x104
2.0e-7
1.23x104
1.35x104
1.0e-7
0.1 N CaCl2
8
10
11
pH
Fig. 4.8 Permeance (Pw ) of Citrus aurantium MX membranes measured at 25 C using tritiated
water. The same MX membranes were employed for studying the effect of salts and pH on
permeance. Numbers are fractional pore areas. (Plotted using data from Schnherr 1976a, b)
81
106 m). This is not a good assumption, as pointed out in Sect. 4.1. DTHO in the
pore fluid is definitely lower, and the path length is greater than due to tortuosity. As the fractional pore area is Pdiffusion /DTHO , the ratio /DTHO in the pore
liquid will be much larger than in a water film having the same thickness as the
MX membranes. However, /DTHO is probably not affected by pH, and for the
sake of argument we have added selected fractional pore areas to Fig. 4.8. Since
permeance of MX membranes in Na+ form increased with pH, Apore /Amembrane
also increased. Apore /Amembrane is proportional to the fractional volume of water
in the membrane (volume of water/total volume of membrane), and this is a quantitative measure of swelling (Kedem and Katchalsky 1961). The absolute values of
Apore /Amembrane are in error, but the increase of Apore /Amembrane with pH reflects
the change in water content of MX. The fractional volume of water in the MX is
independent of pH when the MX is in Ca2+ form, or when carboxyl groups are not
ionised (Fig. 4.8).
Having established that total pore area increases with increasing pH, as long as
the MX is in Na+ form, we can now test if this is due to larger pore radii or to
an increase in number of pores. Size of pores can be estimated using (4.13) when
Pdiffusion and Pviscous are known. Volume flux of water was measured using an apparatus made from glass (Schnherr 1976a) and a number of solutes differing in size. All
measurements were made with identical buffers on both sides and with the osmotic
solutes in the outer compartment facing the morphological outer surface of the MX.
The volume flux was measured in a calibrated capillary (0.24 l mm1 ) connected to
the outer compartment. The entire apparatus was submerged in a water bath maintained at 25 0.02C, and only the tips of the capillaries protruded over the surface
of the water bath. Temperature control is critical, since water volume of water varies
greatly with temperature. A 0.01 moll1 citric acid and Na2 HPO4 buffer was used
in the pH range of 37 and 0.01 moll1 disodiumtetraborate (borax) adjusted with
HCl was used at pH 9. With these buffers in donor and receiver, the MX membranes
are in the Na+ form. Solute concentrations were 0.5 molkg1 with urea, glucose and
sucrose, and with raffinose 0.25 molkg1 were used, which is close to the solubility
limit.
Viscous or volume fluxes of water were determined at pH 3, 6 and 9 with urea
glucose, sucrose and raffinose, and Pviscous was calculated from (4.10). The same
set of membranes was used for all pH values and solutes. Pviscous increased with
increasing pH and solute size, and asymptotically approached the maximum value
of Pviscous (Fig. 4.9). As the differences in Pviscous between sucrose and raffinose
were small, Schnherr (1976a) assumed that at all pH values MX membranes were
impermeable to raffinose, and permeance measured with raffinose represented maximum permeance. Solutes larger than raffinose were not included in the work. Here
we use an approach for estimating maximum Pviscous that is superior to that which
would be obtained with hydrostatic pressure or with solutes to which the memmaximum
branes are impermeable. By fitting a parabola to the data points, Pviscous
can be
obtained and the above assumption can be tested. The curves fitted to the data points
maximum is the max(Fig. 4.9a) represent the hyperbola where is a constant, and Pviscous
imum permeance that would be obtained when solute radius (rsolute ) approaches
82
4 Water Permeability
2.00e-6
pH 9
pH 6
1.00e-6
urea
glucose
5.00e-7
raffinose
pH 3
sucrose
P viscous (m/s)
1.50e-6
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
pH 9
P viscous (m/s)
1.50e-6
pH 6
1.00e-6
pH 3
5.00e-7
0.00
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
83
infinity
Pviscous =
maximum r
Pviscous
solute
.
maximum
Pviscous
(4.14)
Data can also be analysed assuming that Pviscous varies linearly with the reciprocal of
the solute radius. Dependence was in fact linear, as the coefficients of determination
were 0.99 or better at all three pH values. The following regression equations were
obtained:
1
+ 1.87 106(r2 = 0.997),
rsolute
1
+ 1.27 106(r2 = 0.985),
at pH 6: Pviscous = 1.21 107
rsolute
1
+ 7.38 107(r2 = 0.999).
at pH 9: Pviscous = 6.05 108
rsolute
at pH 3: Pviscous = 1.34 107
(4.15)
The constants on the right hand side of the equations are the maximum values of
Pviscous when rsolute approaches infinity, that is, when 1/rsolute is zero. These equations were used to calculate Pviscous for selected solute radii and results (empty
symbols) were plotted in Fig. 4.9b. Experimental data are included as filled symbols.
Pviscous increased in the order urea < glucose < sucrose, showing that these
solutes penetrated the MX membranes to some degree (Fig. 4.9). Inspection of
the figure might suggest that membranes were impermeable to raffinose, but the
maximum values obtained from the hyperbola and inverse functions were slightly
Pviscous
larger than the experimental values (Table 4.3). The difference is smallest at
pH 3 (0.06 106 ), but at pH 6 and 9 the difference amounts to 0.27 106
and 0.12 106 respectively. This indicates that MX membranes were not totally
impermeable to raffinose.
According to our hypothesis, water and polar solutes can penetrate the membrane
only in aqueous pores. This is confirmed by the fact that viscous flow increased with
solute size. Solutes which dissolve in the polymer matrix, that is, solutes having a
high partition coefficient (2.17) would not have induced viscous water flux. Clearly,
large polar solutes are discriminated, and membranes should be impermeable to
solutes larger than the size of the pores (Fig. 4.9).
This was tested by measuring permeability at pH 9 of MX membranes to radiolabelled water, urea and glucose (Schnherr 1976a). Sucrose, raffinose or larger
experimental
Table 4.3 Values of Pviscous
(m s1 ) obtained experimentally with raffinose, and values calcumaximum ) based on a hyperbola or an inverse function. In the last
lated by regression analysis (Pviscous
column, the means of the fitted values are given
experimental
pH
Pviscous
3.0
6.0
9.0
0.68 106
1.08 106
1.80 106
maximum hyperbola
Pviscous
maximum mean
Pviscous
0.80 106
1.43 106
1.97 106
0.68 106
1.27 106
1.87 106
0.74 106
1.35 106
1.92 106
84
4 Water Permeability
1e-4
THO
log Ps = 1.17 1/rsolute
Pd (m/ s)
1e-5
10.51(r2 = 0.96)
1e-6
urea
1e-7
glucose
1e-8
sucrose
raffinose
1e-9
1
Fig. 4.10 Permeances for diffusion of radio-labelled tritiated water (THO) and 14 C-labelled polar
solutes across Citrus MX membranes at pH 9 and 25 C. Red dots represent experimental data,
Green squares were calculated based on the linear regression equation shown in the graph. Solute
size was taken from Longsworth (1953)
solutes were not included, but the data available indicate that membranes are nearly
impermeable to solutes larger than raffinose (Fig. 4.10). Linear regression shows
that log P is a function of 1/rsolute , and it decreases by a factor of 1.17 when 1/rsolute
increases by 1.0. This corresponds to a decrease in P by a factor of 14.8. Purea and
Pglucose are smaller than PTHO by factors of 32 and 2,008 respectively. Predicted
permeances for sucrose and raffinose are 3.94 109 and 1.85 109 m s1 respectively. As the y-intercept is 10.51, the limiting permeance is 3.0 1011 m s1 . A
solute having twice the molecular weight of raffinose, that is 1,008 g mol1 , has a
radius of 0.9 nm, and its permeance would be 6.0 1010 m s1 , which is very low
and not too far from the limit. It would be very difficult to measure it precisely.
The above arguments can be used to illustrate the difficulties encountered in
determining permeability to polar solutes using a steady state experiment. According to (2.2), permeance is the ratio of flux (J) and driving force (Csolute ). With
raffinose the predicted permeance is 1.85 109 m s1 . When working with radiolabelled solutes, which is the most sensitive method, one needs a flux of at least
100 Bq h1 for reasonable counting statistics. The membrane area of cuticles is
rarely larger than 1 cm2 . Under these conditions, we would need a donor concentration of 1.5 105 Bq cm3 . Radiochemical purity is rarely better than 98%. To
make sure that the radioactivity in the receiver is not mainly due to impurities, the
total flux should at least be 10% of the activity of the donor, which in our example would be 1.5 104 Bq. Since the minimum flux should be 100 Bqcm2 h1 ,
the experiment would have to last 150 h or 6.25 days for penetration of 10% of the
solute from the donor to the receiver. This can be done, but it is close to the limit,
because all experimental variables must be closely controlled, all instruments must
work properly and there must be no power failure and the like. This is one of the
85
Table 4.4 Estimating pore size and pore number in MX-membranes of Citrus aurantium in Na+
maximum values were obtained
form. Data for Pdiffusion were taken from Schnherr (1976a), and Pviscous
from Table 4.3
pH
Pdiffusion
(m s1 )
maximum
Pviscous
(m s1 )
Pvisc /Pdiff
rpore
(nm)
Apore (m2 )
Number of
pores/m2
3.0
6.0
9.0
2.56 107
4.16 107
7.30 107
0.74 106
1.35 106
1.92 106
2.89
3.25
2.63
0.50
0.54
0.46
2.79 104
4.16 104
7.96 104
3.55 1014
4.54 1014
11.97 1014
rpore was calculated using (4.13); Apore is the total pore area per m2 membrane calculated according
2 .
to (4.9) using D = 2.44 109 m2 s1 and = 2.66 106 m; number of pores = Apore /rpore
reasons why we have no data for large solutes, even for the MX. Since Psolute for
cuticular membranes is at least 100 times smaller, it is clear that accurate measurements in the steady state are not possible. The problem can be overcome using the
SOFP technique (Sect. 6.4).
maximum , equivalent pore radii can be calculated using (4.13).
From Pdiffusion and Pviscous
The ratio Pviscous /Pdiffusion is larger than 2 (Table 4.4), indicating the presence of
aqueous pores (Nevis 1954). Their radii range from 0.46 to 0.54 nm. Since radii
are calculated from the ratio of two empirical permeances, the differences are not
significant (Schnherr 1976a). The pore radii did not depend on pH, and the mean
is 0.50 nm. The increase in permeance with pH can be attributed to an increase in
number of pores rather than to larger pore radii. The average pore size estimated
from diffusional and viscous permeability (0.5 nm) is larger than that calculated by
Schnherr (1976a), who obtained radii of 0.440.46 nm because he used Pviscous
obtained with raffinose, which is a little smaller than that estimated by curve fitting (Table 4.3). This estimated pore radius of 0.5 nm is too small, since with
sucrose (rsolute = 0.555 nm) and raffinose (rsolute = 0.654 nm) viscous permeance
maximum
was smaller than Pviscous
. Clearly, the MX membranes were not totally impermeable to these solutes. Some reasons for this discrepancy are considered next.
There are a number of assumptions inherent in the above calculations. The determination of Pdiffusion and Pviscous is straightforward and no assumptions are needed.
However, in calculating the pore radius from the permeances the diffusion coefficient and viscosity enter (4.11), and we used bulk properties (4.12). Activation
energies of diffusion of water and of viscous flow in MX membranes are 54 and
46 kJmol1 respectively, while for bulk liquid the level is only about 19 kJmol1
(Schnherr 1976a). The activation energy of a hydrogen bond is about 20 kJmol1
(Nobel 1983). Hence, when water molecules diffuse in bulk only one of the hydrogen bonds is broken at a time, while in the pore liquid more than two H-bonds need
to be broken for a water molecule to move. This suggests that D in the pore liquids
is considerably smaller than in bulk water. This is not too surprising, since pores are
very narrow and the radius of a water molecule is about 0.190.197 nm, depending
on source (Durbin 1960; Renkin 1954).
86
4 Water Permeability
Only about 23 water molecules fit into the diameter of these pores and since
pore walls are made of permanent dipoles and ionised groups, many of these water
molecules represent hydration water. Water molecules bound to permanent dipoles
or to ions are not completely immobilised. They exchange with bulk water, and
at room temperature the mean residence time of water in the primary hydration
shell of monovalent cations is about 109 s1 , and with hydrogen-bonded water
residence time is shorter (1011 s1 ) (Israelachvili 1991). This means that many
water molecules jump from one dipole to the next. Thus, viscosity of water in the
pores is much higher than in bulk. Fortunately, in calculating pore radii the product
D enters rather than D alone (4.11). For diffusion in liquids, the StokesEinstein
relationship states that Dsolute is proportional to the Boltzmann constant ( ) and temperature (T ) and inversely proportional to viscosity ( ) and the radius of the solute:
Dsolute =
T
.
6 rsolute
(4.16)
This implies that at constant temperature (T in Kelvin) the product of the diffusion coefficient and viscosity is constant. It is reasonable to assume this to hold
also for aqueous pores, and deviation of D and from bulk properties should not
greatly affect pore size estimates. However, it could account in part for the fact
that estimated pore size is somewhat smaller than pore size expected from viscous
permeance (Fig. 4.9). Another factor might also have contributed. For a solute to
enter the pore by a diffusional jump it must find the opening and not hit the pore
wall, from which it would be reflected. This steric hindrance increases as the solute
approaches the size of the pore opening and may be estimated. Empirical corrections
are discussed by Lakshminarayanaiah (1969).
Since we have data on sorption of water in MX membranes in H+ form (Fig. 4.7),
which were measured gravimetrically, we can compare them with fractional volume
of water at pH 3 calculated from diffusion of THO (Table 4.4). At pH 3, most carboxyl groups are not ionised and fractional water content was about 2.8 104 .
At 100% humidity (p/p0 = 1.0) the weight fraction of water in Citrus MX was
about 0.08 (Chamel et al. 1991), which can be taken to be the volume fraction, since
specific gravity of water and the MX do not differ much (Schreiber and Schnherr 1990). This figure is 285 times larger than fractional volumes of water derived
from diffusion of water. In calculating fractional pore area and number of pores, the
diffusion coefficient of water in bulk was used and the tortuosity was disregarded.
Absolute values of the fractional pore areas given in Fig. 4.8 could be multiplied by
285, which is the factor by which /D is larger in the pore liquid than in bulk. Such
a calculation results in a fractional pore area and a fractional pore volume of 0.0385
for the MX in Ca2+ form. Thus, the average volume of water in the MX would be
3.85% of its total volume. As total water content is about 8% (Chamel et al. 1991),
48% of the total water would be located in aqueous pores, while 52% should be
sorbed in other compartments, possibly in cutin. In tomato fruit, cutin water sorption amounted to 19 g kg1 , which is 1.9% by weight. Data for Citrus cutin are not
available.
87
In Sect. 1.4 we introduced the terms cuticle proper and limiting skin, which refer
to a thin outer layer of the CM. It has been suggested that the thickness of the limiting skin is only 1/10 of the total thickness of the MX (Schnherr and Riederer 1988).
From transmission electron microscopy we know that the electron-dense reticulum
which marks the location of polar functional groups decreases in density from the
cell wall side towards the outer surface of the CM (Jeffree 2006). Often it is very
hard to detect this reticulum in the cuticle proper of non-laminated cuticles, and it
appears to be absent in cuticles having lamellated cuticle proper. This suggests that
water content of the cuticles decreases from the inner to the outer surface.
Above, we have demonstrated the existence of aqueous pore in the polymer
matrix membranes of Citrus leaves, and we estimated the equivalent pore radius.
A similar study was conducted using onion bulb scale and a different set of Citrus MX membranes (Schnherr 1976b). Pore radii were calculated from Pviscous and
Pdiffusion measurements at pH 7 using a slightly different approach. Pviscous was determined using 0.25 molkg1 raffinose, and it was assumed that values so determined
max . The pore radii in both types of MX membranes were similar
represented Pviscous
(0.41 nm), even though both permeances for onion MX were 5.8 times larger than
for Citrus MX.
In the study of Schnherr (1976b) water permeances measured with MX were
around 500 times higher than with CM, both with Citrus and onion bulb scale.
The volumetric apparatus used in these studies of Schnherr (1976a, b) was not
sensitive enough to accurately measure viscous water flux across CM. Hence, we
have no information concerning how waxes affect the ratio Pviscous /Pdiffusion or pore
radii. Beyer et al. (2005) measured Pviscous and Pdiffusion with pepper and tomato fruit
cuticular membranes at 25 C. Pviscous was determined gravimetrically, and Pdiffusion
was determined with THO. Polyethylene glycol with a molecular weight of 6,000
was used as solute in the receiver facing the morphological inner surface of the CM,
and pH was not controlled. Hence, the water flux was from the outer surface to the
inner surface of the CM. Permeances and estimated pore radii are given in Table 4.5.
These permeances are very high compared to permeances measured with astomatous leaf CM, but they are similar to Pw of Citrus and pear leaf MX (Table 4.1).
Pviscous was about ten times larger than Pdiffusion , and pore radii were much larger
than those measured in Citrus MX. The reason(s) for this difference are not known,
and it would be futile to speculate about it. Appropriate data for CM and MX of
other species are not available, but they are badly needed to get a better picture of
pore structure in CM and MX.
Table 4.5 Water permeance for viscous flux and diffusional flux (Pw ) and pore radii calculated
from (4.13). (Data taken from Beyer et al. 2005)
Species
Pepper fruit CM
Tomato fruit CM
Pviscous (m s1 )
Pdiffusion (m s1 )
1.31 108
0.19 108
1.52 108
0.13 108
3.85
2.12
88
4 Water Permeability
We have demonstrated the presence of aqueous pores in some cuticles for the first
time. Theories and methods are available. For a better understanding as to how cuticles function, we need systematic studies using cuticles from many more species.
Occurrence of aqueous pores in MX and CM of plant cuticles is not an academic
problem. Aqueous pores have been speculated about during the last 5 decades, but
the issue was not approached experimentally. Aqueous pores are involved in humidity effects on transpiration, and they are a prerequisite for penetration of hydrated
ionic species, which are insoluble in cutin and waxes and require aqueous pores to
cross cuticles (Schnherr 2006). We shall return to this topic in Chap. 5.
89
1
Rpore
1
Rcutin
(4.17)
Fig. 4.11 Schematic drawing of the limiting skin of Citrus MX, composed of the lipophilic cutin
matrix and polar pores arranged in parallel (not to scale)
90
4 Water Permeability
Pdiffusion is calculated as the flux per unit membrane area and driving force (4.8),
and it is the only known permeance. Permeance of cutin membranes have never
been determined, and the magnitudes of Ppore and Pcutin must be estimated based on
model II. In model I, it was assumed that all water diffuses in aqueous pores. We
now loosen that restriction by assuming the water can diffuse in pores and in cutin,
while laminar flow is restricted to aqueous pores.
Pdiffusion was determined experimentally, and it characterises the total diffusional
water flux across the MX membranes. The fraction of water which diffuses in aqueous pores is determined by Ppore , which is calculated by multiplying Pdiffusion by the
weight fraction (Wpolar polymers /Wmembrane ) of polar polymers. Pcutin characterises the
diffusional flux across the cutin polymer, and it is obtained by difference, that is
Pcutin = Pdiffusion Ppore , because the two resistances are arranged in parallel (4.17).
Model calculations were restricted to pH 3, since pore size is independent of pH
(Table 4.4) and most carboxyl groups are not ionised, such that counter ions do
not affect the magnitude of permeances at pH 3. It should be remembered that
Pviscous /Pdiffusion did not depend on pH (Table 4.4).
In Fig. 4.12 the effect of Ppore /Pdiffusion on Pcutin /Pdiffusion and on pore radius
is shown. If Ppore /Pdiffusion = 1, the total diffusional flux takes place in pores and
Pcutin /Pdiffusion is zero. As the fraction of water which diffuses across the pore
decreases, more water diffuses across cutin, and when only 10% flows across the
pores the ratio Pcutin /Pdiffusion is equal to 9. When more water penetrates the cutin
phase, less water diffuses in pores, and the ratio of viscous flux over diffusion flux
(which is proportional to Ppore ) increases, and hence pore radii increase (Fig. 4.12b).
Pore radii estimated using model I (0.50 nm) are too small, because raffinose
having a solute radius of 0.654 nm did penetrate MX membranes. This indicates
that the pores are larger than 0.5 nm. Some of the reasons for this deviation have
been pointed out in Sect. 4.5. Taking into account steric hindrance at the pore
entrance, the real average equivalent radius of the pores should be in the range
0.750.80 nm.
Such radii would be obtained if Ppore /Pdiffusion is 0.460.51 (Fig. 4.12b), that
is, about half of the diffusional water flux measured would take place across the
cutin, filling the space between the pores. At Ppore /Pdiffusion = 0.5, both Ppore and
Pcutin are 1.28 107 m s1 , since Pdiffusion is 2.56 107 m s1 . This estimate of
permeances is based on membrane area. Assuming that weight and area fractions
are numerically identical, corrected permeances based on fractional area of polar
cuticular polymers and cutin can be calculated. With a weight fraction of cutin of
0.77, the permeance of a cutin membrane having a thickness of 2.7 106 m would
be about 1.66 107 m s1 . This value is identical to the Pw of 1.60 107 m s1
measured by Schnherr and Lendzian (1981) with Citrus aurantium MX.
Calculations based on model II result in improved estimates of pore size, and
permeance of cutin is consistent with experimental values of Pw of Citrus MX. Permeance of cutin is clearly not zero as assumed in model I. It resembles permeance
of EC, a polyether containing free hydroxyl groups, that is, a polar polymer similar
to cutin. A 3 m-thick EC membrane has a Pw of 1.45 107 m s1 (Table 4.1). In
Citrus MX, water diffuses across two pathways arranged in parallel, and permeances
91
10
a
8
Pcutin / P pore
0
0.0
0.2
0.4
0.6
0.8
1.0
Ppore / P diffusion
2.0
b
1.5
a = 4.354
b = 0.0623
yo = 0.279
1.0
0.5
0.0
0.2
0.4
0.6
0.8
1.0
Ppore / P diffusion
Fig. 4.12 Diffusion of water across cutin and pores and pore radius as effected by Pcutin /Pdiffusion .
Model calculations for Citrus MX at pH 3. Pdiffusion and Pviscous data were taken from Table 4.4, and
values for Pcutin /Pdiffusion were assumed. Pore radius was calculated using (4.13), but substituting
Pdiffusion by Ppore
corrected for the different area fractions are 1.66 107 and 5.56 107 m s1 for
Pcutin and Ppore respectively. Hence, permeance of pores is larger by a factor of 3.35
than permeance of cutin, but water fluxes across the two pathways are the same,
since the weight fraction of cutin is larger by a factor of 3.35 than the weight fraction of polar polymers. In this calculation, the area fraction of polar polymers was
92
4 Water Permeability
used rather than area fraction of pores. This neglects the volume occupied by polar
polymers, which is not known.
Model II is superior to model I, as it provides more realistic pore size estimates.
No assumptions concerning the diffusion coefficient and viscosity of water in the
pores are needed, but it is still assumed that D is the same in pores as in bulk
water. Calculations are based on Pdiffusion which reflects permeance of the cuticle
proper, but pore size estimates do not depend on weight fraction of polar polymers or
distribution of polar polymers between cuticular layer and cuticle proper or limiting
skin. The ratios between Ppore and Pdiffusion are modelled, and the real contribution of
Pcutin to Pdiffusion should be measured experimentally. This can be done, since after
acid hydrolysis intact cutin membranes are obtained. Dependence on partial vapour
pressure of Pcutin can also be determined.
93
Since the effect of partial vapour pressure on permeance of cutin is probably small,
the wax-incrusted cutin may not respond at all to partial pressure of water vapour. In
this case, water vapour pressure would mainly affect permeance of the polar polymer
phase. This aspect is treated more comprehensively in the following section.
Pw (CM)
(m s1 )
Pw (MX)
(m s1 )
8.3 1010
4.9 1010
3.2 1010
1.2 1010
1.0 1010
1.6 107
1.1 107
6.5 107
1.7 108
2.7 108
P(MX)
P(CM)
193
224
2,031
142
270
Wax mass
(g cm2 )
12d
133e
1b
113d
64d
CM mass
(g cm2 )
316f
343f
110b
715f
476f
94
4 Water Permeability
MX, rather than to a particularly low Pw of the CM. Pyrus CM had 130 g cm2
wax, and permeance was higher than that of onion bulb scale CM.
Extraction of waxes increased Pw by orders of magnitude, even though they contribute little to total mass of CM (Table 4.6). With onion bulb scale, waxes amounted
to less than 1% of the total mass of the CM. With Citrus 3.8% wax decreased Pw by
a factor of 193. Pear leaf CM contained 38% wax ,while with ivy and Clivia waxes
amounted to 13% and 16% of the total mass respectively. Clearly, a mechanistic
analysis of water permeability of cuticles must focus on the contribution of waxes
to the water barrier.
95
Fig. 4.13 Schematic drawings for the three models IIIA, IIIB and IIIC showing the water pathways
across cuticular membranes composed of polar polymers, cutin and waxes embedded in the outer
cutin layer of the MX and on the surface of the MX (not to scale)
96
4 Water Permeability
only permeances have been measured, but not diffusion and partition coefficients in
the transport-limiting barrier.
Water permeability of CM has been studied using different approaches. With the
cup method (Schnherr and Lendzian 1981) the inner surface of the CM is in contact with water, and the outer surface is exposed to dry air of nearly 0% humidity
(Sect. 9.7). The amperometric method (Becker et al. 1986) used nitrogen gas saturated with water vapour as donor at the morphological inner surface of the CM, and
dry nitrogen served as receiver facing the morphological outer surface of the CM.
Permeances obtained with these two methods are minimum permeances, because
the outer surface of the CM is not or only weakly hydrated. Other experiments
had been conducted with partial vapour pressures between 0.02 and 1.0 or with
liquid water in contact with the outer surface of the CM while the inner surface
was wet by water (Niederl et al. 1998; Schnherr 1976b; Schnherr and Schmidt
1979; Schreiber 2001). These experiments show if permeance increases with partial
vapour pressure. With 100% humidity or liquid water on the receiver side, maximum
permeances are measured.
97
ratio between crystalline and amorphous fractions of the wax changed and reduced
water permeability. We return to this point when we discuss water permeability
of paraffin waxes (Sect. 4.6.4, subsection: Water Permeance of Polyethylene and
Paraffin Wax).
Wax composition and water permeability as related to exposure to sun light and
leaf age have been studied using Hedera helix leaf CM (Hauke and Schreiber 1998).
Sun and shade leaves of at least eight different developmental stages were harvested
from bud break to leaf senescence, and leaf area, cuticle weight, wax amount, mean
chain lengths and cuticular transpiration were measured (Fig. 4.14).
Leaf area increased rapidly during the first 30 days, and more slowly for another
30 days when maximum leaf size had been reached (Fig. 4.14a). Cuticle weight
continuously increased for 60 days (Fig. 4.14b). Wax amounts increased 1.5-fold
within the first 40 days, and decreased again until senescence at the end of the season
(Fig. 4.14c). Mean chain length of the wax homologues continuously increased from
C27 to C33 within the first 60 days (Fig. 4.14d). Water permeability decreased about
Permeance
(m/s) x 1010
mean chain
length
leaf area
(cm2)
32
24
a - leaf area
16
8
0.5
0.4
0.3
0.2
b - cuticle weight
24
c - wax amount
18
12
6
33
d - mean chain length
30
27
8
e - cuticular transpiration
6
4
2
0
30
60
90
120
leaf age (days)
150
180
210
Fig. 4.14 Leaf and cuticle development of Hedera helix shade leaves from bud break to leaf senescence. (a) The variation of leaf area. (b) Cuticle weight. (c) Wax amount. (d) Mean chain length
of the wax molecules. (e) The decrease of cuticular permeability during about 7 months from end
of April to beginning of November is shown. (Data from Hauke and Schreiber 1998)
98
4 Water Permeability
seven-fold during the first month and remained constant during the remaining part of
the season (Fig. 4.14e). There is no obvious relationship between water permeability
and the other properties studied. These studies give no hints as to how waxes reduce
water permeability.
(4.18)
Species having high water permeance have a wax in which stearic acid mobility is
high, and vice versa. We take this as evidence that water in CM and stearic acid
in reconstituted waxes both diffuse along the waxy pathway characteristic for each
species. Data points above the regression line could indicate that some water transport in aqueous pores might have been involved, but direct evidence is lacking.
Besides, Pw was measured using the cup method, and swelling of CM was minimum. Wax structure, that is, physical arrangement of amorphous and crystalline
fractions, appears to be similar in CM and reconstituted waxes (Sect. 6.5). Once
again, chemical composition appears not to be directly related to barrier properties.
What is the physical meaning of the y-intercept? It is statistically not different
from zero, but we should still consider its possible role in model III. The y-intercept
must be subtracted from the product 6.6 107 DSA , which overestimates Pw . This
correction is more important for CM with low Pw . With Vanilla CM, Pw calculated
from the regression equation is 3.6 1011 m s1 , which is reasonably close to the
value measured of 1.7 1011 m s1 . Had the y-intercept not been subtracted, Pw
calculated would have been 8.1 1011 m s1 . The corresponding values for Citrus aurantium are 2.1 1010 or 2.5 1010 m s1 . Both figures are not far from
99
Table 4.7 Water permeance Pw of CM, diffusion coefficient DSA of stearic acid in reconstituted
wax, mass mcm of the CM, and mass mwax of the wax obtained from the investigation of 24 species.
(Data from Schreiber and Riederer 1996a, b)
Species
Leaf CM
Vanilla planifolia (vanilla)
Monstera deliciosa (breadfruit-vine)
Philodendron selloum
Ficus elastica (Assam rubber plant)
Ficus benjamina (Java fig)
Hedera helix (ivy)
Clivia miniata
Camellia sinensis (tea-plant)
Prunus laurocerasus (cherry laurel)
Nerium oleander (oleander)
Olea europaea (olive-tree)
Citrus aurantium (bitter orange)
Citrus limon (lemon)
Euonymus japonicus (evergreen e.)
Liriodendron tulipifera (tulip-poplar)
Juglans regia (English walnut)
Ginkgo biloba (ginkgo)
Cydonia oblongata (quince)
Ligustrum cf. vulgare (prim)
Forsythia suspensa (golden bells)
Maianthemum bifolium (false lilly-of-the
valley)
Fruit CM
Lycopersicon esculentum (tomato)
Capsicum annuum (bell-pepper)
Malus domestica (apple)
Pw 1011
(m s1 )
DSA 1019
(m2 s1 )
mCM
(g cm2 )
1.7
4.3
6.6
9.4
13.0
5.70
15.7
10.8
13.3
52.2
12.6
12.8
47.0
35.8
42.0
45.8
52.2
62.9
43.4
38.7
111.0
12.3
25.8
8.9
25.1
29.3
2.7
36.0
8.1
63.0
55.7
59.8
38.3
77.9
70.0
74.6
99.8
100.5
34.1
42.7
80.2
152.3
359
808
335
510
306
337
1,020
252
333
664
661
369
1,373
403
233
125
342
191
227
955
68
62.2
134.5
207.0
121.0
222.3
290.5
1,554
2,162
3,217
mWAX
(g cm2 )
122
242
54
87
64
114
285
11.8
83
113
88
32
381
64
72
27
40
51
39
137
36
54
96
1,317
the measured value of 1.3 1010 m s1 . Since the y-intercept lowers calculated
permeance, it is not related to water permeation in a hypothetical parallel aqueous
pathway. These data are consistent with model III A.
The good correlation between Pw of CM and DSA in reconstituted wax is
amazing, because permeance is a composite quantity and depends on mobility
and solubility of water in wax and thickness of the CM. According to (2.18),
Pw = Dw Kww /, while DSA is a pure mobility parameter. In Chap. 2 we defined
as thickness of a membrane, while in reality the lengths of the diffusion path can
be much larger due to the tortuosity factor . Thus, linearity implies that Kww / is
equal to the slope of 6.6 107 m1 , which is the same with all species. However,
Kww and are likely to vary independently among species, and it is not very likely
that they are the same for all species. High permeance could be the consequence
of large Kww or a short diffusion path, that is, thin CM and low . Cuticular wax
is composed of crystalline and amorphous fractions (Reynhardt and Riederer 1991;
1994), and both sorption and diffusion of water should exclusively take place in
100
4 Water Permeability
2.5e-9
Pw = 6.63 x 107 (1/m) DSA - 4.49 x 1011 (m/ s )(r2 = 0.90)
Pw (m/s)
2.0e-9
1.5e-9
1.0e-9
5.0e-10
0.0
0.0
Fig. 4.15 Water permeances Pw of isolated CM plotted as a function of DSA (diffusion coefficient
of stearic acid) in reconstituted cuticular waxes of 24 plant species. (Data from Table 4.7)
the amorphous phase (Riederer and Schreiber 1995), whereas the crystalline phase
is not accessible. With an increasing amorphous fraction in the wax, sorption is
expected to increase. Since diffusion of water and stearic acid takes place in the
same amorphous wax phase, path length of diffusion might increase as well, and
thus the ratio of Kww / could be very similar for all investigated species. This
hypothesis could help to explain why Pw is correlated with DSA .
Diffusion coefficients for lipophilic solutes in CM and wax (Sect. 6.3.2.3: Variability of Solute Mobility with Size of Solutes and Sect. 6.5.2) differ among species
because tortuosity of the diffusion path differs. This implies that differences in DSA
(Table 4.7) are caused by differences in length of the diffusion paths ( ). Since
water in CM of all species diffuses in the waxy pathway, the path lengths of stearic
acid and water should be the same for both. Hence, partition coefficients (Kww ) may
vary little among species, and since Kww / is constant (6.6 107 m1 ) differences
in Pw should mainly be due to differences in lengths of the diffusion path.
Data on sorption and diffusion of water in cuticular waxes could help us to better
understand the waxy barrier. There are data on water concentration in polyethylene and liquid hydrocarbons. Water concentration in polyethylene at 25 C and
100% humidity is about 7 104 g g1 (Table 4.1). According to Schatzberg (1965)
the solubility of water in a liquid alkane (hexamethyl tetracosane) at 25 C is
5.5 105 g g1 or 55 mgkg1 . Sorption of water in isolated and reconstituted solid
cuticular waxes has not been studied, for good reasons as the following example will show. Starting with the assumption that the above paraffin/water partition
coefficient (5.5 105 g g1 ) is valid for cuticular waxes, we can estimate the concentration of tritiated water (THO) needed to detect THO in a wax sample of 1 mg.
For a reasonable counting statistic, we aim at 100 Bqmg1 wax, and we can calculate the concentration of THO in water from the definition of K (2.12). The ratio
101
of the radioactivity in the wax (100 Bqmg1 ) and the partition coefficient Kww
(5.5 105 ) is 1.82 106 Bq mg1 or 1.82 109 Bq g1 water. Transfer from the
vapour phase into the scintillation cocktail requires special equipment to prevent
desorption of water from the thin wax film. Since wax platelets cannot be handled
without support (for instance aluminium foil), water sorption must be measured with
different wax amounts, to be able to correct for sorption on the support.
0.010
benzoic acid (slope 244)
0.008
0.006
salicylic acid (slope 83)
0.004
0.002
0.000
0
1e-5
2e-5
3e-5
4e-5
5e-5
102
4 Water Permeability
(4.19)
The y-intercept of the regression equation (4.19) is 1.32, that is, Pw is 4.79
102 m s1 (i.e., 101.32) when PBA = 1.0. As the slope is 0.86, Pw increases only
by a factor of 7.24 (i.e., 100.86) when PBA increases tenfold. When permeance is
Citrus limon
8.0
Lycopersicon
Juglans
log P w (m/ s)
8.5
Prunus
Pyrus
Ginkgo
Liriodendron
9.0
Philodendron
Monstera
Euonymus
9.5
Camellia
10.0
Hedera
10.0
9.5
log P
9.0
14C-benzoic
8.5
8.0
acid (m/s )
Fig. 4.17 Correlation of water permeance (log Pw ) with permeance of benzoic acid (log PBA )
across isolated cuticular membranes of 12 species. (Data from Niederl et al. 1998)
2.4
CM control
CM methylated
MX control
MX methylated
2.0
103
Effect of humidity
1.6
1.2
0.8
1.6
1.4
1.2
1.0
10
20
30
40
50
60
70
80
90
100
equal to 9.72 1010 m s1 , Pw and PBA are numerically equal. If PBA is lower, then
Pw > PBA , and if PBA is larger than 9.721010 m s1 , Pw < PBA . For example, when
PBA = 108 m s1 , Pw is 6.3 109 m s1 . With species having PBA of 1010 m s1 ,
the calculated Pw is a little higher (1.2 1010 m s1 ). This could be taken as evidence that in CM from species having a low permeance for benzoic acid, some water
diffused in aqueous pores, while in CM having a high BA permeance, all or most
water diffuses in the waxy path, and the contribution of a parallel aqueous paths
goes unnoticed. In view of the large error bars seen in Fig. 4.17, this conclusion
may very well be wrong.
Both permeances are related to D, K and , and this can be written as
log Pw
log(Dw Kww )/
= 0.86.
=
log PBA
log(DBA KBA )/
(4.20)
If water and benzoic acid use the same waxy pathway, is the same and cancels. Kww
for benzoic acid is around 20 for waxes of P. laurocerasus, G. biloba and J. regia.
The respective DBA values in waxes of these species are 3.5 1017, 4.4 1017
and 5.6 1017 m2 s1 . This is the sequence seen on the regression line in Fig. 4.17.
Dw Kww is not known for these three species, but their products should be smaller
by a factor of 7.2 (100.86). The waxwater partition coefficient for water is much
smaller than for benzoic acid, which implies that D for water must be considerably
larger than for benzoic acid.
104
4 Water Permeability
105
60
50
40
30
AgCl
precipitation
20
10
0
0
10
15
24
28
32
Time (h)
Fig. 4.19 Water permeability of an isolated Populus canescens CM before and after counter diffusion of NaCl and AgNO3 . The slope of the linear transpiration kinetic is significantly decreased by
64% after the formation of AgCl precipitations in the CM. Data were taken from Schreiber et al.
(2006)
106
4 Water Permeability
Table 4.8 Permeances (m s1 ) of cuticular membranes isolated from 15 different species measured
AgCl
before Pwtotal and after Pw
the formation of AgCl precipitates. Results are means of at least
aqueous
AgCl
is the difference between Pwtotal and Pw . (Data from Schreiber et al. 2006)
12 CM. Pw
Species
Pwtotal 1010
(m s1 )
AgCl
Pw
1010
(m s1 )
aqueous
Pw
1010
1
(m s )
aqueous
Pw
Pwtotal
Leaf CM
Nerium oleander
Hedera helix
Stephanotis floribunda
Forsythia intermedia
Ligustrum vulgare
Vinca major
Prunus laurocerasus
Citrus aurantium
Juglans regia
Syringia vulgaris
Pyrus communis
Populus canescens
0.71
1.49
4.71
1.97
4.03
1.20
1.10
1.87
4.51
3.51
8.30
26.8
0.73
1.46
4.01
1.58
3.19
0.95
0.76
1.23
2.96
2.06
3.92
9.64
0
0
0.70
0.39
0.84
0.25
0.34
0.64
1.55
1.09
4.38
17.16
0
0
0.15
0.20
0.21
0.21
0.31
0.34
0.34
0.41
0.53
0.64
Fruit CM
Malus domestica
Lycopersicon esculent..
Prunus domestica
3.20
24.8
33.2
2.17
15.7
12.2
1.03
9.10
21.0
0.32
0.37
0.63
107
108
4 Water Permeability
Table 4.9 Water permeance (Pwv ) and diffusion coefficients (Dw ) of cuticular membranes at 25 C
Species
te (s)
(m)
Pwv (m s1 )
Dw (m2 s1 )
Cw (g kg1 )
Cw (g kg1 )a
Schefflera L.
Clivia L.
Hedera L.
Nerium L.
Ficus L.
Citrus L.
Pyrus L.
Solanum F.
Capsicum F.
Lycopersicon F.
930
770
933
960
512
264
550
640
361
215
2.96
6.50
4.33
12.81
5.68
2.87
3.12
6.47
8.03
8.00
8.19 107
1.14 106
2.66 106
3.25 106
4.25 106
1.20 105
1.22 105
2.23 105
9.28 105
1.42 104
1.57 1015
9.14 1015
3.35 1015
2.84 1014
1.05 1014
5.20 1015
2.95 1015
1.08 1014
2.98 1014
4.96 1014
33
17
73
34
48
139
270
244
523
477
24
30
63
43
38
43
D was calculated from the hold-up time and the total thickness () of CM; Cw is sorption of water
at 25 C and 100% humidity calculated from P /D [(3.17) and (3.20)] using the data by Becker
et al. (1986). L is leaf CM and F is fruit CM. (Data from Becker et al. 1986)
a Data taken from Chamel et al. (1991) derived from water vapour sorption
Permeance varied by a factor of 173, and ranged from 8.19 107 (Schefflera
leaf) to 1.42 104 m s1 (tomato fruit). Diffusion coefficients varied by a factor of
only 32, and ranged from 1.57 1015 (Schefflera) to 4.96 1014 m2 s1 (tomato
fruit). According to theory [Chap. 2; (2.18)] one might conclude that variations in
membrane thickness and partition coefficient caused these differences. The Dw values are much lower than those for synthetic polymers, PVA being the only exception
(Table 4.1). With some CM (Nerium and Ficus), water sorption (Cw ) derived from
the Pwv /Dw ratio is low and similar to sorption in CM when determined gravimetrically (Table 4.9, last column). With the other CM, water concentration calculated
from Pwv /Dw is unreasonably high, and much larger than that determined by a
sorption experiment. This indicates structural heterogeneity of these membranes.
When calculating Dw from hold-up time, the thickness of the CM enters into consideration. Becker et al. (1986) used the weight average thickness, while the waxy
limiting skin or the cuticle proper is the limiting barrier both in water and solute
diffusion (Sects. 4.6 and 6.5). The thickness of the limiting skin in CM of various
plant species is not known, but plausible estimates are 100500 nm (Sect. 1.4). In
calculating Dw from (2.5), thickness of the limiting barrier enters as 2 , and using a
thickness less than total thickness of the CM would result in lower diffusion coefficients than those in Table 4.9. In Sect. 6.5.2 we estimate the diffusion coefficient
of water in cuticular wax as 1.2 1016 m2 s1 . This is about a factor of 10 lower
than Dw values in leaf CM estimated from the hold-up time (Table 4.9). With Citrus
CM, a Dw of 1.2 1016 m2 s1 would have been obtained with equal to 0.44 m.
This amounts to 15% of the total thickness of the CM and appears plausible. This
neglects the fact that the waxy diffusion path of water is tortuous, but in calculating
Dw for synthetic polymers membrane thickness () is used (Table 4.1) and tortuosity
is also disregarded.
We can further test these cuticles for homogeneity by plotting Pwv vs 1/ and Dw
vs 1/6 hold-up time. In homogenous membranes, these plots should be linear. The
109
60
80
100
120
140
160
6e-14
1.4e-4
1.2e-4
Lycopersicon F
5e-14
Lycopersicon F
4e-14
1.0e-4
Capsicum F
3e-14
Capsicum F
8.0e-5
6.0e-5
2e-14
2.0e-5
Citrus
0.0
Clivia
0.10
Solanum F
Ficus
4.0e-5
0.15
Solanum F
Pyrus
Ficus
Hedera
0.20
0.25
Clivia
Pyrus
1e-14
Hedera
Citrus
Schefflera
20
1.6e-4
Schefflera
0.30
0.35
0.40
1/Thickness (1/m)
Fig. 4.20 Test for homogeneity of cuticular membranes. Pwv was plotted vs 1/ (circles), and Dw
was plotted vs 1/6 te (squares). (Data from Becker et al. 1986)
plot Pwv vs 1/ should have a slope of Dw Kwv (2.18), while a plot Dw vs 1/6 te
should have a slope equal to 2 (2.5). These plots are shown in Fig. 4.20.
The two plots are not linear, and there is considerable scatter. Pwv is highest with
tomato and pepper fruit CM, and no dependence on 1/ is detectable. Similarly,
no dependence of Dw on 1/6 te can be seen. With leaf CM and Solanum fruit
CM, data are clustered and no dependence of Pwv on thickness or Dw on hold-up
time is detectable. It is obvious that no simple relationship between Pwv and Dw on
total thickness of CM exists. Such a dependence can not really be expected, because
extracting small amounts of waxes increases permeance by orders of magnitude, and
the weight fraction of waxes in cuticles is by no means constant (Table 4.6). Furthermore, even MX membranes are not homogeneous (Sect. 1.4), and CM contain
waxes in addition to polar polymers and cutin. Polar polymers form a separate phase
(Sects. 4.5 and 4.6.2, subsection: Effect of Partial Vapour Pressure (Humidity) on
Permeability of CM), while waxes occur in cutin and on the surface of the cuticles
(Sect. 1.3).
110
4 Water Permeability
measured (for details see Sect. 6.5). Plotting the logarithm as a function of the
molar volume, good linearity was obtained for the wax of the three species Prunus
laurocerasus, Ginko biloba and Juglans regia (Kirsch et al. 1997). Thus, with the
molar volume known, Dw in cuticular waxes of any of other compound can be
estimated. Using the molar volume of water (18 cm3 mol1 ) and the equations in
Table 6.10, diffusion coefficients of 1.19 1016 m2 s1 , 1.60 1016 m2 s1 and
1.06 1016 m2 s1 can be calculated for the three species Prunus laurocerasus,
Ginko biloba and Juglans regia respectively. These are fairly low values, and compared to Dw obtained from extrapolated hold-up times (Table 4.9) they are by 12
orders of magnitude lower. However, Dw values in Table 4.9 were calculated using
the thickness of the CM and not the thickness of the wax layer. Assuming that cuticular wax forms the transport-limiting barrier of the CM and not the thickness of
the CM itself, Dw of most of the species shown in Table 4.9 can be recalculated
(Table 4.10) if wax coverage of the CM is known. The thickness of the wax layer is
calculated dividing the wax amount per area by wax density (0.9 g cm3 ).
Depending on the wax amounts used for calculating the thickness of the wax
layer, this estimation of diffusion coefficients results in values for leaf CM ranging from 0.11 1016 (Citrus) to 56.6 1016 (Nerium). Dw calculated for Nerium
leaf CM and fruit CM from tomato and pepper clearly differ from the other CM
of the data set. The reasons are not known. Most of the estimated Dw are around
1016 m2 s1 , and this agrees fairly well with the Dw estimated from diffusion of
organic non-electrolytes in reconstituted cuticular waxes. If Dw calculated for CM is
much higher than Dw values in reconstituted wax, some water flow in aqueous pores
Table 4.10 Estimated diffusion coefficients (Dw ) of water in cuticular waxes calculated from
extrapolated hold-up times of water permeation across the CM. Thickness of the wax layers were
calculated from amounts of wax per unit area (coverage)
Species
te (s)a
Wax coverage
(g cm2 )
(m)d
Dw in waxe
(m2 s1 )e
Leaf CM
Clivia miniata
Hedera helix
Nerium oleander
Ficus elastica
Citrus aurantium
Pyrus communis
770
933
960
512
264
550
106b 113c
64c 85b
381c 514b
87c 114b
12b 32c
133b
1.171.25
0.710.94
4.235.71
0.971.26
0.130.35
1.44
Fruit CM
Solanum melongena
Capsicum annuum
Lycopersicon esculentum
640
361
215
48b
96c 197b
54c 152b
0.53
1.062.18
0.601.69
0.73 1016
5.18 1016 21.9 1016
2.79 1016 22.1 1016
111
could be responsible for the difference. Unfortunately, in the two sets of experiments
different species were used. Nevertheless, it is interesting that these two independent approaches yield estimates for Dw of the same order of magnitude. It is an
advantage of these approaches that solubility of water in cuticular wax (wax/water
partition coefficients) are not needed for estimating Dw . Unfortunately, assumptions
concerning the thickness of the limiting skin must be made, and these assumptions
enter as the square.
112
4 Water Permeability
Table 4.11 Water vapour transmission rate (WVTR) of cellophane membranes coated with molten
paraffin wax and cooled at various temperatures either in water or air. WVTR rates measured at
23 C and 50% humidity
Cooling T ( C)
1.7 (water)
7.2 (water)
12.8 (water)
18.3 (water)
23.0 (air)
Wax
load
(g m2 )
of
wax
(m)
WVTR
(first day)
(g m2 day1 )
WVTR
(after 45 days)
(g m2 day1 )
Pwv (m s1 )
11.7
10.9
9.6
9.8
10.7
12.9
12.0
10.6
10.8
11.8
0.15
0.12
0.05
0.07
0.09
0.08
0.03
0.03
0.02
0.02
8.9 108
3.3 108
3.3 108
2.2 108
2.2 108
113
By microscopic inspection Fox (1958) detected significant changes in the structure of the wax films. After waxing, paraffin films exhibited numerous cracks.
During storage at 35 C these cracks and fissures healed, and grain size of the crystals increased. Apparently, the paraffin recrystallised. When storage at 35C was
long enough, the crystals became so large and compacted that the wax film began
to resemble one large crystal. Furthermore, very thin layers of recrystallised wax
formed on the top surface of the film. X-ray diffraction studies showed that the aircooled films contained crystals predominantly oriented with their c-axes (long axes)
perpendicular to the cellophane sheet. Such wax crystals oriented parallel to the
sheet gave a low WVTR. Formation of such plates was aided by slow air cooling, or
by recrystallisation and reorientation of the water-cooled films during storage. Wax
crystals in cuticles are also oriented parallel to the surface of the CM, and c-axes are
perpendicular (Sect. 1.4).
Fox (1958) concluded that vapour transmission occurred through defects between
crystals and that a high WVTR was the result of more numerous defects, while the
crystals themselves were impermeable to water vapour. However, paraffinic waxes
are complex mixtures of alkanes varying in chain lengths. Le Roux and Loubser
(1980) estimated for paraffinic wax having a melting point of 59 C that 83% of
the molecules were incorporated into crystals at room temperature, 16% formed a
rigid amorphous phase and 1% was liquid oil (1%). The technical paraffin used by
Fox most likely contained amorphous wax which is permeable to water, and water
vapour penetrated across defects and in amorphous wax. It is unfortunate that wax
coverage was not varied systematically. Thus, we do not know if number and healing of defects depend on film thickness. If it is assumed that this is not the case,
Pwv should be of the order of 2.6 1013 m2 s1 , which is two orders of magnitude smaller than Pwv for polyethylene (Table 4.1) or parafilm. Since crystals are
impermeable, a very thin wax layer should suffice to build an excellent water barrier.
We can calculate the thickness of a paraffinic film on the CM (2.4) necessary
to obtain the permeances measured (Table 4.9). For instance, with Schefflera a wax
layer of 317 nm would suffice, and with Hedera 98 nm, while with Pyrus and Citrus
a wax layer of 22 nm thick would be enough if we disregard the contribution of the
MX to Pwv . With Lycopersicon a wax layer of only 2 nm would be necessary, but
with such a thick CM the contribution of cutin to Pwv cannot be neglected. Since
a wax layer of 11 nm thickness has a weight of 1 g cm2 , the coverages of wax
shown in some of the previous tables (Tables 1.1, 4.6, 4.7 and 4.11) are far in excess
of the amount needed for a wax barrier on top of the cuticle.
In these calculations, we have assumed that cuticular waxes have water permeability and structure similar to that of the paraffin wax used by Fox (1958).
However, this is not the case since cuticular wax is characterised by functional
groups (Sect. 1.3.2), and this must be considered in models of the cuticular transpiration barrier. The methods of Fox (1958) should also work with isolated cuticular
waxes, and it is amazing that experiments using this approach have not yet been
carried out. Permeability across cuticular wax films could be measured. Since cellophane is isotropic, molecular orientation and degree of crystallinity of these wax
films can be investigated using polarised light and X-ray diffraction.
114
4 Water Permeability
= 0.154 nC cos35 ,
(4.21)
107
106
extrapolated values
105
104
103
Permeance (m/s)
log resistance (s / m)
where nC is the number of carbon atoms. A monolayer with 40 carbon atoms has a
thickness of 5 nm, and Pwv would be 1.22 106 m s1 . With nC equal to 34, which
corresponds to the mean chain length of ivy wax (Fig. 4.14), thickness would be
4.3 nm and Pwv would be 9.77106 m s1 (Fig. 4.21). The monolayers observed by
Koch et al. (2004) had a thickness of 35 nm. Permeances Pwv measured for ivy CM
in different studies range from 2.66 106 m s1 (Table 4.10) to 4.3 106 m s1
(Table 4.6) or 1.55105 m s1 (Table 4.7). Comparing these estimated permeances
of monolayers with measured permeances of ivy, we see that a single monolayer
could in theory account for water permeability of the CM.
experimental values
2
102
10
15
20
25
30
35
Number of carbon atoms
40
45
Fig. 4.21 Resistances and permeances (Pwv ) of monolayers of fatty alcohols as a function of
number of carbon number. (Data taken from LaMer et al. 1964)
115
Fig. 4.22 Transport chamber used for measuring the flux of 3 H-labelled water from the donor
across stomatous cuticles into the receiver. In the receiver was a water-saturated filter paper
(depicted in dark blue) absorbing 3 H-labelled water which diffused across the CM. The revolving rod allows sampling of the receiver without changing the atmosphere in the receiver. (Modified
from Santrucek et al. 2004)
The fact that resistance of fatty alcohols is a function of log nC could explain why
evolution selected very long chain wax monomers for building a water barrier. At
ambient temperatures these monomers are in the solid state, and very small amounts
of 12 g cm2 suffice. We are again confronted with the question why wax coverage is much higher with most plants (Tables 1.1, 4.6, 4.7 and 4.11). Leaves can be
subjected to considerable abiotic (e.g., wind, rain, ice and storm) and biotic forces
(e.g., insects, fungi and bacteria). This should lead to a continuous disturbance of
a highly ordered wax structures on the leaf surface, and losses of wax might even
occur during the season. A fast and efficient compensation of this disturbance, keeping the cuticular transport barrier intact, might require fairly high amounts of wax
116
4 Water Permeability
in the CM and on the surface of the CM. The onion bulb scale CM is well-protected
within the bulb, and abrasion and wear are not likely to occur. Hence they have and
need only minimum amounts of wax.
These model calculations show convincingly that waxes which would form
mono- or bilayers on the surface of cutin, as is suggested by AFM investigations
(Koch et al. 2004), could be very effective as water barriers. These waxy barriers can be very thin and still have a low permeance. A simple polymeric membrane
similar to polyethylene or parafilm would have to be much thicker, and energetically
this would be much more costly.
Table 4.12 Diffusion coefficients in wax (Dw ), permeances (Pw ) of water across the CM, and
thickness of the wax layers in Ginkgo biloba, Juglans regia and Prunus laurocerasus. Wax/water
partition coefficients Kww are calculated by multiplying Kww / by . Thickness of the wax layer
was calculated dividing Kww by Kww /
(m2 s1 )a
Dw
Pw (m s1 )b
(nm) calculated from wax amountsc
Pw /Dw = Kww /
Kww calculatedd
(nm) calculated for Kww = 0.01
(nm) calculated for Kww = 0.04
a Calculated
Ginkgo
Juglans
Prunus
1.60 1016
1.06 1016
4.3 1010
6.3 1010
433
2.69 106
1.16
3.7
14.9
566
5.94 106
3.36
1.7
6.7
1.19 1016
1.33 1010
922
1.11 106
1.03
9.0
36.1
117
from Kww /. These calculated partition coefficients vary between 1 and 3. This is
definitively too high, since this would imply that solubility of water in lipophilic
wax is the same as in the polar water phase.
Alternatively, Kww can be assumed and calculated. Partition coefficients of
water in different lipophilic phases and water vary depending on the chemistry of
the lipid phase. Solubility of water at 25 C in C16 hexadecane and in a branched
liquid C30 hydrocarbon (hexamethyl tetracosane = squalene) is 4.2 105 and
4.4 105 g cm3 (Schatzberg 1965) respectively. For squalene this amounts to
5.5 105 g water per g hydrocarbon, and thus the partition coefficient Kww is
5.5 105. Much higher partition coefficients of 0.0014, 0.013 and 0.04 have been
published for olive oil, ether and octanol respectively (Wolosin and Ginsburg 1975).
Even higher values of 0.06 (Potts and Francoeur 1991) and 0.162 (Schwindt et al.
1998) were estimated for stratum corneum, the transport-limiting lipid barrier of
the mammalian skin which also contains squalene. Cuticular waxes contain small
but significant amounts of polar functional groups which are expected to raise the
partition coefficients somewhat. On the other hand, a large fraction of the waxes is
in the crystalline state and probably sorbs no water in crystals and little on crystal
surfaces. If these factors cancel, Kww for cuticular waxes is likely to be similar to
that for the liquid paraffin. In Table 4.1 Kwv values for solid polymers are given,
and from these Kw can be obtained by multiplying them with 43,394 (3.11), (3.16),
(3.17). This calculation gives Kw for polyethylene and polyethylene terephthalate
of 4.5 104 and 0.011 respectively. These Kw are higher by factors about 10200
than that for the liquid paraffin. For model calculations they may be accepted to
mimic water contents of cuticular waxes.
Water sorption in cuticular waxes may also be estimated based on concentrations
of polar functional groups. If we assume that polar functional groups amount to 4%
of the wax and each oxygen atom would bind one water molecule, the wax/water
partition coefficient for water would be 0.041. If only 10% would sorb a water
molecule due to intermolecular hydrogen bonding, the partition coefficient would be
0.0041. Working with partition coefficients of 0.01 and 0.04 for model calculations
seems reasonable. Using (2.18), the thickness of the wax barrier can be estimated
(Table 4.12). Depending on magnitude of Kww , the required thickness of the waxy
barrier ranges from 1.7 to 9 nm (Kww = 0.01) or 6.7 to 36.1 nm (Kww = 0.04). Since
1 g wax per cm2 gives a wax film having 11 nm thickness, the required thickness
of the waxy barriers ranges from about 0.2 to 4 g cm2 .
Wax coverage of most plant species is much higher (Tables 4.7 and 4.11) and the
question is why? In many cuticles substantial amounts of waxes occur as embedded
waxes (Fig. 1.6), which contribute little to barrier properties (Sects. 6.3 and 6.4).
The function of these useless and hidden waxes is obscure. Not all CM have such
high wax coverage as shown in Table 4.7. Allium epidermis (Table 4.6) has a wax
coverage of only 1 g cm2 , which results in a wax layer of only 11 nm. A similar
low wax coverage of about 1.6 g cm2 was reported for Arabidopsis leaves (Jenks
et al. 1996). According to our model calculations (Fig. 4.13), a functional transpiration barrier can be built in Allium and Arabidopsis leaves. The average mean
chain length of the linear long-chain aliphatic molecules in Arabidopsis leaf wax is
118
4 Water Permeability
about 31 carbon atoms (Jenks et al. 1996), and using (4.21) the average thickness
of a monolayer would be 4.0 nm. With a wax amount of 1.6 g cm2 at most, 45
monomolecular layers of wax molecules could be established.
(4.23)
(4.24)
This experimental approach is based on the fact that the diffusion coefficient of
water in helium DwHe is 3.6 times higher than the diffusion coefficient of water in
nitrogen DwN (Cussler 1984). Thus, using membranes with pores (e.g., stomatous
cuticles) higher fluxes will be measured in a helium atmosphere compared to a nitrogen atmosphere (4.25). However, no differences occur with a non-porous membrane
(e.g., astomatous cuticle) and fluxes in both gases (helium and nitrogen) will be the
same
FstomaHe
DwHe
=
= 3.6.
(4.25)
FstomaN
DwN
The ratio DwHe /DwN will be called d, and y is d/(d 1). Substituting FstomaHe in
(4.23) by (4.25) and combining (4.23) and (4.24), the following solution is obtained
describing the flux of water across the solid phase of a stomatous cuticle
Fcuticle = y FtotalN (y 1) FtotalHe.
(4.26)
Using this approach and (4.26) with stomatous and astomatous CM isolated from
ivy leaves, it was found that Pwv of the astomatous cuticle was 3.12 106 m s1 ,
whereas Pwv of the stomatous cuticle was 3.57 105 m s1 (Santrucek et al. 2004).
The ratio of both permeances is 11.4. This indicates that water permeability of the
abaxial CM was 11-fold higher than water permeability of theadaxial CM. So far,
this new approach was used only with ivy CM, and additional studies with different
plant species are necessary. We expect this ratio to be similar in other plant species.
Much higher permeability to ions of cuticles from abaxial leaf surfaces compared to
adaxial surfaces has also been observed (Chap. 5).
120
4 Water Permeability
6
5
4
3
2
1
0
LD old
CM old
LD young
CM young
parafilm
Fig. 4.23 Permeance Pw measured with old and young Prunus laurocerasus leaf disks (LD) and
isolated cuticles (CM), using 3 H-labelled water. (Data from Schreiber et al. 2001)
of several months old leaves. This indicates that cuticular permeability increases
slightly when leaves age. A similar observation was also reported for ivy (Fig. 4.14e;
Hauke and Schreiber 1998).
Problems
121
Our present knowledge does not permit us to decide which model best describes
water permeability of all cuticles. In fact, there are indications that different models
describe permeability of cuticles of different species adapted to different habitats.
We have presented a number of hypotheses regarding the shape of cuticular barriers.
The current data base is insufficient to rigorously test these hypotheses. Additional
data are need to test these hypotheses. For instance, sorption and diffusion of water
in cuticular waxes should be measured directly, and permeation of water across
wax films using the approach of Fox (1958) should be carried out. The observation
that monolayers and bilayers can spontaneously and rapidly form on the smooth
stripped cuticle at the plant/atmosphere interface (Koch et al. 2004) is exciting, and
must be analysed in more detail. Species should be used for which data on water
permeability are available or can be measured accurately.
Characterisation of the aqueous pathway during leaf development of many more
plant species is badly needed. Pore size must be estimated, and the contribution of
water flux across pores to total water permeability should be estimated using the
approach of blocking polar aqueous pores. More information on the structure and
spatial arrangement of the polar polymers in the MX should be collected. This can
be obtained using immunological techniques and high-resolution microscopy. With
these data available, our models could be refined and it would be possible to test
which experimental data can be fitted to these models.
It is likely that different species follow very different strategies in adapting to
their specific environmental conditions. There is no reason why the cuticular transpiration barrier should be the same with all species. Species with thin cuticles and
very low wax amounts, like Allium or Arabidopsis, might in fact have to rely on a
fragile monolayer deposited on top of the MX. Species with thick cuticles and much
higher wax loads, like Hedera helix or Prunus laurocerasus, might follow the different strategy of impregnating and covering the MX with large wax amounts, with
some polar pores still contributing to the water permeability.
Problems
1. What is the permeance at 25 C of a polyethylene bag having a thickness of
20 m and Pwv of 4 1011 m2 s1 ? How much water (g) penetrates across m2
per day if the bag is filled with water and stored at 50% humidity?
2. Using the data given in Table 4.1, calculate the partition coefficients Kwv and
Kw for ethyl cellulose. What is the concentration of water (Cw ) in the polymer
(g water/cm3 polymer) at 20% humidity?
3. (a) How many meq kg1 of carboxyl groups are ionised in apricot leaf MX at
pH 3.4, which is the isoelectric point? (b) What percentage is this compared to
total exchange capacity at pH 8?
4. Which condition must be fulfilled for all carboxyl groups of cutin acids to
ionise?
122
4 Water Permeability
Solutions
1. P is 2 106 m s1 , and J is 1.99 g m2 per day.
2. Kwv is 1,000, while Kw is 0.023. Cw at 100% humidity is 4.6 mgcm3 .
3. (a) At the isoelectric point, positive and negative net charges are equal. Hence,
19 meqkg1 carboxyl groups must be ionised to balance the ionised basic
groups. (b) 6.55%.
4. The pH in the epidermal wall must be 8.0, which is two pH units higher than
the pKa of 6.
Solutions
123
5. Ca2+ , because selectivity for divalent cations is very high. Mg2+ , Cu2+ and
Fe3+ may also be exchanged in trace amounts.
6. Water concentration of cuticles in Ca2+ form is lower, because the concentration
of counter ions is only half that of Na+ , and Ca2+ ions bind much stronger to
COO groups. This reduces osmotic pressure and electrostatic free energy.
7. I would measure Pdiffusion and Pviscous and Pviscous /Pdiffusion > 2. Penetration of
hydrated ions across an intact CM also indicates the presence of aqueous pores.
8. Because aqueous pores arise by swelling in presence of water, and specimens
embedded in plastic resins contain no water.
9. The membrane is impermeable to the osmotic solute.
10. Using (4.16) we obtain D = 1.21 1010 m2 s1 .
11. Three different models with three different options how waxes can be incorporated in the polymer matrix have been suggested. Model III A assumes that a
thin layer of wax is deposited on the outer surface of the MX and forms the limiting barrier. Model III B assumes that all waxes are embedded in cutin and on
the outer surface of the MX, leaving all aqueous pores unaffected. Model III C
is a mixture of the two other models, assuming that the superficial wax layer
covers a fraction but not all of the aqueous pores.
12. So far no convincing correlations between cuticular transpiration and thickness
of the CM, thickness of the wax layer, and chemical composition of waxes have
been detected.
13. Using (4.18) a permeance Pw of 1.88 109 m s1 can be estimated.
14. Using (4.19) a permeance Pw of 1.55 1010 m s1 can be estimated for water.
15. This problem can be solved using (2.5). Using the thickness of the cuticle which
is 3 m, a D of 1.15 1015 m2 s1 is calculated. Assuming that the transportlimiting barrier of the cuticle is formed by the layer of cuticular wax, which
corresponds to about one tenth of the thickness of the cuticle, a D of 1.15
1017 m2 s1 is obtained.
16. Using (4.20) it can be calculated that a monolayer composed primarily of C28
wax molecules has a thickness of 3.5 nm. A wax layer having 1.0 g cm2 has a
thickness of 11 nm. Thus, not more than three monolayers could be formed.
Chapter 5
In Chap. 4, we characterised the pathways for water in cuticles. Cutin is the major
constituent of the polymer matrix. It is lipophilic and constitutes the lipophilic pathway. The polymer matrix contains polar polymers which sorb water and swell. This
hydration water is continuous, and gives rise to aqueous pores which traverse the
cuticle (Sect. 4.5). Waxes occur both sorbed in cutin and as epicuticular wax on the
surface of the polymer matrix. Waxes associated with cutin greatly reduce permeability of the lipophilic pathway, and for this reason we have also used the term
waxy pathway. Permeance of the waxy pathway is proportional to the partition
coefficient that is to solubility of solutes in cutin and waxes. Polar solutes have very
low partition coefficients, and for this reason permeance of the waxy pathway is
very low but finite (Sect. 4.6).
With ionic solutes the situation differs, because under physiological conditions
ionic groups are surrounded by water molecules. This hydration water is bound
very strongly by iondipole interactions which renders them essentially insoluble
in oils, fats, cutin and waxes. For this reason, hydrated ions cannot access the waxy
pathway. Penetration of inorganic and organic ions is limited to the aqueous pathway
(Schnherr 2006). Negative and positive ions must penetrate in equal numbers to
maintain electroneutrality. Each cation must be accompanied by equivalent amounts
of anions. For instance, Ca2+ must be accompanied by two Cl ions. This is true
as long there is no drop of electric potential across the cuticle, which is always
the case under natural conditions. Thus, the appropriate term is salt or electrolyte
permeability, not ion permeability.
Whenever salt or electrolyte penetration is observed in the field or in the laboratory, this is definitive evidence for the presence of aqueous pores in the cuticles of
leaves and stems investigated. Strugger (1939) was one of the first to demonstrate
presence of aqueous pores in plant cuticles. Agriculturalists and horticulturalists
interested in foliar nutrition have studied salt permeation into leaves or isolated
CM (cf. Yamada et al. 1964; McFairlane and Berry 1974; Tuckey 1970; Schnherr 2000, 2001; Schlegel and Schnherr 2002; Schreiber 2005). Many agricultural
chemicals are ionic (bentazon, glyphosate, paraquat) and penetrate into the foliage
only when aqueous pores occur in cuticles of these leaves. Penetration of glyphosate
125
126
127
In Fig. 5.1a the anticlinal ledges are in focus, and fluorescence can be seen clearly.
Figure 5.1b shows the same specimen with focus on cuticular ledges. In all three
species, glandular trichomes also fluoresced intensely (cf. Fig. 5.1f).
Schnherr (1969) and Schlegel et al. (2005) used silver nitrate as an ionic tracer
for localising aqueous pores. Drops of silver nitrate solutions were placed for 1 h
on the surface of Phaseolus vulgaris and Vicia faba leaves, and treated areas of epidermis were viewed with the bright field microscope. Black silver precipitates were
observed in anticlinal cell walls, in trichomes and in cuticular ledges (Fig. 5.2). This
indicates again that these were sites of preferential penetration of AgNO3 . Using
energy dispersive X-ray analysis (EDX) and Vicia leaves, it was shown that these
precipitates were AgCl. This is strong evidence that silver nitrate penetrated the
cuticle and was precipitated as AgCl in the apoplast of the leaf. These investigations
show that ionic compounds penetrate the lipophilic cuticle. However, penetration
was not uniform, and specific sites exist where electrolytes penetrate.
Leaves treated with Gilson fixative containing mercuric chloride (HgCl2 ) exhibited crystalline precipitates of mercurous chloride in anticlinal walls and guard cells.
Post-treatment with potassium iodide reduces these precipitates, and metallic mercury can be seen as black dots in the outer epidermal wall (Schnherr and Bukovac
1970a, b). These precipitates are arranged in rows over anticlinal walls, as in onion
leaves (Fig. 5.3a). Adaxial leaf surfaces of Convallaria leaf (Fig. 5.3b) exhibit a
more random distribution of mercury precipitates, but over veins rows of precipitates over anticlinal walls are seen. Dense precipitates are also evident in guard cells.
Lightly brushing the leaf surface or rinsing it briefly with chloroform destroyed the
typical pattern. After brushing, new rows of precipitates appeared along the tracks of
the bristles. When cuticles were isolated enzymatically from onion leaves or onion
bulb scales and mounted on gelatine or agar containing ascorbic acid as reducing
agent, the precipitate pattern was the same as in epidermal strips. Clearly, precipitates are formed in the cell wall or in the agar at sites where the cuticle is selectively
permeable to HgCl2 , provided the matrices contain a reducing agent which is needed
for the formation of insoluble HgCl (Schnherr and Bukovac 1970a).
Aqueous HgCl2 solutions have an extremely low electrical conductivity, as mercury and chlorine are bound by divalent rather than ionic bonds. HgCl2 dissolves in
water, alcohols, ether, benzene and other organic solvents (Falbe and Regitz 1995).
Non-ionic HgCl2 is not surrounded by a hydration shell. It is lipid soluble and does
not depend on aqueous pores, as do berberine sulphate or silver nitrate. Yet the distribution pattern in the cell wall of berberine sulphate (Fig. 5.1) mercury (Fig. 5.2)
and silver (Fig. 5.3) is very similar. This raises the question as to the nature of sites in
cuticles selectively permeable to HgCl2 . The Gilson solution is very acidic (pH 1.0),
and carboxyl groups or phenolic hydroxyl groups are certainly not ionised at this pH
value, while amino groups are. Polypeptides occur in cuticles, albeit only in small
amounts (Schnherr and Bukovac 1973; Schnherr and Huber 1977). Possibly, Hg
precipitates mark sites with non-ionic functional groups such as hydroxyl, aldehyde,
phenolic hydroxyl, and ether or ester bonds. Carboxyl groups would be non-ionised
at these acidic pH values, but they may also be present along the HgCl2 diffusion
paths.
128
Fig. 5.1 Fluorescence micrographs of stomatous leaf surfaces of Helxine soleirolii (ac), Phaseolus vulgaris (d, e) and Vicia faba (fh) treated with berberine chloride (1 g l1 ) for 23 h in light.
The photographs were taken using a Zeiss Axioplan 2 microscope equipped with a Zeiss AxioCam
digital camera and AxioVision 3.1 software (Zeiss, Germany). The Zeiss filter set No. 02 (excitation: G 365 nm; beam splitter FT 395 nm, excitation: LP 420 nm) was used. (Taken from Schnherr
2006)
129
Fig. 5.2 Bright field micrographs of leaf surfaces of Phaseolus vulgaris after treatment with silver
nitrate (AgNO3 ) solution for 1 h. Sites of a strong silver precipitation are anticlinal cell walls,
cuticular ledges and glandular trichomes. Data from Schnherr (1969)
Fig. 5.3 Surface view of mercury precipitates in Allium (a) and Convallaria (b) leaf epidermal
walls. (Taken from Schnherr and Bukovac 1970a)
130
131
Fig. 5.4 (a) Transport chambers used for studying penetration of salts and other electrolytes across
isolated CM. The chambers are positioned in wells of a thermostated aluminium block. Air of
constant humidity is blown on the salt residues (arrows) at about ten air changes per second.
Temperature and humidity can be varied (taken from Schnherr 2006). (b) Penetration unit used
to study salt penetration into leaf disks. The leaf disk is positioned on a short hollow Teflon tube
and covered with a stainless steel lid. Teflon and lid are coated with silicon grease. The units are
placed on moist filter paper in Petri dishes. Humidity is always 100%
132
b
100%
75
90%
80%
50
98
4.0
100%
3.5
70%
25
-ln (1 - Mt / M o )
100
3.0
97
90%
95
2.5
87
2.0
92
1.5
78
1.0
80%
63
0.5
70%
39
0.0
0
10
20
30
Time (h)
40
50
Percentage penetrated
Percentage penetrated
0
0
10
20
30
40
50
Time (h)
Fig. 5.5 Time course of penetration of the isopropylamine salt of glyphosate across poplar CM.
(a) Percentage penetrated vs time. (b) Natural logarithm of the fraction of IPA-glyphosate left on
the surface of the CM is plotted against time. Humidity (%) over the residue is shown on each
plot. The same set of CM was used at different humidities. Donor solutions contained 0.2 g l1
Glucopon 215 CSUP as wetting agent. Water served as receiver solution. Bars are 95% confidence
intervals. (Redrawn from Schnherr 2002)
additional disadvantage. The leaf disk itself is the receiver, and repeated sampling is
not possible. For each time interval a new set of leaf disks (usually 50 or 100) must
be used, and the method of paired comparison cannot be applied as with SOFP.
In most of the experiments measuring salt penetration by SOFP it was found that
penetration of salt was best described by a first-order process. This means that the
relative amount of salt (Mt /M0 ) deposited on the cuticle decreased exponentially
with time:
Mt
= 1 ekt .
(5.1)
M0
Plotting ln (1 Mt /M0 ) vs time t resulted in straight lines at all humidities.
The slopes of the regression lines are the rate constants k (h1 ) of penetration
(Fig. 5.5b). With this rate constant known, amounts of salt that penetrated the cuticle
can be calculated for any time interval. Rate constants for salt penetration measured
with different species, different ions or different boundary conditions (humidity,
temperature) can directly be compared.
Another useful measure of permeability is the time needed for half of the dose
to penetrate (half-time t1/2 ). To calculate the half-time, (5.1) is solved for the case
Mt /M0 = 0.5. Thus ln 0.5 = kt or t1/2 = 0.693/k. After two half-times, 75% of
the salt has penetrated and after three half-times 87.5% has penetrated. For instance,
the slopes at 70% and 100% humidity (Fig. 5.5b) are 0.056 and 0.127 h1 and halftimes are 12.4 and 5.5 h respectively. For 87.5% of the dose to penetrate, 37.2 or
16.5 h are required. Penetration at 100% humidity was 2.25 times faster than at 70%.
133
4.0
98
3.5
97
Plantacare 1200 P
ln (1 Mt /M o )
95
APG 325
2.5
92
2.0
87
Glucopon 215 CSUP
1.5
78
1.0
63
Percentage penetrated
3.0
no surfactant
0.5
39
0.0
0
0
20
40
60
80
100
Time (h)
(0.2 g l1 )
134
80
60
calcium salts
potassium salts
50
60
nitrate
carbonate
40
30
40
chloride
20
20
propionate
10
acetate
0
50
60
70
nitrate
lactate
80
Humidity (%)
90
100
0
70
80
90
100
Humidity (%)
Fig. 5.7 Rate constants of penetration of calcium (a) and potassium salts (b) across astomatous isolated pear leaf CM (Pyrus communis). A 5-l drop of 5 g l1 of the salt solution spiked with 45 Ca2+
calcium salts or 86 Rb potassium salts as tracers containing 0.2 g l1 Glucopon 215 CSUP as wetting agent was added to the outer surface of the CM. Temperature was 20 C and humidity over the
salt residues was varied. Error bars are 95% confidence intervals. (Redrawn from Schnherr 2001,
2006)
135
three (Fig. 5.7a). POD of calcium chloride and calcium nitrate are 32% and 50%,
respectively (Appendix B). Rate constants with the organic calcium salts were lower,
and with acetate and lactate very little penetrated at 70% or 80% humidity. POD of
these salts are much higher, and amounted to 95% (propionate), 95% (lactate) and
100% (acetate) respectively. At 80% humidity and below, all organic salt residues
on the CM had a whitish appearance, indicating that they had crystallised. All these
three salts should not have penetrated at 90% humidity and below, but significant
rates were in fact measured. This is due to stagnant air layers directly over the
CM. Since water constantly penetrates the CM from the receiver, this leads to thin
water films between salt and CM. The POD of potassium nitrate (KNO3 ) is 94%
(Appendix B). As a consequence, KNO3 penetration across the cuticle ceases at
humidities below the 94% because the salt crystallises. However, potassium carbonate [K2 (CO3 )2 ] having a POD of 45% penetrated at all humidities investigated
(Fig. 5.7b).
Humidity has a dual function in cuticular penetration of salts. Humidity must be
higher than POD for the salt to deliquesce. However, even above the POD penetration rates of the salts increased with increasing humidity (Figs. 5.5 and 5.7). The
driving force for cuticular penetration is the donor concentration (Chap. 2). Inspection of residues shows that salt solutions are present on CM if humidity is above
POD, and the salt is crystalline when humidity is below POD. However, the salt concentration is not known in these experiments, and for this reason ln (1 Mt /M0 )
was plotted. Linearity shows that the salt fraction left on the CM decreased exponentially with time, and we accept this as evidence that the salt concentration also
decreased exponentially with time. At high humidity the salt concentration is probably lower than at low humidity, and this implies that driving force is lower at high
humidity. Nevertheless, rate constants increase with humidity, indicating permeability of CM did not depend on concentration. Concentrations decreased exponentially
with time, and this did not depend on the magnitude of the initial amount or concentration (M0 or C0 ). Schnherr (2000) studied the effect of initial CaCl2 in the donor
droplets. At concentrations of 2, 4, 6 and 10 g l1 and 90% humidity, penetration
plots were linear and rate constants were in fact independent of initial donor concentration and amounts of CaCl2 deposited initially. At a concentration of 1 g l1 ,
the rate constant decreased when more than 60% of the salt had penetrated. This
was attributed to an inhomogeneous distribution of the salt residue on the cuticle.
The effect of humidity on rate constants indicates a change in permeability of CM.
In Sects. 4.5 and 4.6 it was shown that water permeability and water content of
CM increased with increasing humidity. This leads to an increase of the number of
aqueous pores available for cuticular penetration of salts.
136
98
3.5
97
Populus
Pyrus
95
2.5
92
Malus
2.0
87
Stephanotis
1.5
78
1.0
Percent penetrated
ln (1Mt / M o )
3.0
63
Schefflera
0.5
39
0.0
0
0
20
40
60
80
100
Time (h)
Fig. 5.8 Penetration of CaCl2 across astomatous CM isolated from Populus canescens, Pyrus communis, Malus domestica, Stephanotis floribunda and Schefflera actinophylla leaves. A 5- l donor
droplet containing 5 g l1 45 CaCl2 and 0.2 Glucopon 215 CSUP as wetting agent was applied to
the outer surface of the CM and after droplet drying, penetration of CaCl2 was measured at 20 C
and 90% humidity. Error bars are 95% confidence intervals. (Redrawn from Schnherr 2000)
137
able. There are indications that frequency of aqueous pores in cuticles decreases
during leaf expansion and maturation. Permeability to an Fe-chelate of Vitis vinifera
and Prunus persica leaves decreased dramatically during leaf expansion (Schlegel
et al. 2006). The upper astomatous leaf cuticle of poplar leaves can be isolated only
from leaves which are just fully expanded. With these leaves, relatively high rate
constants were measured for CaCl2 , while permeability of the upper cuticle of older
leaves is almost zero (unpublished data). These two facts indicate a considerable
dynamic in development of aqueous pores and their closure in older leaves.
138
glutamate
600
400
300
200
propionate
500
chloride
700
lactobionate
pantothenate
heptaglutamate
800
100
0
0
100
200
300
400
500
600
700
800
Fig. 5.9 Molar volumes (Vx ) of a set of aliphatic and aromatic organic compounds plotted against
their molecular weights (green circles). The slope (0.895) was used to estimate Vx of calcium salts
(red squares) used in Fig. 5.10
100
200
300
400
500
600
700
800
1.8
0.4
2.8
0.6
0.8
4.4
1.0
7.0
1.2
11
1.4
18
Populus canescens
28
1.6
44
1.8
0
100
200
300
400
500
600
700
800
139
Table 5.1 Parameters of the regression lines shown in Fig. 5.10 and rate constant (k) calculated
for salts having molar volumes of 100 or 500 cm3 mol1
Species
Vicia light (MW)
Vicia light (Vx )
Vicia dark (MW)
Vicia dark (Vx )
Populus (MW)
Populus (Vx )
log k0 (h1 )
(mol cm3 )
k(100) (h1 )
k(500) (h1 )
k(100)
k(500)
0.37
0.37
0.63
0.63
0.49
0.49
1.15 103
1.28 103
1.21 103
1.35 103
2.11 103
2.34 103
0.32
0.17
0.19
0.098
0.050
0.022
3.3
3.4
8.7
log k0 is the y-intercept, and corresponds to the slope of the regression lines in Fig. 5.10
responsible for the difference in rate constants between broad bean and poplar.
This is in accord with preferential penetration of berberine chloride at these sites
(Fig. 5.1).
Slopes and y-intercepts of the straight lines which quantify selectivity of poplar
and broad bean cuticles (Fig. 5.10) have physical meaning. The y-intercepts are
the log k0 values for a hypothetical compound of zero molecular weight or molar
volume (cf. Sect. 6.3.2, subsection: Variability of Solute Mobility with Size of
Solutes). The slopes ( ) of the lines characterise size selectivity. These parameters
are summarised in Table 5.1.
These k0 -values characterise permeability of cuticles from different species and
at different experimental conditions. With broad bean (dark) k0 is 0.23 h1, while
with poplar CM lacking stomata the k0 was 0.32 h1. Since slopes also differ, the
difference between species increases with molar volume of solutes (Fig. 5.10). Permeability of broad bean in light (k0 = 0.40 h1) was 1.7 times higher than in the
dark. As was already pointed out, the difference indicates that cuticles over stomata
are more permeable when stomata are open (cf. Fig. 6.13). As size selectivity was
not affected by light, higher permeability appears to be due to an increased number
of pores. Since k0 -values mark permeability of a salt having zero molar volume
or molecular weights, they are the same no matter which size variable is used in
calculation.
Slopes of the lines ( ) are negative, which implies that log k decreases by the
factor Vx . Size selectivity of aqueous pores was larger with poplar CM than
with bean leaf cuticles. Size selectivity was not very pronounced, because increasing molar volume by a factor of 5 decreased rate constants by factors of only 3.38.6
(Table 5.1). Size selectivity of the lipophilic path ( ) in cuticles has been studied [(6.21) and (6.23); Table 6.8] and was found to be the same with all species
investigated. Average sized dependence is 9.5 103 mol cm3 . Thus, size discrimination of lipophilic solutes in the waxy pathway is 47.4 times larger than
discrimination of ionic solutes in aqueous pores.
Rate constants are proportional to permeance (2.26), and permeance depends
on the diffusion coefficient, partition coefficient and on thickness of the membrane
(2.18). For a given species, the thickness of the cuticle or the lengths of the aqueous
140
pores are the same for all solutes. Partition coefficients should be around 1.0, since
the salts are dissolved in the aqueous phases of the donor and the pore fluid. There
might be a slight decrease with increasing molar volume, but there are no data
available. Diffusion coefficients decrease as molecular weights or molar volumes
increase (4.16), and this is more pronounced in narrow pores than in bulk liquid.
Hence, size-dependent rate constants measured for the cuticles of different species
mainly reflects differences in diffusion coefficients, thus they are mobility parameters. Rate constants observed for different plant species probably also depend on
thickness of cuticles and path lengths.
141
100
90
80
70
60
50
40
30
betaine
CaCl2
20
proline
10
K-glyphosate
putrescine
Ca-glyphosate
0
70
80
90
100
Humidity (%)
Fig. 5.11 Permeability of Populus canescens CM to selected organic ions and to CaCl2 as affected
by humidity and POD. Donor solutions contained 0.2 g l1 Glucopon 215 CSUP as wetting agent;
solute concentration was 5 g l1 and temperature 20 C. Maximum rate constants at 100% humidity
were 0.99 h1 (putrescine), 0.66 h1 (CaCl2, , proline and betaine) and 0.33 h1 (IPA-glyphosate).
(Redrawn from Schnherr 2006, and Schnherr and Schreiber 2004a, b)
0.2
1.0
1.2
14C
1.4
y = 3.63 x 103 x 0.16 (r2 = 0.97)
1.6
Ca-Gluconate
0.8
Ca-GLY
0.6
K-GLY
Ca-chloride
0.4
45Ca
1.8
50
100
150
200
250
300
Molar volume (cm3/ m ol)
350
400
Fig. 5.12 Effect of molar volume of selected ionic compounds on rate constants of penetration
across Populus canescens CM at 20 C and 100% humidity. Donor solutions contained 5 g l1
solutes and 0.2 g l1 Glucopon 215 CSUP as wetting agent. The same set of CM was used for
all experiments, and duplicate determinations were made with all compounds. The calcium salt of
glyphosate was labelled either as 45 Ca-glyphosate and or as Ca-14 C-glyphosate. The slope of the
regression line is 3.63 103 mol cm3 (Schnherr and Schreiber 2004a)
142
was observed. The slope of the regression line is 3.63 103 mol cm3 , and the
y-intercept was 0.16. Both values are larger than the values for the lot of poplar
CM shown in Table 5.1. For this reason the same lot of CM should be used to compare different ionic solutes and test dependence on molar volumes of rate constants.
By reference to Fig. 5.12, it is clear that duplicate determinations using the same lot
of CM give very similar results, and rate constants are the same within experimental
error if the Ca-glyphosate is labelled with 45 Ca2+ or with 14 C-glyphosate.
Many growth regulators such as abscisic acid, indolacetic acid, 2,4-D, NAA and
gibberellic acids are carboxylic acids. Their Ca2+ salts have molar volumes almost
twice as high as their K+ salts, and their POD values are close to 100%. This is no
problem in scientific experiments, where deionised water can be used. But in the
field, sprays are prepared with water from wells or rivers, and if this water contains
Ca2+ ions these weak acids form calcium salts and biological activity may be greatly
reduced or lost. This problem is much greater than with Ca-glyphosate, because the
above growth regulators are used at very low concentrations of 100500 ppm.
Problems
143
-0.4
-0.6
CaCl2 + FeEDTA
-0.8
-1.0
-1.2
FeEDTA
-1.4
FeIDHA
-1.6
-1.8
0
10
15
20
25
Fig. 5.13 Penetration at 100% humidity of 59 FeIDHA and 59 FeEDTA across Populus CM at concentrations increasing from 0.002 to 0.02 mol l1 , and penetration of 45 CaCl2 in the presence of
non-radioactive FeEDTA. Glucopon 215 CSUP was added to the donor solutions. Temperature
was 20 C. The same set of CM was used for all experiments. (Redrawn from data of Schnherr
et al. 2005)
blockage of aqueous pores in the Populus CM, serving as polar path of transport for
both Fe chelates and Ca salts, and as a consequence rates of penetration decrease.
Leaf age greatly affected penetration of Fe chelates. Highest rates of penetration
were observed with young unfurling leaves, whereas penetration into fully expanded
leaves of different species was hardly measurable. These results show that young
growing leaves should be sprayed, and humidity must be 100%. Hence, spraying
in the evening is recommended when due to decreasing temperatures the dew point
may be reached. Fe chelates are destroyed by UV radiation, which requires spraying
after sun set (Schnherr et al. 2005).
Problems
1. Why is the cuticular permeability of polar compounds very low?
2. Why is the diffusion of ionic solutes in the lipophilic cutin and wax phase
impossible?
3. Which are preferential sites in the leaf surface where aqueous pores are located?
4. What is the half-time of cuticular penetration t1/2 of a Ca2+ salt having a rate
constant k of 0.0001 s1?
5. How does relative humidity affect the penetration of a salt across the cuticle?
144
6. How is cuticular penetration across grey poplar CM affected when the molecular
volumes of Ca2+ salts increase from 100 to 500 cm3 mol1 ?
7. How does light affect cuticular penetration of Ca salts across leaf surfaces of
Vicia faba?
Solutions
1. The partition coefficient of polar compounds (e.g., sugars) between the external
aqueous phase and the lipophilic cutin and wax phase is very low. Consequently,
according to (2.18) permeance P is very low.
2. Ionic solutes strongly bind hydration water, and this renders them insoluble in
lipophilic phases like cutin and wax.
3. Trichomes, stomatal ledges and anticlinal cell walls are sites of the leaf surface
where aqueous pores are preferentially located.
4. For this problem, (5.1) must be solved for Mt /M0 = 0.5. The half-time of
penetration t1/2 is 6,931 s or 1.92 h.
5. Humidity affects cuticular penetration of salts in two different ways. It interacts
both with the salt deposit on the cuticle surface and with the cuticular membrane. (a) Humidity must be higher than the POD of the salt, otherwise the salt
crystallises and it becomes immobile. The salt dissolves only above the POD. (b)
With increasing humidity, more water is sorbed to polar functional groups in the
cutin matrix, and this increases the number of aqueous pores, which in turn leads
to increased rates of salt penetration.
6. Based on the regression equation shown in Fig. 5.12, rate constants decrease
from 0.30 to 0.011 h1, which is a factor of 27.
7. Size selectivity is not affected (Table 5.1), but rate constants of penetration are
higher in light (0.32 h1) than in the dark (0.17 h1). This is attributed to an
increased number of aqueous pores in stomatal ledges in light when stomata are
open.
Chapter 6
Diffusion of Non-Electrolytes
Moctanol
moctanol
Mwater
mwater
mwater
Moctanol
.
Mwater
moctanol
(6.1)
Kow -values have been measured and tabulated for a large number of substances
(Hansch and Leo 1979; Leo et al. 1971; Sangster 1997). A partition coefficient of
145
146
6 Diffusion of Non-Electrolytes
1.0 indicates that solubility is the same in both phases. Compounds having partition coefficients >1 are lipophilic, and they are hydrophilic when Kow < 1. Partition
coefficients vary by several orders of magnitude, and to avoid exponents log values
(e.g., log Kow ) are used.
Partition coefficients can also be determined for solid lipid phases such as fats,
waxes or cuticles. Solutes sorbed in a solid constitute a solid solution (Fig. 2.6).
Sorption sites in a solid are finite, and for this reason partition coefficients decrease
with increasing concentration in the aqueous phase (Riederer and Schnherr 1986a).
Partition coefficients CM/water (Kcw ) can easily be determined using radiolabelled solutes. Isolated CM are equilibrated with an aqueous solution of a radiolabelled compound at constant temperature. After equilibration, the amounts of
radioactivity in water are determined by scintillation counting. The amounts of
radioactivity in the CM can be calculated from the decrease in the concentration
in water after equilibration. If this method is used, the drop in concentration should
be large, especially when radiochemical purity is less than 99%. It is better to determine radioactivity in both phases after equilibration. Care should be taken to remove
water films adhering to the cuticles by blotting with soft tissue paper. Cuticles are
thin, often only about 3 m thick or less. The inner surface of the cuticles is easy to
wet, and water films cannot be avoided. If partition coefficients are >10, liquid films
of the same mass as the cuticular materials introduce little error. The error can be
estimated and corrected by weighing the CM after blotting and after air drying. With
the weight of both phases (CM and water) known, Kcw can be calculated according
to (2.12). Similarly, partition coefficients can also be measured with MX (Kmxw ),
cutin (Kcuw ) and cuticular waxes (Kww ) as solid lipid phases.
Time needed to establish equilibrium depends on diffusion coefficients in cuticles
and on membrane thickness. Equilibration usually takes only a few hours (Sect. 6.3,
Figs. 6.13 and 6.14). However, with compounds carrying a carboxylic group (e.g.,
2,4-D) and cuticles with epoxyfatty acids (Chap. 2), it was observed that partition
coefficients slowly but constantly increased for many days (Riederer and Schnherr
1986b). This was due to formation of ester bonds between reactive epoxide groups
and carboxyl groups of 2,4-D. Hence, partition coefficients increased with time and
were overestimated. This problem can be avoided by washing the CM in 1.5 M HCl,
which converts epoxy groups in vicinal hydroxyl groups.
147
Citrus and Ficus and tomato and pepper fruit CM cover the full range of partition
coefficients observed with 2,4-D.
In the same study, Kmxw and Kcuw for 2,4-D were also measured. Both partition coefficients were larger than Kcw . These CM contain different amounts of wax
(Table 1.1), which is either sorbed in the MX or deposited as epicuticular wax.
Kmxw were 20160% higher than Kcw , depending on species. There was a positive
correlation between increase in partition coefficients on extraction of waxes and the
weight fraction of waxes in cuticles. This indicates that additional sorption sites
became available after wax extraction. Kww are considerably lower than Kcw (see
below), and this most likely contributed to the difference between Kcw and Kmxw .
Variability of Kcw among plant species could also be caused by differences in the
cutin fraction. With most species Kcuw values were higher than Kmxw , but variability
between species did not disappear when polar polymers were hydrolysed and eliminated from the MX. This indicates that sorptive properties of cutin from different
species are not the same. This is not too surprising, since in some species cutin is
composed of two fractions (Sect. 1.2), ester cutin and non-ester cutin (cutan), and
their sorptive properties probably differ.
Using cuticles isolated from Lycopersicon and Capsicum fruits and from Ficus
and Citrus leaves, Kcw of eight different organic chemicals was measured (Kerler
and Schnherr 1988a). Log Kcw values ranged from 2 to 8 and variability between
species was small, compared to the large differences in log Kcw values between different compounds (Table 6.1). The mean log Kcw calculated from all values of these
four species were very similar to log Kow values (Table 6.1). These results show
that plant cuticles are very efficient sorbers for lipophilic environmental chemicals,
and non-volatile lipophilic compounds accumulate from the environment over time
(Schnherr and Riederer 1989). Kmxw for these eight compounds and four plant
species were all slightly higher than log Kcw values (Kerler and Schnherr 1988a).
Table 6.1 Cuticle/water partition coefficients (log Kcw ) measured with the CM of Citrus aurantium, Ficus elastica, Lycopersicon esculentum and Capsicum annuum and eight substances
(log Kcw and log Kow ). Data taken from Kerler and Schnherr (1988a)
Substance
4-NP
2,4-D
AT
2,4,5-T
PCP
HCB
PER
DEHP
log Kcw
Citrus
log Kcw
Ficus
log Kcw
Lycopersicon
log Kcw
Capsicum
log Kcw
mean
log Kow
1.79
2.47
2.15
3.13
4.42
5.70
6.45
7.22
1.80
2.50
2.16
3.11
4.55
5.74
6.20
7.28
1.89
2.63
2.12
3.19
4.57
5.83
6.50
7.32
1.97
2.76
2.19
3.21
4.66
5.80
6.55
7.48
1.87
2.61
2.16
3.16
4.56
5.77
6.36
7.34
1.92
2.50
2.64
3.40
4.07
5.47
6.50
7.86
4-Nitrophenol (4-NP), 2,4-dichlorophenoxyacetic acid (2,4-D), atrazine (AT), 2,4,5-trichlorophenoxyacetic acid (2,4,5-T), pentachlorophenol (PCP), hexachlorobenzene (HCB), perylene
(PER) and diethylhexylphthalate (DEHP)
148
6 Diffusion of Non-Electrolytes
Table 6.2 Wax/water partition coefficients (log Kww ) measured with cuticular wax isolated from
Hordeum vulgare, Prunus laurocerasus, Ginkgo biloba and Juglans regia, mean log Kww values and mean log Kcw values of ten compounds. Values in brackets indicate log Kww values of
Hordeum corrected for the crystallinity of 50%, assuming that the crystalline wax fraction does not
contribute to sorption
Substance
MET
4-NP
BA
AT
SA
TRI
2,4-D
TB
BIT
PCP
log Kww
Hordeum
log Kww
Prunus
log Kww
Ginkgo
log Kww
Juglans
log Kww
mean
log Kcw
mean
0.54 (0.84)a
1.48 (1.78)a
1.51 (1.81)b
1.66 (1.96)b
2.81 (3.11)a
3.02 (3.32)b
3.55 (3.85)b
1.11c
1.15c
1.32c
1.45c
1.66c
2.13c
1.35c
1.67c
2.14c
1.34c
1.68c
2.16c
0.82
1.15
1.34
1.45
1.62
1.51
2.02
2.81
3.02
3.55
1.48c
1.87d
1.71c
2.16d
2.03c
2.88b
2.61d
3.54e
4.05b
4.56d
Metribuzin (MET), 4-nitrophenol (4-NP), benzoic acid (BA), atrazine (AT), salicylic acid (SA),
triadimenol (TRI), 2,4-dichlorophenoxyacetic acid (2,4-D), tebuconazole (TB), bitertanol (BIT)
and pentachlorophenol (PCP).
a Burghardt et al. (1998)
b Schreiber and Schnherr (1992a)
c Kirsch et al. (1997)
d Kerler and Schnherr (1988a)
e Baur et al. (1996b)
149
the Kww values should be doubled (Table 6.2) before they are compared to Kcw or
Kow . After this adjustment, Kww values are still much smaller than Kcw . Thus, even
amorphous barley wax sorbs much less than cuticles. Crystalline wax fractions for
the other species are not known, but they are likely to be smaller than 50%.
(r2 = 0.97).
(6.2)
This equation is based on 13 different chemicals with log Kcw values varying over
eight orders of magnitude. Using (6.2), cuticle/water partition coefficients in the
range of 102 and 108 can be estimated for low solute concentrations in water.
Organic solutes with no or few polar groups (i.e., OH, COOH, CHO, NO2 ,
NH2 ) are hydrophobic and have a low water solubility. Large Kow values are mainly
caused by low water solubility, rather than high solubility in octanol (Sangster
1997). For this reason Kow can be predicted from water solubility. This alternative approach offers the advantage that log Kcw values can be calculated if log Kow
150
6 Diffusion of Non-Electrolytes
values are not available, or if values appear unreliable. For a set of 13 compounds
and water solubilities (Swater ) ranging from 101 to 1011 mol l1 (6.3) has been
established (Schnherr and Riederer 1989).
log Kcw = 1.118 0.596 logSwater
(r2 = 0.96).
(6.3)
The coefficient of determination (r2 ) is only slightly lower than that of (6.2), and
both equations are valuable tools for the prediction of log Kcw values. However, Kcw
of compounds with infinite water solubility (e.g., methanol and ethanol) cannot be
predicted from (6.3).
Molecular connectivity indices have been used to predict log Kcw values (Sabljic
et al. 1990). Molecular connectivity indices are exclusively derived from the structure of the molecules (type and number of atoms and bonds), and they do not
represent experimental values. The advantage of this approach is the fact that molecular connectivity indices are not subject to experimental errors, which are always
associated with experimental values.
When log Kww values are plotted against mean log Kcw (Table 6.2), a reasonable
correlation is obtained (Fig. 6.1). Equation (6.4) shows that sorption in wax is lower
by a factor of about 6.8 (100.83 ) than sorption in the CM
log Kww = 0.29 + 0.83 log Kcw
(r2 = 0.93).
(6.4)
0
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Fig. 6.1 Plot of the logarithm of mean wax/water partition coefficients (mean log Kww ) measured
with isolated wax of four species and ten compounds as a function of the logarithm of mean
cuticle/water partition coefficients (mean log Kcw ). Dotted lines represent the 95% confidence
interval of the regression. Data are taken from Table 6.2
151
1
.
(10 pKa pH ) + 1
(6.5a)
1
(10 pHpKb ) + 1
(6.5b)
152
6 Diffusion of Non-Electrolytes
153
on the surfaces of the cuticles containing dissolved sugars are most likely the cause
for this difference.
The above two model calculations leave little doubt that partition coefficients for
highly water soluble compounds and very thin cuticles cannot be determined with
sufficient accuracy, and they should be looked at with suspicion.
KD
(Cdonor Creceiver ) .
(6.6)
Permeance (P) is calculated by dividing the steady state flux (J) of a solute by the
driving force, which is the difference of the solute concentration between donor
and receiver. In the steady state the concentration in the receiver can be maintained
negligibly small, and driving force is simply the donor concentration. P can be
determined using isolated CM, leaf disks or detached leaves. We shall demonstrate
application of (6.6) using examples taken from the literature.
154
6 Diffusion of Non-Electrolytes
2.5
a
ivi
Cl
1.0
F
m
an
u
So
l
Capsicum F.
1.5
Lycopersicon F.
2.0
a
le
us
Citr
Ficu
0.5
m
Neriu
0.0
0
10
20
30
40
50
60
70
80
Time (h)
Fig. 6.2 Time course of 2,4-D diffusion across CM of various plant species at 25 C. The steady
state flow was extrapolated to the time axis, which yields the extrapolated hold-up time (te ). Fruit
CM were obtained from tomato, pepper and egg plants; all others were isolated from astomatous
adaxial leaves. (Redrawn from Riederer and Schnherr 1985)
Steady state flow rates and the hold-up times (te ) varied greatly among species.
The amount diffused was greatest with fruit CM, and te was short. With leaf CM,
slopes are considerably smaller and hold-up times are longer (Fig. 6.2). Permeance calculated from these data range from 2.72 108 (pepper) to 1 1010 m s1
(Ficus), that is, among species they differed by a factor of 272. With P known, the
steady state fluxes caused by a given concentration can be calculated. For instance,
if donor concentration is 1 103 mol l1 , the steady state flux in 24 h would be
2.35 103 mol m2 s1 and 8.64 106 mol m2 s1 across CM of pepper fruit
and Ficus leaf, respectively. At the same driving force and time interval, 272 times
more 2,4-D penetrates into a pepper fruit than in a Ficus leaf. It should be realised
that this represents a rather small number of species, and that with more species
included variability might likely be larger.
In the laboratory, growth regulators and other biologically active materials can be
applied to leaves under controlled conditions, and the steady state can be maintained
for a long time. Applying the same substance at constant concentration for the same
time period, the dose delivered to leaves, stems or fruits of different species, genotypes or mutants differs if permeance is not the same. If P are not known, this type
of experiment is likely to lead to wrong conclusions in doseresponse experiments.
By reference to Fig. 6.2 it is clear that penetration experiments with only one time
point are not a good practice. Permeance can still be calculated using (6.6), but holdup time is not known and must be assumed to be zero. With Citrus CM, 28 mol 2,4D penetrated in 24 h and extrapolated hold-up time was 7.9 h. Had only one sample
155
been taken after 24 h, the calculated flow would have been 1.17 mol h1 . However,
time available for steady state penetration was only 16.1 h (247.9 h), and the proper
slope is 1.74 mol h1 . Neglecting the hold-up time results in an erroneous estimate
of flow, which is too small by a factor of 0.67. In the vast majority of published data,
foliar penetration was measured only after one time interval.
In the field, chemicals are applied by spraying plants with small droplets. They
dry up quickly, concentration in the droplets increases, 2,4-D probably crystallises
and wetting of cuticles may be a problem. These practical problems reduce steady
state penetration to a very short time, and we shall address these and other practical
problems and their solutions later (Sects. 6.3 and 6.4).
Inspecting Fig. 6.2 immediately raises the question as to what might have caused
the differences among species. Permeance is a mixed quantity and proportional
to the diffusion and partition coefficients and inversely proportional to membrane
thickness (6.6). From these quantities only and P are known, and D can be obtained
from the hold-up time (2.5). The partition coefficient K can be calculated as P /D
(6.6). P, D and Kcalc are summarised in Table 6.3.
Thickness of CM ranged from 2.6 to 10.7 m, while permeances differed by a
factor of 272, and there is no correlation between P and 1/ as suggested by (6.6).
Citrus CM is the thinnest in this collection, and its P is similar to permeances of the
thick CM of Clivia, Ficus and Nerium. Tomato and pepper fruit CM are also very
thick, but their permeances are more than 200 times higher than that of the rubber
leaf CM.
Diffusion coefficients ranged from 6.1 1015 (Lycopersicon) to 5.4
17
10 m2 s1 (Citrus), and D values of fruit CM are about an order of magnitude
higher than in leaf CM. The lowest D was measured with the thinnest CM (Citrus). Most strikingly, calculated partition coefficients (Kcalc ) are much smaller than
partition coefficients determined directly (Kdet ) in sorption experiments (Table 6.3).
Table 6.3 Permeance (P), diffusion (D) and partition coefficients (Kcalc ) obtained with cuticular
membranes from the species shown in Fig. 6.2. For comparison, partition coefficients determined
directly (Kdet ) by sorption experiment are included (Riederer and Schnherr 1985)
Species
Capsicum F
Lycopersicon F
Solanum F
Olea
Citrus
Clivia
Ficus
Nerium
(m)
P(m s1 )
D(m2 s )
Kcalc
Kdet
P(MX)/P(CM)
9.2
8.1
6.3
6.2
2.6
8.9
9.8
10.7
2.72 108
2.55 108
3.36 109
2.67 109
2.80 1010
1.30 1010
1.00 1010
1.80 1010
5.20 1015
6.08 1015
7.97 1015
2.63 1016
5.40 1017
2.22 1016
2.28 1016
1.44 1016
48
34
2.7
63
14
5.2
4.3
13
579
428
424
469
300
240
315
300
46
29
1,557
2,442
1,767
3,876
9,192
656
D and Kcalc were obtained using average values from 613 CM for and P respectively. In the
original publication, calculations were performed for individual CM and averaged. For this reasons,
above values differ somewhat from those of the original publication. Kdet (6th column) taken from
Riederer and Schnherr (1984)
156
6 Diffusion of Non-Electrolytes
Table 6.4 The effect of extraction of waxes on 2,4-D permeance; partition coefficients calculated
(Kcalc ) for the MX from the P/D ratio. Partition coefficients obtained in a sorption experiment
(Kdet ) are shown for comparison
Species
Capsicum fruit
Lycopersicon fruit
Solanum fruit
Olea leaf
Citrus leaf
Clivia leaf
Ficus leaf
Nerium leaf
P(MX)/P(CM)
46
29
1,557
2,442
1,767
3,876
9,192
656
Kcalc for CM
48
34
2.7
63
14
5.2
4.3
13
Kcalc for MX
Kcalc correct.
Kdet for MX
670
470
350
700
430
160
180
240
989
635
522
1,000
558
200
240
324
768
612
755
990
435
307
485
648
Data taken from Riederer and Schnherr (1984, 1985). Corrected Kcalc were obtained by dividing
Kcalc by the weight fraction of cutin in MX taken from Table 1.1
157
log K / Vx (mol/cm3)
0.020
5
0.022
0.024
0.026
0.028
0.030
6
6
7
log Permeance (m / s)
0.032
9
1
10
3 2
11
1
log K
158
6 Diffusion of Non-Electrolytes
159
(6.8)
This equation can be used to calculate Kcw from the aqueous solubility (mol l1 ).
The data base includes solutes shown in Fig. 6.3, and aqueous solubilities ranged
from 0.17 to 2.4 1011 mol l1 .
160
6 Diffusion of Non-Electrolytes
161
1.0
0.9
0.8
0.7
Mx / M o
0.6
0.5
0.4
0.3
6h
24 h
0.2
0.1
0.0
0
12
15
Fig. 6.4 Distribution of 14 C-triadimenol in barley leaves which had been dipped with their cut
edges 1 mm deep for 6 or 24 h into radio-labelled aqueous triadimenol. Pink symbols are experimental values, while cyan symbols were calculated using a D of 2 1010 m2 s1 Vertical bars are
95% confidence intervals. Redrawn from Schreiber and Schnherr (1992a)
162
6 Diffusion of Non-Electrolytes
40
35
30
25
measured
20
15
50
100
Time (min)
150
200
Fig. 6.5 Foliar penetration at 25 C of PCP into barley leaves. Amounts penetrated increased
linearly with time, but measured penetration (red symbols) was biphasic and the regression line
intersects the ordinate at a positive value
163
penetrated vs time has a positive intersection with the time axis (extrapolated holdup time seen in Fig. 6.2), because it takes some time before the first solute molecules
appear in the receiver and penetration becomes steady. When penetration across CM
is measured, concentration of the receiver is monitored and sorption in the CM goes
unnoticed. During penetration into leaves, solutes are first sorbed in epicuticular
waxes and in cuticles before they reach the tissue (apoplast and the symplast). Penetration of PCP into barley leaves was biphasic. During the first 30 min it was much
faster than later on. The rapid penetration represents soprtion to the leaf surface and
diffusion into epicuticular wax, while slow penetration marks cuticular penetration
into the leaf apoplast. Compartmental analysis substantiates this conclusion.
1.0
0.9
0.8
30 min
0.7
Mt /M0
0.6
90 min
0.5
0.4
0.3
180 min
0.2
0.1
0.0
0
60
120
180
240
300
360
Time (min)
Fig. 6.6 Desorption of PCP from barley leaves preloaded with PCP for 30, 90 or 180 min. During
preloading, PCP penetrated from the donor solution at pH 3 into leaves. After being briefly blotted
between soft tissue paper, the leaves were submerged in borax buffer at pH 9. This changed the
direction of the PCP concentration difference, and PCP diffused out of the leaves. (Redrawn from
Schreiber and Schnherr 1992a)
164
6 Diffusion of Non-Electrolytes
Table 6.5 Distribution of PCP in the compartments (CPT) of barley leaves as affected by duration
of preloading. CPT1 and CPT2 were obtained by non-linear regression analysis (6.10). CPT3 is the
fraction of PCP unaccounted for by CPT2 and CPT1
Preloading for
CPT1
CPT2
CPT3
30 min
90 min
180 min
0.56
0.41
0.15
0.10
0.08
0.10
0.34
0.51
0.75
Desorption kinetics were analysed by non-linear regression. The best fit (r2 >
0.99) was obtained with a model consisting of two compartments (CPT1 and CPT2 )
and two rate constants (k1 and k2 ):
Mt
(6.10)
= CPT1 1 ek1t + CPT2 1 ek2t .
M0
Rate constants were independent of duration of preloading, and amounted to 8.5
103 and 3.7 104 s1 for k1 and k2 respectively. Rate constants were defined by
(2.6). From the rate constant, the half-time (t1/2 ) required for 50% sorption or desorption (Mt /M0 = 0.5) can be calculated as t1/2 = ln 0.5/k. Hence, t1/2 is 81.5 and
1,873 s for compartments 1 and 2 respectively. It takes about five half-times before
the compartments are empty. In the case of barley leaves and PCP this amounted to
6.8 and 156 min for compartments 1 and 2, respectively.
The compartment sizes in (6.10) represent fractions. The absolute size of a
compartment in Bq is obtained by dividing radioactivity in the CPT by total radioactivity in the leaf. The fractions of PCP contained in the compartments are given in
Table 6.5.
Sizes of CPT1 and CPT3 depended on duration of preloading, while CPT2 was
constant and 810% of total PCP was sorbed in this compartment. CPT1 decreased
and CPT3 increased with duration of preloading. PCP in CPT1 and CPT2 was
reversibly sorbed, while PCP in CPT3 increased with time and could not be recovered from the leaves. This indicates that this fraction of PCP was in the leaf tissue in
dissociated form and was held there by an ion trap mechanism. pH in the apoplast
and symplast are around 56, and this favours dissociation.
If the absolute amounts contained irreversibly in CPT3 are plotted vs time, a
straight line is obtained (Fig. 6.5, plot calculated from desorption) which intersects the origin and has the same slope as the plot amount penetrated vs time.
Permeance calculated from desorption experiments is 1.4 107 m s1 , and is
identical within experimental error to permeance obtained from the slope of a
penetration experiment.
The parallel displacement is caused by PCP reversibly sorbed on the leaf surface,
in epicuticular wax and in the cuticle underneath (cutin and intracuticular wax).
The donor solution is in contact only with the tips of the epicuticular wax crystallites. Hence, epicuticular waxes are filled first and serve as intermediate phase
between aqueous donor and cuticle. PCP sorbed in wax continues to diffuse into the
165
cuticle and eventually into the leaf tissue. When PCP is desorbed from leaves, the
efflux takes place at first from the epicuticular wax and later from the remainder
of the cuticle. Comparing the two rate constants, it is seen that k1 is 23 times
larger than k2 , and for this reason diffusion across epicuticular wax was not ratelimiting. Diffusion across cutin and embedded waxes was the rate-limiting step in
foliar penetration of PCP.
The y-intercept seen in Fig. 6.5 has practical implications. Permeance can only
be calculated if penetration is measured for more than one time interval. From the
slope, rate of penetration and permeance can be calculated. If penetration is measured using only one time interval, sorption in wax and cuticle is overlooked and
permeance estimated is too high. For instance, after 90 min penetration amounted to
24 1012 and the y-intercept was 11.3 1012 mol cm2 (Fig. 6.5). Subtracting
the y-intercept, the flux is 1.3 1013 mol cm2 min1 , while flux calculated from
the amount penetrated would have been 2.7 1013 mol cm2 min1 . Permeance
calculated without correcting for the y-intercept would be 2.1 times too high. Furthermore, a desorption experiment provides more information, as rate constants and
compartment sizes can be estimated.
Half-time of desorption for the first compartment, that is, for desorption from
epicuticular waxes is only 82 s. Frequently, adhering donor is rinsed off using
water, buffer, or aqueous acetone. In the experiment shown in Fig. 6.6, this would
have reduced the magnitude of the y-intercept but it would not have eliminated it.
Extended rinsing time will remove some more PCP from the cuticle, but complete
elimination is unlikely because the half-time for the second compartment (the cuticle) is 31.2 min. If leaves are washed or rinsed after the penetration experiment, a
variable and unknown fraction of solute sorbed in the cuticle is considered to have
penetrated, even though it had not yet reached the leaf tissue. The error is larger
with short experiments. A controlled desorption experiment after blotting leaves
to remove adhering donor solution is clearly the better approach, since it provides
information about number of compartments, compartment sizes and rate constants
by which they drain.
Using the approach outlined above, penetration of other lipophilic solutes into
barley leaves was studied (Fig. 6.7). Permeance increased with partition coefficients.
The approach used with barley leaves was successfully applied to study penetration of PCP and other lipophilic chemicals into conifer needles (Schreiber and
Schnherr 1992b). With conifer needles amounts penetrated vs time were also
biphasic, but magnitudes of y-intercepts differed greatly among species (Fig. 6.8).
Rates of penetration (slopes) have the dimension amount PCP penetrated per min
and mm needle length. The projected areas of needles were 5 mm2 mm1 with the
Abies species and 3 mm2 mm1 with all others. Dividing the slopes of the plots
by projected needle area (Apro ) and donor concentration yields the permeance in
m s1 if SI units were used in calculations (Table 6.4). P differed greatly among the
species.
Desorption analysis as shown for barley leaves in Fig. 6.6 resulted again in two
compartments having different rate constants. Rate constants of desorption of PCP
from the first compartment (k1 ) ranged from 8 to 11 103 s1 , that is, PCP was
166
6 Diffusion of Non-Electrolytes
TRI
8
2,4-D
log P ( m / s)
BIT
PCP
10
2.5
3.0
3.5
4.0
4.5
5.0
Log K CM/water
Fig. 6.7 Penetration into barley leaves at 25 C of 2,4-D, triadimenol (TRI), bitertanol (BIT)
and pentachlorophenol (PCP). Permeance was calculated from rates of penetration. Vertical bars
represent 95% confidence intervals. (Data taken from Schreiber and Schnherr 1992a)
200
Abies koreana
160
120
Abies alba
80
Picea pungens
40
Pinus sylvestris
Picea abies
0
0
60
120
180
240
300
360
Time (min)
Fig. 6.8 Penetration of PCP into conifer needles at 25 C. Penetration was biphasic. Rates of
penetration (slopes) and y-intercepts differed among plant species. Vertical bars represent 95%
confidence intervals. (Redrawn from data of Schreiber and Schnherr 1992b)
167
desorbed from epicuticular waxes of conifers at similar rates to those from barley
leaf wax. Rate constants of desorption (k2 ) from the second compartment (i.e., the
cuticle underneath the epicuticular wax) differed somewhat depending on species.
They were a little higher with Picea abies and Taxus baccata (2.4 104 s1 ) than
with Abies koreana and Abies alba (1.5 104 s1 ). These rate constants are also
similar to k2 measured with barley leaves (1.4 104 s1 ). As with barley leaves,
the size of the second compartment (CPT2 ) did not depend on time of loading and
was similar for all conifers. About 7% of PCP in needles was sorbed in compartment 2, that is in the cuticle. Fractions of PCP in compartment 1 decreased and
compartment 3 increased with time, as was the case with barley leaves.
Permeances obtained from penetration were not significantly different from permeances obtained from desorption experiments. When rates of penetration were
plotted against amount sorbed in compartments 1 and 2, a straight line was obtained.
Hence, rates of penetration into compartment 3 (mesophyll) were proportional to
amounts of chemicals sorbed in waxes and cuticles (Fig. 6.9). The amounts of chemicals sorbed are proportional to mass of wax, mass of cutin and partition coefficients.
The mass of epicuticular wax per mm needle length was determined by dipping the
needles for 12 s into chloroform. This method can be questioned (Sect. 2.2) but it
is likely that most epicuticular waxes were dissolved without extracting too much
embedded wax. Since compartments 1 and 2 were added (Fig. 6.9), the problem is
not crucial. Amounts of surface wax varied among species (Table 6.6) and ranged
from 1.56 to 7.1 g mm1 needle length (Schreiber and Schnherr 1993b). Abies
koreana and A. alba had the highest amount of surface wax, and this is the reason
15
16
Abies koreana
Abies alba
Picea pungens
Pinus sylvestris
Picea abies
17
18
13
12
11
10
Fig. 6.9 Dependence of rate of penetration of 2,4-D, triadimenol, bitertanol, lindane and PCP into
conifer needles on amounts of chemicals sorbed reversibly in compartments 1 and 2. (Redrawn
from data of Schreiber and Schnherr 1992b)
168
6 Diffusion of Non-Electrolytes
Table 6.6 Amounts of surface wax, projected and specific surface areas and permeances of conifer
needles from Abies koreana, Abies alba, Picea pungens and Pinus sylvestris (Schreiber and
Schnherr 1992b)
Species
A. koreana
A. alba
P. pungens
P. sylvestris
P. abies
A. koreana
A. alba
P. pungens
P. abies
P. pungens
P. sylvestris
A. koreana
A. alba
P. pungens
P. abies
A. koreana
A. alba
P. pungens
P. sylvestris
P. abies
Surf. wax
Aprojected
Aspecific
Solute
(g mm1 ) (mm2 mm1 ) (mm2 mm1 )
7.10
2.50
1.56
7.10
2.50
1.56
7.10
2.50
1.56
7.10
2.50
1.56
5
5
3
3
3
5
5
3
3
3
3
5
5
3
3
5
5
3
3
3
683
254
65.7
41.3
29.4
683
254
65.7
29.4
65.7
41.3
683
254
65.7
29.4
683
254
65.7
41.3
29.4
2,4-D
2,4-D
2,4-D
2,4-D
2,4-D
Triadim
Triadim
Triadim
Triadim
Lindane
Lindane
Bitertanol
Bitertanol
Bitertanol
Bitertanol
PCP
PCP
PCP
PCP
PCP
Pspecific
(m s1 )
Pprojected
(m s1 )
2.71 1011
3.11 1011
2.24 1011
3.78 1011
3.51 1011
2.54 1011
5.58 1011
7.00 1011
4.00 1011
4.23 1010
5.01 1010
4.23 1010
6.84 1010
7.95 1010
4.36 1010
4.20 109
3.90 109
6.63 109
3.30 109
5.00 109
3.70 109
1.58 109
4.91 1010
5.22 1010
3.43 1010
3.47 109
2.83 109
1.53 109
3.92 109
9.26 109
6.91 109
5.78 108
3.47 108
1.74 108
4.27 109
5.74 107
1.98 107
1.45 107
4.55 108
4.90 108
why both amounts penetrated and y-intercepts were highest (Fig. 6.8). The other
chemicals had smaller partition coefficients than PCP, and for this reason sorption
is smaller, and rates of penetration as well (Fig. 6.8).
This correlation between rates of penetration and sorption in surface wax and
cuticles is not really surprising, since amounts sorbed and rates of penetration are
proportional to concentration in the donor (6.6). After loading compartments 1 and
2 from the aqueous solution, the concentration in waxes and cuticles is the driving
force for loading the mesophyll, at least as long as concentration of non-ionised
PCP in the mesophyll remains small and insignificant and external concentration
does not change.
169
are in contact with water. Hence, the real contact area may be smaller or larger than
the projected area. This problem was generally ignored, and the projected surface
area was used as reference.
The standard method for estimating porosity and surface area of solids is sorption
of N2 . This gas penetrates into porous solids, and knowing the area of a N2 molecule
the total internal and external surface is estimated from monolayer sorption. The
amount in the monolayer is obtained by measuring N2 sorption at various pressures
(Gregg and Sing 1982).
Schreiber and Schnherr (1992b) attempted to measure the amount of PCP
sorbed in a monolayer on the surface of epicuticular wax crystallites. PCP was dissolved in an aqueous buffer to ensure a high concentration of non-ionised species.
The amount of PCP associated with needles was studied at various PCP concentrations, and data were analysed as BET isotherms. PCP is a planar lipophilic
solute, and its area when laying flat on the surface of wax is known. From these
isotherms the PCP in the monolayer was obtained, and assuming all to be sorbed
superficially the area of this monolayer was calculated. The specific surface areas
so obtained are shown in Table 6.6. Depending on species they vary between 29 and
1
683 mm2 mm , which means that the specific surface area is larger by factors of
10137 than the projected needle surface.
Permeances calculated using these specific areas (Pspecific ) eliminated all differences between plant species, and permeance depended only on type of solute via its
cuticle/water partition coefficient. However, large differences in P are evident when
it is calculated based on projected needle area. With 2,4-D, Pprojected was largest
with Abies koreana and smallest with Picea abies, and the difference amounts to
a factor of 10.8 (Table 6.6). Only permeances based on projected leaf area can be
compared to permeances calculated for isolated CM or with barley leaves. With barley leaves, P for the same solutes ranged from 1.1 107 (PCP) to 5 1010 m s1
(2,4-D) (Fig. 6.7). Similar Pprojected were obtained with Picea pungens (Table 6.6).
Permeances measured with isolated CM can also be compared. 2,4-D permeability of Citrus CM was 2.8 1010 m s1 (Table 6.3), and this is similar to 2,4-D
permeability of Picea abies (Table 6.6).
Y -intercepts were obtained by extrapolating steady state penetration of PCP
(Figs. 6.5 and 6.8). Specific surface area of needles, as calculated from sorption
isotherms of PCP, are based on the assumption that all PCP molecules are located in
a monolayer on the surface of wax crystallites (Schreiber and Schnherr 1992b). The
two measurements are completely independent but they are correlated (Fig. 6.10).
The slope is 0.82, showing that Aspecific was underestimated somewhat, but the
correlation between the two parameters is convincing evidence that initial sorption of PCP molecules as surface monolayers and concomitant penetration into
surface waxes cannot be separated. Model calculations based on amounts of epicuticular wax of the needles and wax/water partition coefficients show that 2550%
of all PCP, estimated from the positive y-intercepts (Fig. 6.8), were located inside
the epicuticular wax and not on the waxy surface as assumed. This conclusion is
supported by the fact that Aspecific increased with the amount of surface wax. Specific surface area estimated from the BET isotherms was larger with species having
170
6 Diffusion of Non-Electrolytes
160
140
40
20
Abies koreana
Abies alba
60
Pinus sylvestris
80
Picea pungens
100
Picea abies
Aspecific / A projected
120
0
0
20
40
60
80
100
120
y-Intercept x 1012 (mol / mm)
140
160
180
Fig. 6.10 Correlation between y-intercept measured by a penetration experiment (Fig. 6.8) with
ratio Aspecific /Aprojected estimated from sorption of PCP in conifer needles. The slope is 0.82. (Data
taken from Schreiber and Schnherr 1992b)
more epicuticular wax (Table 6.6). Thus, specific surface areas estimated from BET
isotherms are overestimates and not very precise.
Monolayer formation and sorption in waxes are related, and the sum of both
constitutes the driving force of cuticular penetration. The y-intercept measured
by steady state experiments (Figs. 6.5 and 6.9) characterise the sizes of the two
compartments in which lipophilic chemicals are reversibly sorbed. Their sizes are
proportional to the amount of wax and cutin and to partition coefficients of solutes
(Table 6.5). CPT1 and CPT2 are intermediate compartments from which solutes penetrate into apoplast and symplast. Rates of penetration into CPT3 are proportional
to the sizes of CPT1 and CPT2 . The absolute amounts of solutes sorbed reversibly
in CPT1 and CPT2 are proportional to the solute concentration in the donor. This
follows from the definition of the partition coefficient. For this reason, permeance is
also proportional to the y-intercept.
171
a relatively high surface tension. With leaves of Zebrina it was shown that infiltration of stomata will not occur if surface tension is 35 mN m1 or higher (Schnherr
and Bukovac 1972a). This even permits using low concentrations of surfactants to
improve wetting of leaf surfaces. There is no need to worry that infiltration of stomata occurs but is not noticed. Infiltration can be detected with the bare eye, because
dark spots will be seen in incident light which look bright in transmitted light. This
phenomenon is due to a local change in refractive index when intercellular air spaces
are filled with water.
Diffusion of solutes into the wound caused by cutting off the leaf at the petiole
is no problem, because it can be quantified and corrected for easily (Fig. 6.4). The
donor solution must be agitated to ensure mixing. If donor solutions are at ambient
pressure (vessels open), there is no need to worry about pressure forcing liquid into
open stomata. When working with barley leaves and conifer needles this was not a
problem, even though test tubes were tightly closed.
So far the methods have been used only with lipophilic solutes. There is no reason
why it should not work with polar non-electrolytes or with ions. With polar solutes
the sizes of CPT1 and CPT2 are probably very small, and the y-intercept is close to
zero. Permeance can be calculated from the slope of the penetration or the desorption graphs which are superimposed if sorption in wax and cuticles is insignificant
(cf. Fig. 6.13). With leaves that are easily wetted, a surface film of donor can be
estimated by desorption, and all donor solution will be washed off with the first
change of desorption medium. This offers the possibility to measure permeability
of delicate leaves such as Arabidopsis.
The method works well as long the leaf surface is not densely populated by
microorganisms, as was observed when working with older conifer needles sampled
from forest trees (Schreiber and Schnherr 1992c). Plants grown in growth chambers or greenhouses usually have clean surfaces. In any case, it is good practice to
check for surface contaminations.
6.2.3 Steady State Penetration into Leaf Disks Using the Well
Technique
Broadleaved plants can have very large leaves which are not suitable for the submersion technique. In these cases, penetration can be measured using a droplet
method. Small droplets of donor solutions are placed on the upper or lower surfaces of leaves attached to or dissected from plants. This approach is much closer
to the situation after spray application to the foliage, and this is often considered
an advantage. However, experiments of this kind are beset with severe problems,
as penetration proceeds under uncontrolled conditions. For instance, concentrations
and pH of donor solutions change during droplet drying, temperature of the donor
differs from leaf and surrounding air, contact area between donor and leaf is difficult to estimate precisely and may vary with time, and the solutes may solidify or
crystallise. These problems are almost as bad in growth chambers than in the field.
172
6 Diffusion of Non-Electrolytes
If researchers manage to distinguish between solutes in and on the leaves, the best
result of such experiment is fractional penetration during some arbitrary time after
droplet application.
Even in this case it is generally not realised that the velocity of penetration
depends on size of droplets, more precisely on the ratio droplet volume (Vdroplet )
over area of contact (Acontact ) between droplet and leaf surface. The situation can be
demonstrated assuming a hemispherical droplet positioned on a leaf. This means
that the leaf is difficult to wet and the contact angle is 90 . It is assumed that
Vdroplet , Acontact P and Cdonor are constant and do not vary with time. Hence, the
droplet must not dry up. Our starting point is (2.25), which is repeated here with
appropriate subscripts:
P Acontact t
Cdonor
= ln
.
Vdroplet
C0
(6.11)
0.693 Vdroplet
P
Acontact
(6.12)
depends on the volume of the droplet and the contact area. For a hemispherical
droplet Vdroplet /Acontact = (2/3) rdroplet . We have calculated half-times for frequent
values of permeances of cuticles and droplet sizes produced by conventional spraying equipment (Fig. 6.11). Such spherical droplets have mean diameters ranging
from 100 to 500 m, which corresponds to volumes of 0.565 nl.
When droplet radii increase from 33 to 133 m, half-times increase by a factor
of 1,000; and depending on permeance, half-times were in the range of minutes
to 280 h. If permeance is very high (107 m s1 ) it might be possible to maintain
Vdroplet /Acontact fairly constant, but with lower P this is impossible. Contact angles on
leaves vary greatly, and they depend on surface tension of the donor solutions. Both
factors greatly affect half-times because they affect Vdroplet /Acontact . Better wetting
leads to smaller Vdroplet /Acontact , even with constant droplet volumes, and this greatly
reduces half times.
These purely physical considerations have consequences for spray applications.
Loss of agrochemicals by rain and volatilisation can be minimised by using a larger
number of small droplets. There is a limit to this strategy because very small droplets
can be lost by drift. However, for rapid penetration it is a good strategy to deliver a
constant dose with more droplets of small size, or use higher concentrations instead
of low concentrations and large droplets.
Apart from these practical aspects, it should be clear that experiments with
small droplets are extremely difficult to analyse, and misinterpretations of cause and
effect are unavoidable. However, such experiments can be meaningful if fractional
173
1e+6
278 h
1e+5
27.8 h
1e+4
133
100
67
33
1e+3
1e+2
2.78 h
16.7 min
1.67 min
1e10
1e9
1e8
Permeance (m/ s )
1e7
Fig. 6.11 Half-times for solute penetration from hemispherical droplets of different size as a
function of permeance
penetration of a constant dose is aimed at, and we demonstrate this in Chap. 5 and
Sects. 6.3.16.3.4.
In an attempt to circumvent problems associated with droplet experiments, glass
wells have been glued to leaf surfaces using silicone rubber (Fig. 6.12). Relatively
large volumes of up to 1 ml donor can be pipetted into these wells, and both contact
area and donor volume can be kept constant. Problems may arise if the glue is phototoxic or when the solute is sorbed in the glue. Schnherr (1969) and Schnherr and
Bukovac (1978) have used this approach for studying foliar penetration of succinic
acid-2,2-dimethyl hydrazide (Alar), which is a zwitterion. Small glass tubes (10 mm
diameter and 7 mm height) were attached to leaf discs using silicon rubber and a
non-toxic catalyst. Silicon rubber provides a good seal even over veins, and surfactant solutions did not leak out. At the end of the experiment the rubber remained
attached to the glass and the leaf disk could be peeled easily and did not interfere
with subsequent processing of leaf disks (autoradiography and counting radioactivity). Rates of penetration were constant, as penetration plots were linear with all
treatments. Plots intersect the origin, that is, there was no measurable hold-up time
and no positive y-intercepts due to sorption in wax and cutin. From the slopes and
the donor concentration, permeance can be calculated. Permeance was very low,
depending on treatment. It ranged from 5 1011 to 25 1011 m s1 (Fig. 6.13).
Permeability of the lower leaf surface was higher than that of the upper one
(Fig. 6.13). Light increased permeability of both leaf surfaces, and the wetting agent
Tween 20 (polyoxylethylene sorbitane monolaurate) increased rates of penetration.
This wetting agent did not cause stomatal infiltration, and its effect on rates of penetration was related to increased contact areas between donor and leaf. The light
174
6 Diffusion of Non-Electrolytes
Fig. 6.12 Penetration units consisting of bean leaf disks (17 mm in diameter) and glass tubes
(10 mm in diameter) attached with silicon rubber. The units were positioned on moist filter paper
in Petri dishes which permitted studying the effect of light on rates of penetration (taken from
Schnherr 1969)
6e-10
-2
-1 )
lc
5e-10
2
-1
mo
45
0(
4e-10
x1
n2
e
we
+T
LS
3e-10
ht
lig
2e-10
x
(32
LS
-2
-12
10
l cm
mo
-12
1e-10
light
-1 )
1
-2 h- )
mol c
0
15 x 1
n 20 (
e
-2 -1 )
e
w
2
cm h
US+T
0-1 mol
US(9 x 1
0
0
6
Time (h)
12
Fig. 6.13 Penetration of succinic acid-2,2-dimethylhydrazide (Alar) into primary leaves of kidney
bean at 25 C. Donor concentration was 5 104 mol l1 and was buffered with citratephosphate
buffer at pH 5. Upper (US) and lower (LS) leaf surfaces are marked on the plots. Fluorescent light
(5.25 mW m2 ) was used when indicated and Tween 20 was added to the donor at 0.1%. Rates of
penetration are given in parentheses on the plots. (Data taken from Schnherr and Bukovac 1978)
175
effect on rates was shown to be caused by stomatal opening which increased permeability of cuticular ledges (Schnherr and Bukovac 1978). Alar is an electrolyte,
and at pH 5 it is neutral because negative and positive charges are present in equal
amounts (Schnherr and Bukovac 1972b). The role of stomata in foliar penetration
of ionic compounds is treated comprehensively in Chap. 5.
Alar penetration into bean leaves using the leaf disk method with attached wells
is a good example to demonstrate the merits of the method. The main advantages
are the facts that permeability of large leaves can be measured, and it is possible to
test if permeability of lower and upper leaf surfaces differ. With submerged leaves
this is not possible. Kirsch et al. (1997) have used this method to compare solute
permeability of isolated CM with non-isolated cuticles (Sect. 6.5). It is a somewhat
laborious undertaking, since sampling is destructive and when rates of penetration
(that is the time course of penetration) are studied, different leaf disks must be used
for each time interval. This increases variability, and a large number of leaf disks
(25 and more) must be used for representative sampling and for testing linearity. We
have shown above why this is absolutely essential.
Autoradiography makes it possible to study distribution of radioactive labels,
provided the leaves are freeze-dried quickly to avoid redistribution and metabolism.
Autoradiographs of selected bean leaf disks show that in the presence of Tween
20 more succinic acid-2,2-dimethylhydrazide penetrated and radio-label was much
more uniform (Fig. 6.14). Sometimes the label spread along the veins and reached
the cut edges. In later experiments with CaCl2 , this was avoided by placing the leaf
disks on stainless steel washers rather than directly on moist filter paper (Fig. 5.4b).
Permeances for non-ionised 2,4-D, salicylic acid and benzoic acid were measured using the upper, astomatous leaf surfaces or CM obtained from Prunus
laurocerasus, Ginkgo biloba and Juglans regia leaves (Kirsch et al. 1997). With
leaf disks and CM, penetration plots were linear and permeances could be calculated from slopes. Permeances measured with leaf disks and CM did not differ
significantly with all three species and compounds. Clearly, enzymatic isolation of
cuticles did not affect permeability of cuticles.
Fig. 6.14 Autoradiographs of bean leaf disks after penetration of 14 C labelled succinic acid-2,2dimethylhydrazide (Alar) in light for 12 h. Penetration without (a) and with 0.1% Tween 20 (b) as
wetting agent
176
6 Diffusion of Non-Electrolytes
177
1.0
0.8
M t / Mo
0.6
CM inside
MX inside
CM outside
MX outside
0.4
0.2
0.0
50
100
150
Time (min)
200
250
1.0
0.8
M t / Mo
0.6
CM inside
MX inside
MX outside
CM outside
0.4
0.2
0.0
0
20
40
60
(Time)1/2
80
100
120
(s)1/2
Fig. 6.15 Simultaneous bilateral desorption of 2,4-D from CM and MX membranes of Citrus
aurantium leaves. The membranes had been preloaded with 14 C-2,4-D, and were desorbed at 25 C
with borax buffer having a pH of 9.18. M0 is the amount of 2,4-D initially contained in the membrane and Mt is the amount desorbed at time t. In (a) Mt /M0 is plotted vs time, while in (b) it was
plotted vs the square root of time. (Redrawn from Schnherr and Riederer 1988)
178
6 Diffusion of Non-Electrolytes
MX membranes this asymmetry factor was only 10, because desorption from the
outer surface was higher. This is still a high asymmetry, since with a homogeneous
membrane the factor should have been unity.
This asymmetrical desorption pattern indicates that CM and MX membranes are
composed of at least two compartments. The bulk of the 2,4-D was contained in
the inner volume element, and it was desorbed through the inner surface. We call
this inner domain of the cuticle the sorption compartment (soco), and morphologically it is identical with the cuticular layer(s) seen in TEM (Sect. 1.4). The outer
domain across which only very small amounts of 2,4-D were desorbed is the cuticle
proper, and we refer to it as limiting skin or limiting layer (Fig. 6.16). Volumes and
thicknesses of these two layers cannot be deduced from desorption plots. As in 4 h
only 5% 2,4-D diffused across the outer surface of the CM, diffusion coefficients
in the limiting skin must have been very low and much lower than in the sorption
compartment. The data do not reveal if it is a wax layer on top of the cuticle or if the
barrier consists of waxes embedded in the outer fraction of the MX. A combination
of both is possible as well. In any event waxes are involved, since extracting them
reduced asymmetry greatly (Fig. 6.15).
When Mt /M0 (desorption through the inner surface) was plotted against the
square root of time (Fig. 6.15b), plots were not linear up to Mt /M0 equal to 0.5, as
would be expected with homogeneous membranes (Fig. 2.10b), but diffusion coefficients can still be estimated from the initial slope using (2.35). Since both CM and
MX are heterogeneous, these D-values are some kind of average characterising diffusion of 2,4-D in the sorption compartment (cuticular layer). For these calculations,
Fig. 6.16 Schematic drawing of a cross section of a cuticle showing the thin limiting skin and the
thick sorption compartment (not to scale). Modified from Bauer and Schnherr (1992)
179
the thickness () of the compartments which drained through the inner surface of
the membranes must be estimated. Using the weight average thickness (2.6 m),
which amounts to neglecting thickness of the limiting skin, mean diffusion coefficients for desorption from the Citrus CM and MX membranes are 3 1015 m2 s1
and 2 1015 m2 s1 respectively. Since thickness enters as the square (2.35), the
difference is not significant. Thickness of the cuticle proper ranges from 0.05 to
0.5 m (Jeffree 2006), and if it is assumed that in Citrus 10% of the mass represents limiting skin, diffusion coefficients for CM and MX are 2.2 1015 (CM) and
1.7 1015 m2 s1 (MX). These D values are a little smaller since is only 90% of
the total thickness of the cuticles. Averaging these four values, we obtain a mean D
of 2 1015 m2 s1 for desorption of 2,4-D from the sorption compartment through
the inner surface of Citrus CM and MX.
Desorption plots obtained with fruit (Lycopersicon esculentum, Capsicum
annuum) and Ficus decora leaf CM resemble those shown in Fig. 6.15. Again, in
6 h only 23% of the total amount of 2,4-D was desorbed through the outer surfaces of these CM. With MX membranes, efflux of 2,4-D across the outer surface
amounted to 1226%. Extraction of waxes increased efflux through the outer surface
of the MX significantly, but asymmetry was not eliminated. Diffusion coefficients
calculated from the first 3 min desorption intervals are 7 1015 m2 s1 (Ficus),
4 1014 m2 s1 (Capsicum) and 5 1014 m2 s1 (Lycopersicon) respectively. The
D values for fruit CM are larger than for leaf CM, but this may be related to extensive
cutinisation of anticlinal walls. This leads to overestimation of cuticle thickness by
factors of about 2 (Riederer and Schnherr 1985). If calculations are repeated using
half of the gravimetric thicknesses, diffusion coefficients become 9 1015 m2 s1
(Capsicum) and 1.4 1014 m2 s1 (Lycopersicon), which is still a little higher than
the value estimated for Citrus and Ficus leaf CM.
Asymmetry as revealed by these desorption experiments is remarkable. It is
excellent evidence that the CM and MX membranes have a limiting barrier at their
outer surfaces in which solute mobility is much lower than in the sorption compartment. With all fruit and leaf CM, efflux through these limiting skins amounted to
only 23% of the total 2,4-D. Asymmetry was smaller with MX membranes but it
was still pronounced, showing that waxes greatly contributed to barrier properties of
the limiting skin, but diffusion coefficients in cutin itself differ at the outer surface
and in the sorption compartment.
Extraction of waxes had little effect on diffusion coefficients in the sorption compartments. This is astounding, since these sorption compartments probably contain
embedded waxes. At least for Ficus cuticles, strong birefringence in the cuticular
layer has been demonstrated (Sitte and Rennier 1963), yet extraction of waxes had
little effect on diffusion coefficients in the sorption compartments (Schnherr and
Riederer 1988). Only waxes in the limiting skin reduce solute mobility, but D cannot
be calculated from simultaneous bilateral desorption, simply because solutes escape
nearly quantitatively through the inner surface of the membranes.
180
6 Diffusion of Non-Electrolytes
Fig. 6.17 Apparatus used for UDOS (unilateral desorption from the outer surface) experiments
181
formed, and lipophilic solutes are sorbed in these PLS vesicles. This maintains the
solute concentration in the water surrounding the vesicles at practically zero, and it
ensures good wetting of the waxy cuticle surfaces, because surface tension is lower
than in water. The desorption medium is periodically withdrawn quantitatively and
replaced by fresh medium. At the end of the experiment the cuticle exposed in the
orifice of the lid is cut out, and residual radioactivity in the CM is extracted with
scintillation cocktail. Radioactivity in desorption media and cuticles is determined
with a scintillation counter.
Radioactivity in the desorption media at time t is Mt and the sum of the radioactivity in desorption media and cuticle is M0 , which was routinely compared to the
amount applied; recovery was always 100%. Mt /M0 is the solute fraction desorbed,
and (1 Mt /M0 ) is the solute fraction remaining in the CM. Plotting the natural
logarithm of (1 Mt /M0 ) vs time always resulted in straight lines (Fig. 6.18). The
slopes of the plots are the rate constants (k ) as defined by the equation
ln 1 Mt M0 = kt.
(6.13)
These rate constants are related to permeance (P) as shown in (2.26), which for
convenience is repeated here
PA
ln (Cdonor /C0 )
=
= k
t
Vdonor
(6.14)
2.0
86
Capsicum CM
slope = 5.4 x 106 s1
78
63
1.0
Citrus CM
slope = 1.8 x 106 s1
0.5
39
0.0
0
0
20
40
60
80
Percentage desorbed
ln (1Mt /Mo)
1.5
100
Time (h)
Fig. 6.18 Unilateral desorption of pentachlorophenol from the outer surface of Citrus and Cap
sicum CM. Slopes of the plots are the rate constants (k ). (Redrawn from Bauer and Schnherr
1992)
182
6 Diffusion of Non-Electrolytes
with the exception that amounts (M) are used instead of donor concentrations
(Cdonor ). Equation (6.14) states that the donor concentration decreases exponentially
with time, while in UDOS the fraction of solute contained in the sorption compartment (1 Mt /M0 ) decreases exponentially with time. It is convenient to use
amounts rather than concentrations, because the volume of the sorption compartment is not known precisely (Fig. 6.16). Using amounts instead of concentrations
introduces no error, since Cdonor = M/Vdonor and the volume of the sorption compartment is constant during the experiment. At the beginning of the experiment, the
solutes are dissolved in the lipids (cutin and wax) of the sorption compartment, and
an aqueous donor phase is absent. Hence, the driving force in UDOS is not the concentration of an aqueous donor but the concentration in the sorption compartment.
The ratio of this two concentrations is the partition coefficient
Ksoco/water =
Csoco
Cwater
(6.15)
and this is taken care of by marking this type of permeance with an asterisk (P ).
With these definitions, (6.14) becomes
ln (Mt /M0 ) P Asoco
P
=
=
= k .
t
Vsoco
soco
(6.16)
183
Table 6.7 Comparison of partition coefficients and permeances determined at 25 C in the steady
state and with UDOS
CM
1
2
3
4
Steady state
UDOS
Kcuticle/buffer
P(m s1 )
P (m s1 )
Ksoco/buffer
P (m s1 )
416
396
326
398
1.05 108
1.49 108
4.76 108
11.20 108
2.52 1011
3.76 1011
14.60 1011
28.10 1011
400
386
325
389
1.75 1011
3.02 1011
12.60 1011
24.50 1011
PUDOS
Psteady
state
0.69
0.86
0.86
0.87
Taken from Bauer and Schnherr (1992). Donor solutions had a pH of 3.0
calculated from the mass of the CM, the volume of the donor solution, the decrease
in donor concentration, and the equilibrium concentration of the donor. The donor
solution was removed, and borax buffer was added as receiver and k was measured
in an UDOS experiment. P was calculated from (6.16) using the weight average thickness (CM ) of the CM, rather than the unknown thickness of the sorption
compartment (soco ).
Partition coefficients were virtually identical in the two types of experiments
(Table 6.7), except that Ksoco/buffer tended to be slightly lower, possibly because the
limiting skin was not yet in equilibrium after 3 h of loading. Steady state permeance (P) varied among CM by a factor of about 10, which is typical for CM of
most species. P values calculated for steady state experiments varied by the same
factor because Kcuticle/buffer varied between CM only slightly. Agreement between
P obtained from rate constants determined in UDOS experiments (6.16) and those
calculated from steady state data (6.17) is very good, considering that both permeances varied among CM by a factor of more than 10. This shows that both types of
experiment provide comparable data, and P can be calculated from rate constants
(k ) measured using UDOS.
P calculated as CM k (UDOS) is consistently smaller than P calculated
from steady state data (Table 6.7). The factor averaged over all four CM is 0.805,
and this cannot be attributed to differences in partition coefficients, which amount
for only 2% on average. The limiting skin has an unknown but finite thickness,
hence soco k should be smaller than CM k . However, P calculated from
rate constants were smaller than P calculated from steady state permeance P and
partition coefficients. It appears that CM systematically underestimates the real path
length.
184
6 Diffusion of Non-Electrolytes
P=
(6.18)
(6.20)
which shows that the rate constant characterises solute mobility in the limiting skin.
D could be calculated from the rate constant if the two thicknesses were known.
They are not known, however, but for the sake of argument reasonable assumptions
can be made.
For an order of magnitude estimate of D it suffices to assume that the limiting
skin has the same thickness of the cuticle proper seen in TEM. Jeffree (2006) has
summarised the available data and even though these are not always well-defined he
estimated that in most species the CP has a thickness ranging from 0.05 to 0.5 m.
To obtain thickness of the sorption compartment [equated to the cuticular layer(s)],
these values can be subtracted from total thickness. As already pointed out, weight
average thickness overestimates thickness of cuticles over periclinal walls due to
anticlinal pegs, and in fruits extensive cutinisation of cell walls in a multiple epidermis can occur (Schnherr and Riederer 1988). Since we have no alternative we have
to live with this situation, and since we only aim at an order of magnitude estimate
these assumptions can be tolerated.
Let total thickness be 11 and 2.5 m for pepper fruit and Citrus leaf CM respectively. Their limiting skins are taken to be 0.5 (Capsicum) and 0.25 m (Citrus).
With these thicknesses and the rate constants shown in Fig. 6.18, PCP diffusion
coefficients in Capsicum and Citrus CM calculated from (6.20) are 2.8 1017 and
1 1018 m2 s1 respectively.
In Fig. 6.19, a model calculation demonstrates the effect of thickness of the limiting skin on magnitude of diffusion coefficients, when total thickness (3 m) of the
CM is kept constant. With increasing thickness of the limiting skin, D increases.
When thickness of the limiting skin increases from 0.1 to 0.5 m, D increases by a
factor of 7.75. This shows that an order of magnitude estimate of D is possible, even
when the thickness of the limiting skin is not precisely known.
In most instances there is no need for calculating D, because rate constants can be
used as measures of solute mobility. A case in point is when plant species or solutes
are to be compared, or when effect of temperature and accelerators on solute mobility must be quantified. In determining rate constants, no assumptions regarding
thicknesses of limiting skin and sorption compartment must be made.
There is one assumption implicit in calculating rate constants using UDOS. In
all CM the bulk of the CM is the sorption compartment, in which the solutes are
185
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2.5e-18
2.0e-18
1.5e-18
1.0e-18
5.0e-19
0.0
Fig. 6.19 Effects of thicknesses of cuticular compartments on diffusion coefficient. Total thickness
of cuticle is 3 m, and rate constant was taken to be 1 106 s1
dissolved initially. It is implicitly assumed that desorption from the outer surface is
not limited by diffusion in anticlinal pegs and other portions of the sorption compartment remote from the limiting skin. This can be taken for granted as long as
diffusion coefficients in the limiting skin is 50100 times lower than in the sorption
compartment. Whenever this is the case, desorption plots (Fig. 6.18) are linear, and
in this case there is no need to worry.
Using simultaneous bilateral desorption, the diffusion coefficient of 2,4-D in the
sorption compartment was estimated to be 1014 to 1015 m2 s1 (Fig. 6.15). D values estimated from Fig. 6.18 are 1018 to 1019 m2 s1 , which is lower by more
than three orders of magnitude. We can also estimate D in the sorption compartment using unilateral desorption. If PCP is desorbed from the inner surface of the
CM a nonlinear plot is obtained with an initial slope of 0.0017 s1 (Fig. 6.20). This
is larger by a factor of 944 than measured for desorption from the outer surface
(Fig. 6.18). Rate constants decrease with time, because the sorption compartment is
heterogeneous, as was seen already in Fig. 6.15. Desorption from the outer surface
of MX-membrane was also non-linear, and linearity lasted only for 2 h (Fig. 6.20).
The initial rate constant was 155 times larger than that measured with Citrus CM.
After 2 h, rate constants decreased because diffusion in the sorption compartment
became rate-limiting. Comparing the initial slope obtained with MX with that of
UDIS demonstrates that PCP mobility in the outer layer of extracted CM is lower
by a factor of 6 than mobility in the sorption compartment (UDIS). This difference is too small to guarantee linear desorption plots until membranes are empty.
Apparently, diffusion from the anticlinal pegs to the outer layer of the MX was too
186
6 Diffusion of Non-Electrolytes
4
98
UDIS CM
95
86
Percentage desorbed
ln(1Mt /Mo)
slope 0.0017 s1
63
UDOS MX
slope 2.8 x 104 s1
0
0
3
Time (h)
Fig. 6.20 Unilateral desorption of pentachlorophenol from Citrus aurantium CM or MX. Desorption from the inner surface of the CM (UDIS) or desorption from the outer surface (UDOS) of MXmembranes. Initial slopes are indicated
slow and the distance too large. However, from the initial slopes obtained by UDOS,
valid mobilities can be estimated for the limiting skins of MX-membranes.
The UDOS experiment with MX demonstrates that solute mobility in the outer
layer of extracted CM is lower than in the sorption compartment. There is an outer
limiting layer in the MX, but mobility is much larger than mobility in the limiting
skin of the CM. Waxes in the limiting skin or on top of the CM reduced PCP mobility
155-fold.
187
Ilex paraguariensis
Vanilla planifolia
Hedera helix
Melicoccus bijugatus
Ginkgo biloba
Strophanthus gratus
Citrus aurantium
Prunus laurocerasus
Ilex aquifolium
Prunus serotina
Citrus grandis
Malus domestica cv. Gloster
Malus domestica cv. Golden Delicius
Pyrus pyrifolia
Pyrus communis
Malus baccata
Stephanotis floribunda
Prunus armeniaca
Pyrus communis
Pyrus pyrifolia
Juglans regia
Populus canescens
Tilia cordata
Prunus persica
(6.21)
188
6 Diffusion of Non-Electrolytes
Hedera helix
7
Malus domestica
6
5
Populus canescens
3
100
150
200
250
300
350
Fig. 6.22 The effect of molar volume (Vx ) of solutes on solute mobility (k ) in CM of three
different plant species. Averages of 1620 CM and 95% confidence intervals are shown. (Redrawn
from Buchholz et al. 1998)
and this is demonstrated in Fig. 6.22. Slopes of the lines are selectivity coefficients
( ) and the y-intercepts (k0 ) are the solute mobilities of a hypothetical compound
having zero molar volume (Vx ). Parameters of (6.21) are given in Table 6.8. The
species differed only in the y-intercepts, which varied from 2.33 (equivalent to
k0 = 4.68 103 s1 ) to 5.27 (5.63 106 s1 ). Thus, rate constants for a solute
with zero molar volume differed by a factor of 832. This may be compared to difference in bifenox mobility for the same range of species (Fig. 6.21), which is a
factor of 770. This is an excellent agreement in view of natural variability between
CM in rate constants (Fig. 6.21) and variability in y-intercepts (Table 6.8). Hence,
differences in solute mobility among species is fully accounted for by differences in
y-intercepts, which is a characteristic property of the species and is independent of
solute properties such as K and Vx .
Size selectivity ( ) varied among species between 0.007 and 0.012. Confidence intervals are relatively large, such that differences in are not significant.
Size selectivity was the same with all species, even though their k0 differed
by about three orders of magnitude. The mean value of over all species is
0.0095 mol cm3 , and provided k0 is known, the rate constant for any lipophilic
solute with equivalent volume between 100 and 350 cm3 mol1 can be calculated
using (6.21). For instance, for log k0 equal to 4.25 (pear leaf), mobility of a
solute having zero molar volume k is 5.62 105 s1 . If a solute has a molar vol1
ume of 100 cm3 mol , k is 6.31 106 s1 which is smaller by a factor of 8.9.
1
With Vx equal to 200 or 300 cm3 mol , k is 7.08 107 s1 and 7.94 108 s1
189
Table 6.8 Y -intercepts ( log k0 ) and size selectivity ( in mol cm3 ) measured at 25 C using
1
various solutes differing in molar volumes (cm3 mol )
Species
Populus canescens
Pyrus communis cv. Conference
Capsicum annuum
Stephanotis floribunda
Malus domesta cv. Golden Delicious
Pyrus communis cv. Bartletta
Pyrus communis MXa
Citrus aurantiuma
Strophantus gratus
Hedera helix
Ilex paraguariensis
Average
log k0 CI
CI
r2
2.33 0.62
3.66 0.39
3.95 0.38
4.11 0.44
4.11 0.18
4.25 0.36
1.99 0.57
4.28 0.53
4.94 0.36
5.22 0.41
5.27 0.80
0.011 0.002
0.009 0.002
0.009 0.002
0.007 0.001
0.010 0.002
0.009 0.003
0.009 0.003
0.012 0.002
0.009 0.002
0.009 0.004
0.010 0.003
0.0095
0.98
0.93
0.89
0.81
0.99
0.96
0.91
0.86
0.93
0.91
0.95
a Data from Baur et al. (1996b); all others were taken from Buchholz et al. (1998). CI is the 95%
confidence interval
respectively. Doubling molar volume from 100 to 200 cm3 mol1 reduces solute
mobility by a factor of 8.9, and increasing Vx threefold reduces mobility by a factor
of 79.3. These factors are the same no matter what the numerical value of k0 is,
because is the same for all species.
Using pear leaf cuticles, Baur et al. (1996b) studied the effect of extraction of
waxes on rate constants and size selectivity. This is the only UDOS study of size
selectivity in MX membranes. Extraction increased the y-intercept of (6.21), but
size selectivity was unaffected, and was the same as with CM. It is astounding that
extraction of waxes had no effect on size selectivity, while rate constants and the
y-intercept k0 increased by a factor of 182 (Table 6.8).
Solute mobility in plant cuticles at 25 C is completely determined by k0 and
, and this poses the question concerning their physical meaning. Size selectivity
is related to the free volume available to diffusion (Potts and Guy 1992), which is
the reciprocal value of 2.3 . In CM and MX the free volume of diffusion is
1
45.77 cm3 mol . Free volume of diffusion is proportional to viscosity, and since it
is the same in CM and MX it appears that viscosity of amorphous waxes and cutin in
the limiting skin of MX-membranes are the same. If waxes embedded in the limiting
skin do not reduce viscosity, which mechanism is then responsible for the effect of
waxes on solute mobilities (k0 and k ) in plant cuticles?
The only examples available are the pear leaf CM and MX. Extracting waxes
increased k0 by a factor of 182, and had no effect on size selectivity (Table 6.8).
Baur et al. (1996b) suggested that waxes increase the diffusion path in the CM. The
upper pear-leaf cuticle contains about 30 weight percent of waxes, and a substantial
portion of this occurs as epicuticular wax plates. Baur (1998) compared UDOS rate
constants for bifenox in the CM of Ilex paraguariensis and Pyrus pyrifolia prior
to and after stripping surface wax with cellulose acetate. Stripping did not increase
rate constants, while extracting total waxes with chloroform greatly increased them.
190
6 Diffusion of Non-Electrolytes
This suggests that surface wax did not contribute to barrier properties. However,
it is not known if stripping removed surface waxes completely or if a thin layer
remained. We discussed this problem in Chaps. 1 and 4. Baur (1998) proposed that
only waxes deposited in the limiting skin contribute to barrier properties by obstructing the diffusion path. Lipophilic solutes freely dissolve and diffuse in amorphous
waxes (Sects. 6.2 and 6.5), and the only candidates for obstructing the diffusion
path in amorphous waxes are crystalline wax plates (Riederer and Schreiber 1995).
We return to this problem when we discuss temperature effects on solute mobility
(Chap. 8).
191
2.5
95
2,4-D
2.0
92
-ln (1-Mt /M 0 )
1.5
86
0.047
1.0
78
0.026
tebuconazole
0.021
0.5
Percentage penetrated
0.17
63
urea
0.071
8 x 10-4
0.0
0
0
10
20
30
40
50
60
Time (h)
Fig. 6.23 Simulation of foliar penetration at 25 C using astomatous isolated Stephanotis CM.
Small aqueous droplets (2 l) were pipetted on the centre of the outer surface of the CM, and
during the first 48 h evaporation was prevented by 100% humidity over the donor droplets. At 48 h,
humidity was lowered to allow evaporation of solvent water, and desorption from the inner surface
was continued. Means of 1520 CM are shown. Numbers on regression lines are rate constants in
s1 . (Redrawn from Schnherr and Baur 1994)
192
6 Diffusion of Non-Electrolytes
exponentially with time. Rate constants were higher after droplet drying, but the
effect of drying differed among compounds. The effect was spectacular with urea,
where the two slopes differ by a factor of 93. Urea is a highly water soluble compound (1 kg urea dissolves in 1 kg water), and above 90% humidity it deliquesces.
On droplet drying, it was most likely present as concentrated aqueous solution, and
an increase in urea concentration by a factor of 93 implies that the volume of the
donor decreased by the same factor, because according to (2.19) Cdonor = M/Vdonor .
If permeance is constant and independent on urea concentration, rate constants
should be proportional to Adroplet /Vdroplet (2.26).
Tebuconazole and 2,4-D are both lipophilic (Appendix B), and their initial rate
constants were relatively high. These two compounds dissolve in the surface wax,
and the situation resembles that discussed in Sect. 6.2 when we dealt with the submersion technique. Surface waxes served as intermediate donor phase. With these
lipophilic solutes, equilibration between water and surface wax must have been fast,
and during the first 48 h the surface wax was the donor phase, and 60% (tebuconazole) to 70% (2,4-D) of the amount in the donor droplets penetrated into the receiver
in 48 h. Penetration of 2,4-D was a little faster than penetration of tebuconazole,
1
1
which has a greater molar volume (308 cm3 mol ) than 2,4-D (241 cm3 mol ).
Why rate constants of these two compounds increased on droplet drying is a matter
of conjecture. With 2,4-D, pH and degree of ionisation probably decreased during
droplet drying, while with tebuconazole the factor was only 2.2 and here an increase
in droplet area during drying could have been responsible. Change in droplet area
[cf. (6.14)] is of course also a factor to be considered with urea and 2,4-D.
These speculations show that simulation of foliar penetration produces very
complex data, and it is difficult to explain differences among chemicals and plant
species. This should not distract from the fact that SOFP can provide us with quantitative data about rates of penetration as affected by experimental conditions, which
can be close to the situation in the field. The method has been used extensively to
study the effects of humidity, adjuvants, plasticisers, wetting agents and temperature on rates of penetration of ionic species (Chap. 5). No other method discussed
in Chap. 6 is as versatile as SOFP.
193
cuticular waxes of grape berries had previously been used by Grncarevic and Radler
(1967) to assess their effect cuticular transpiration. A refined method allowing the
measurement of diffusion coefficients of lipophilic molecules in cuticular wax was
developed with barley leaf wax (Schreiber and Schnherr 1993b).
194
6 Diffusion of Non-Electrolytes
1.0
0.10
Lindane
Mt / M o
0.9
Tetracosanoic acid
0.09
0.8
0.08
0.7
0.07
0.6
0.06
0.5
0.05
0.4
0.04
0.3
0.03
0.2
0.02
0.1
0.01
0.0
0.00
0
600
1200
2400
3000
Time (min)
Fig. 6.24 Desorption of 14 C-labelled lindane and 14 C-labelled tetracosanoic acid from reconstituted barely wax. Relative amounts desorbed (Mt /M0 ) vs time (min) are shown. Data redrawn
from Schreiber and Schnherr (1993b)
by adding the amounts desorbed at each sampling time plus the residual amount
in wax. Mt is the total amount desorbed at each sampling time. Non-linear desorption kinetics are obtained when relative amounts (Mt /M0 ) are plotted vs time t
(Fig. 6.24).
Within 48 h about 95% of the 14 C-labelled lindane could be desorbed, whereas
only 9% of the 14 C-labelled tetracosanoic acid was desorbed in 72 h (Fig. 6.24).
When relative amounts desorbed were plotted vs the square root of time, desorption
kinetics could be linearised up to 50% desorption (Fig. 6.25).
Using (2.35) and the slopes of the linear regression lines fitted to the desorption
kinetics (Fig. 6.25), diffusion coefficients D for lindane and tetracosanoic acid can
be calculated if the length of diffusion in the wax layer is known. The thickness
of the wax layer for each individual wax sample was determined by weighing the
aluminium disks prior to and after wax reconstitution and assuming a wax density
of 0.9 g cm3 . On average, reconstituted wax layers had a thickness between 1.5
and 2.5 m. With a slope of 0.0246 min1/2 for lindane and a wax layer of 1.67 m
thickness, the calculated D is 5.55 1018 m2 s1 . For tetracosanoic acid, the wax
layer had a thickness of 1.52 m and the slope was 0.00127 min1/2 . This results in
a D of 1.22 1020 m2 s1 . Thus, D of lindane is more than two orders of magnitude larger than D of tetracosanoic acid. This difference in solute mobility explains
why desorption of lindane from barley wax proceeds much faster than desorption of
tetracosanoic acid.
0.10
0.9
M t / Mo
195
Lindane
0.8
0.08
0.7
0.07
0.6
0.06
0.5
0.05
0.4
0.04
0.3
0.03
0.2
0.02
0.1
0.01
0.0
0.00
0
10
20
Tetracosanoic acid
0.09
30
40
50
10 20 30 40 50 60 70
196
6 Diffusion of Non-Electrolytes
Table 6.9 Diffusion coefficients D and molar volumes Vx of lipophilic molecules in reconstituted
wax of Hordeum vulgare, Prunus laurocerasus, Ginkgo biloba and Juglans regia
D 1017 (m2 s1 )
Substance
BA
4-NP
SA
2,4-D
AT
MET
TRI
TB
BIT
Vx (cm3 mol )
Hordeuma
Prunusb
Ginkgob
Juglansb
93
95
99
138
162
162
219
241
267
2.4
1.9
1.2
0.36
0.58
0.19
3.54
3.23
2.74
1.63
1.15
0.91
4.37
3.21
2.01
5.59
3.45
2.22
Benzoic acid (BA), 4-nitrophenol (4-NP), salicylic acid (SA), 2,4-dichlorophenoxyacetic acid (2,4D), atrazine (AT), metribuzin (MET), triadimenol (TRI), tebuconazole (TB), bitertanol (BIT)
a Data from Burghardt et al. (1998)
b Data from Kirsch et al. (1997)
(6.22)
197
16.2
16.4
BA
log D (m2/ s)
SA
16.6
4-NP
2,4-D
16.8
AT
17.0
MET
17.2
90
100
110
120
Vx
130
140
150
160
170
(cm3/mol)
Fig. 6.26 Logarithms of the diffusion coefficients D of lipophilic molecules in reconstituted wax
of Prunus laurocerasus as a function of the molar volumes Vx of the molecules. Benzoic acid (BA),
4-nitrophenol (4-NP), salicylic acid (SA), 2,4-dichlorophenoxyacetic acid (2,4-D), atrazine (AT),
metribuzin (MET). Error bars represent 95% confidence intervals. Data from Kirsch et al. (1997)
(mol cm3 )
log D0 (m2 s1 )
r2
0.0065
0.0074
0.0070
0.0083
15.94
15.79
15.67
15.83
0.91
0.97
0.91
0.97
This model, originally developed by Potts and Guy (1992), states that the logarithm
of D linearly decreases with increasing molar volume Vx . The slope (mol cm3 )
gives the size selectivity, characterizing the dependence of D on Vx , whereas
D0 (m2 s1 ) represents the diffusion coefficient of a hypothetical molecule having a
molar volume of zero. Regression equations fitted to plots of log D vs Vx gave very
similar values for and D0 (Table 6.10), indicating that mobility of the investigated
lipophilic molecules in reconstituted wax of the four species was similar.
Calculating the means of and D0 (Table 6.10), a more general equation can be
established, which permits the prediction of D in reconstituted cuticular wax for an
arbitrary lipophilic molecule of any molar volume:
198
6 Diffusion of Non-Electrolytes
(6.23)
This equation can be very helpful when D is not easily measured due to experimental limitations. As mentioned above, solubility of small polar molecules, such
as water, urea or glucose, is too low in the amorphous phase of reconstituted cuticular wax, and D cannot be determined experimentally. However, using (6.23), D of
these compounds in wax can be estimated. For example, for water having a Vx of
18 cm3 mol1 , a D of 1.23 1016 m2 s1 can be calculated.
Size selectivities measured with UDOS experiments for a similar set of lipophilic
molecules and CM isolated from 11 species ranged from 0.007 to 0.012
(Table 6.8). Mean size selectivity for CM was 0.0095 (Table 6.8), which is somewhat larger than mean size selectivity of isolated wax, which had a value of 0.0076
(6.23). Nevertheless, this comparison shows that size selectivities in reconstituted
cuticular wax are in a similar range to that of size selectivity for cuticular membranes. This is important evidence that D values obtained in diffusion experiments or
predicted from (6.23) are reliable since they are comparable to values obtained from
isolated CM. Size selectivities measured for linear long-chain aliphatic molecules
in reconstituted wax of Hordeum, Fagus and Picea were somewhat higher, ranging
from 0.015 to 0.020 (Schreiber and Schnherr 1993b; Schreiber et al. 1996a).
However, these experiments included a very different set of compounds, and radiolabelled probes were always added to the wax prior to reconstitution. Therefore,
a direct comparison with the results obtained for lipophilic molecules as they are
listed in Table 6.9 should not be made.
P wax
.
Kww
(6.24)
Equation (6.24) states that D (m2 s1 ) and P/Kww (m s1 ) should only differ by the
thickness of the wax layer wax (m). D (Table 6.9), Kww (Table 6.2) and P have been
199
10.0
10.2
BA
SA
10.4
4-NP
10.6
2,4-D
10.8
AT
11.0
MET
11.2
90
100
110
120
130
140
150
160
170
Vx (cm3/mol)
Fig. 6.27 Logarithms of the ratios Pcm /Kww of lipophilic molecules in Prunus laurocerasus CM
as a function of the molar volumes Vx of the molecules. Benzoic acid (BA), 4-nitrophenol (4-NP),
salicylic acid (SA), 2,4-dichlorophenoxyacetic acid (2,4-D), atrazine (AT), metribuzin (MET). Data
from Kirsch et al. (1997)
measured for cuticles of Prunus, Ginko and Juglans (Kirsch et al. 1997). Isolated
CM (Pcm ) or leaf disks (Pleaf ) as described in Sect. 6.2.3 were used. As shown for
Prunus laurocerasus CM, a plot of Pcm /Kww vs. Vx gives a reasonable correlation
(Fig. 6.27), as was also observed with diffusion in reconstituted Prunus laurocerasus
wax (Fig. 6.26).
Using (6.22), regression equations similar to those obtained for diffusion in
reconstituted wax (Table 6.10), were derived for transport across isolated CM and
leaf disks of the three species (Table 6.11). From these regressions, size selectivities
were obtained for the transport across CM cuticles and for non-isolated cuticles of
leaf disks. Size selectivities ranged from 0.0074 to 0.013, and large differences
between intact leaves and isolated CM were not observed. This is good evidence that
isolation of the cuticle does not alter transport properties. The mean value for all
in Table 6.10 is 0.0073. This is similar to the mean obtained with CM (Table 6.8).
Cuticles appear to be very robust, since comparable results were obtained with four
different experimental approaches: (1) diffusion in wax (Sect. 6.5.1), (2) UDOS
(Sect. 6.3.2), (3) steady state penetration across the isolated cuticle (Sect. 6.2.1),
and (4) steady state penetration into leaf disks (Sect. 6.2.3).
Path length of diffusion calc can be calculated dividing D0 in wax (Table 6.10)
by D0 obtained from transport experiments across CM and intact leaf surface
(Table 6.11). Values obtained for the thickness of the transport-limiting wax barrier
range from 50 nm (Juglans CM) to 800 nm (Prunus CM). These are reasonable values, since they are of the same order of magnitude as those determined from wax
200
6 Diffusion of Non-Electrolytes
Table 6.11 Slopes , y-intercepts D0 and coefficients of determination r2 of the regression equations fitted to plots of log Pcm /Kww and Pleaf /Kww vs Vx . Path length of diffusion calc are calculated
by dividing D0 obtained in wax (Table 6.10) by D0 measured for CM and leaf respectively. Path
length of diffusion meas are calculated from wax coverage determined for the same set of cuticles
used in transport experiments (Kirsch et al. 1997)
Species
(mol cm3 )
Prunus laurocerasus
CM
Prunus laurocerasus
Leaf
Ginkgo biloba CM
Ginkgo biloba Leaf
Juglans regia CM
Juglans regia Leaf
D0 1010
(m2 s1 )
r2
calc (nm)
meas (nm)
calc /meas
0.0074
1.93
0.93
839
1,600
0.52
0.012
5.51
0.99
294
1,600
0.18
0.0095
0.010
0.013
0.011
13.01
20.20
30.13
13.14
0.94
0.94
0.97
0.93
164
106
49
113
210
210
570
570
0.78
0.50
0.09
0.20
coverage of the CM (Table 6.11). However, it is obvious that path length of diffusion meas , obtained from total wax coverage is always higher than calc . This could
indicate that only a fraction of the total wax (0.10.8) contributes to the limiting
barrier, while the remainder is deposited as intracuticular wax in cuticular layer(s).
Results of diffusion experiments in reconstituted wax agree fairly well with
results of transport experiments using isolated cuticles and leaf disks. Size selectivities are comparable, and reasonable values for the thickness of the transport
limiting barrier of the CM are obtained. This justifies the following conclusions:
(1) The transport-limiting barrier of the CM for lipophilic molecules is formed by
cuticular waxes deposited in/on the limiting skin, (2) water penetrates cuticles using
two parallel pathways, the waxy pathway and aqueous pores (Chap. 4), and (3) penetration of ionic compounds is restricted to aqueous pores, and the waxy pathway
cannot be accessed (Chap. 5).
Several micrometres away from the living epidermal cell, wax molecules spontaneously arrange themselves, which leads to the formation of an efficient transport
barrier. Cuticular waxes deposited at the outer surface of the CM follow the rules of
self-organisation. When wax is reconstituted on an artificial surface, barrier properties of reconstituted waxes are very similar as those in isolated CM and intact
leaves. Sorption and diffusion in waxes can give valuable insights into the structure
and function of the cuticular transport barrier. This experimental approach has been
used to analyse the effect of plasticisers on solute diffusion in CM and waxes. This
is the topic of Chap. 7.
Problems
201
Problems
1. The mean log Kcw of PCP is 4.56 and the mean log Kww is 3.55 (Table 6.1).
How much (mol) of PCP is sorbed in 1 mg CM and in 100 g waxes after equilibration in a large volume of an external aqueous PCP solution of 1 mg l1 ?
What is the ratio of the amounts of PCP in CM and wax?
2. At 25 C, water solubility of PCP is 20 mg l1 and the mean Kow is 11,749
(Table 6.1). Calculate Kcw from Kow (6.2) and from water solubility (6.3).
3. Let the Kcw of two solutes be 30 or 0.03. Pieces of 1 mg CM are equilibrated
aqueous solutions of 1 mg l1 . How much is sorbed in the CM, and which
amount is contained in a thin water film of 0.3 mg which remains on the CM
after equilibration. How much of the solutes is sorbed in the CM and in the
water film?
4. A piece of CM having a mass of 1 mg is equilibrated in 1 ml (=1 g) aqueous
buffer which contains 20 mg kg1 non-dissociated 2,4-D. Calculate the final
amounts of 2,4-D in the CM and in the solution. What is the final amount of PCP
in the cuticle and in the solution, assuming the same experimental conditions?
5. In Fig. 6.2, hold-up times of up to 45 h are shown, while in Fig. 6.5 the plot
amount penetrated vs time intersects the y-axis at a positive value. What is the
reason?
6. Diffusion coefficients in leaf CM (Table 6.3) are much lower than in leaf MX
membranes (1.3 1014 m2 s1 ). In Citrus this ratio is 241, while the effect of
extraction on permeance was 1,767. Which other factors might have contributed
to the very low P of the CM?
7. Using (6.7), data of Table 6.1 and an equivalent molar volume of 2,4-D of
138 cm3 mol1, calculate permeance for 2,4-D of Citrus CM. How good is this
estimate?
8. With compartment sizes given in Table 6.5, calculate Mt /M0 for compartments 1, 2 and 3 after 180 min of desorption. Use (6.10).
9. Rates of penetration of lipophilic solutes into conifer needles are proportional
to sorption in surface wax and cuticles (Fig. 6.9). How can this be explained?
10. When calculated using the specific surface area of the needles, permeance
increased with partition coefficient of the solutes (Table 6.6). What does this
imply?
11. Half-time of penetration from a sessile droplet depends on the volume of the
droplet and the contact area between droplet and cuticle (6.12) You measured
permeance using droplets having contact angles of 90 . In a second experiment
you added a small amount of wetting agent, such that the droplet spread on the
cuticle. Half-time was reduced by factor of 0.5. Did the wetting agent increase
permeance of the cuticle and how would you test this?
12. How would you interpret the autoradiographs seen in Fig. 6.14?
13. The average diffusion coefficient calculated from a desorption experiment
of 2,4-D in the inner sorption compartment of the Citrus CM is about 2
1015 m2 s1 . With a steady state penetration experiment, D of 5.4
202
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
6 Diffusion of Non-Electrolytes
1017 m2 s1 was determined from the hold-up time (Table 6.3). How do you
explain this?
What is the difference between k and k ?
Size selectivity is the same with all species investigated. What does this
imply?
k values measured with CM from various plant species vary by more than
three orders of magnitude (Fig. 6.21). Why?
1
Using (6.21) calculate log k for bifenox (Vx = 2.67 cm3 mol ) and the species
listed in Table 6.8, and compare these values with those given in Fig. 6.21. What
is the ratio log k (measured)/logk (calculated) for these eight species?
Experimental values for log k0 are available only for the species listed in
Table 6.8. If it is assumed that the is equal to 0.0095 mol cm3 for cuticles of
all species, logk0 can be calculated if only one experimental value for logk is
known for this species. How would you do that?
Rate constants of desorption (k ) of PCP from the second compartment of
barley leaves and conifer needles range from 1.4 104 to 3.7 104 s1 .
Rate constants of desorption from the outer surfaces of Capsicum and Citrus
CM are 5.4 106 and 1.8 106 s1 respectively (Fig. 6.18). What could be
responsible for this large difference in the two types of experiments?
Using (2.26), calculate urea permeance of Stephanotis CM prior to and after
droplet drying. Assume that initial droplet volume was 2 l and that it decreased
by a factor of 93 on droplet drying. Contact area between droplet and CM was
0.125 cm2 and it did not change during droplet drying.
A lipophilic molecule can be desorbed from a reconstituted wax layer of
120 g cm2 at a rate of 0.01 min1/2 . What is the diffusion coefficient D in
m2 s1 ? What is the effect on slope if the thickness of the wax layer increases
by a factor of 2?
What is the diffusion coefficient D in m2 s1 of a molecule having a molar
1
volume Vx (cm3 mol ) of 200?
What is the thickness in m of the transport-limiting barrier of cuticular wax,
if the permeance P is 5.01011 m s1 , the wax/water partition coefficient Kww
is 35 and the diffusion coefficient D is 8.5 1018 m2 s1 ?
Solutions
1. The molecular weight of PCP is 266 g mol1 (Appendix B), hence the molar
concentration of PCP is 3.76 106 mol l1 . Using (6.1), we calculate that
in 1 mg CM 1.36 107 mol PCP are sorbed, and in the wax sample of
100 g 1.33 109 mol PCP. The cuticle contains about 100 times more PCP
than the wax sample.
2. Kcw calculated from (6.2) is 10,113. This value is 3.6 times lower than the
experimental Kcw value. Kcw calculated from (6.3) is 3,765. This value is 9.6
times lower than the measured Kcw value.
Solutions
203
5.
6.
7.
8.
9.
1 mg
407 1000
mg Mwater . Hence, MCM + Mwater = 20 g and MCM is 0.407 Mwater .
Combining these two equations, we obtain 20 g-Mwater = 0.407Mwater . We next
divide both sides of this equation by Mwater , and after rearranging we obtain
Mwater = 20 g/1 + 0.407 = 14.21 g. Thus, after equilibration the amount of
2,4-D in water is 14.21 g and the amount in the CM is 20 g 14.21 g =
5.79 g. Thus, about 25% of the initial amount of 2,4-D are sorbed in the cuticle at equilibrium, and 75% remain in the external solution. With PCP having
a mean Kcw of 36,308 (Table 6.1), it can be calculated that 19.46 g are in
the cuticle at equilibrium, whereas the external solution contains only 0.54 g.
Thus, at equilibrium 97% of the PCP will be sorbed in the cuticle. This calculation is essential for the experimental design, since in the case of PCP nearly
all of the PCP will be sorbed to the cuticle and rarely will anything stay in the
donor solution, making the experimental determination of Kcw difficult. This
problem can easily be solved using an external donor solution of 50 ml instead
of 1 ml.
In steady state experiments with CM the appearance of solutes in the receiver
solution is measured, and it takes some time before the first solutes have
penetrated the CM. When fluxes are measured by the submersion technique
accumulation in the wax, the cuticle and the leaf tissue are estimated, and these
processes are almost instantaneous.
In calculating D, the thickness enters as the square, and with MX membranes
total thickness results in relatively good D values, as seen from the fact that
Kcalc. and Kdet for Citrus MX are similar. The limiting barrier of the CM is only
a fraction of the total thickness, and this introduces large errors in both D and K.
The calculated P is 1.35 1010 m s1 , while the value in Table 6.3 P is
2.8 1010 m s1 . The agreement is quite good, considering natural variability
among individual CM and CM lots of different origins.
For CPT1 , 0.15 is obtained, and for CPT2 , 0.086. That means that in CPT3 is
(1 0.236) = 0.764. That is, 76.4% of the PCP are desorbed in 180 min.
In this type of experiment, sorption in epicuticular wax and cuticles are the first
steps in foliar penetration. Amounts sorbed are proportional to the amount of
wax (which varied among species) and to the partition coefficient Kww (which
varied among solutes). Rates of penetration are proportional to permeance, and
permeance is proportional to solute concentration in the waxy barrier (6.6).
204
6 Diffusion of Non-Electrolytes
10. Diffusion coefficients in the barrier must have been similar for all solutes.
11. If the ratio volume/area decreased by a factor of 0.5 and the half time by the
same factor, this implies that P was constant.
12. The wetting agent improved the contact between donor solutions and cuticle.
This increased contact area and uniformity of rates of penetration. As Tween 20
is not an accelerator adjuvant (Chap. 7) and Alar is an ionic solute, this is the
best explanation.
13. In steady state penetration, diffusion in the waxy limiting skin is rate-controlling,
while in simultaneous bilateral desorption the limiting skin is not involved
because most solutes are desorbed from the inner surface of the CM.
14. They differ in the nature of the donor. With a liquid donor, (2.27) k is determined. If solutes dissolved in cutin and wax as in UDOS, the rate constant (k )
is marked with an asterisk. k is independent of the partition coefficient, while
k depends on K.
15. Diffusion of lipophilic solutes proceeds in the amorphous wax fraction, and
fluidity of this fraction is apparently the same in waxes of all species.
16. Differences among species in solute mobility observed with the same solute are
proportional to k0 , which reflects differences in the tortuosity factors.
17. These ratios vary between 0.87 and 1.03 and the average of these values is 0.95,
which is not bad since different populations were used for these determinations.
18. According to (6.21), the product Vx must be added to log k .
19. If the same solute is used for determining k , differences in k among species
are proportional to the ratio A/Vdonor (6.14) and (6.16).
20. Prior to droplet drying P was 1.22 107 m s1 , and after droplet drying it was
1.28 107 m s1 . Hence, permeance was independent on urea concentration.
21. A thickness of 1.33 m can be calculated by dividing the amount of reconstituted wax of 120 g cm2 by wax density of 0.9 g cm3 . Using (2.35), D is
3.47 1017 m2 min1 or 5.79 1019 m2 s1 . Increasing the thickness of the
wax layer by a factor of 2 leads to a four-fold smaller slope, because at constant
D the product of 2 slope2 must be constant.
22. Using (6.23), a D of 5.25 1018 m2 s1 can be calculated.
23. Rearranging (6.24) or (2.18), a thickness of 5.95 m can be calculated.
Chapter 7
Many agrochemicals are sprayed on leaves of weeds and crop plants. Foliar
application minimises contamination of the soil and inactivation or degradation of
active ingredients by soil microorganisms. Binding to constituents of the soil is also
avoided. Systemic active ingredients must penetrate cuticles before they reach their
sites of action in the leaves or in other organs of the plants following translocation
(Kirkwood 1999). Pesticides are always formulated to improve wetting, deposition,
rain fastness and rates of cuticular penetration. Formulations are mixtures of active
ingredient, solvents, carriers, emulsifiers, wetting agents, etc. Compounds added to
active ingredients are called adjuvants. Most adjuvants are biologically inert, but
they improve biological performance (Kirkwood 1993). Surface active agents (surfactants) are typical adjuvants, and among other things they improve adhesion and
spreading of spray droplets on the leaf surface. Surfactants may also act as emulsifiers for active ingredients having a low water solubility, and after droplet drying
they can maintain the spray deposits on the cuticle in the liquid state by solvent and
by hygroscopic action (Baur 1999; Baur et al. 1997b, 1999; Tadros 1987).
Some adjuvants increase diffusion coefficients of solutes in wax and cutin. This
is accomplished by increasing fluidity of waxes and cutin polymer chains. As a
consequence, permeability of cuticles to solutes is increased (Schnherr and Bauer
1994). In the technical polymer literature, compounds which render brittle polymers more flexible by increasing fluidity of polymer chains are called plasticisers.
They intercalate between polymer chains, and they are added to the polymer melt
during production (Gchter and Mller 1990). Plasticisers useful for increasing diffusion coefficients of solutes in cuticles have been termed accelerators (Schnherr
1993a, b). Some surfactants are very effective plasticisers, but surface activity is not
a prerequisite for the plasticising activity. Accelerators must be added to the formulation, and they are applied to the cuticle at the same time as the active ingredient.
Hence, it is a prerequisite for their usefulness that they penetrate faster into the waxy
limiting barrier of the cuticle than the active ingredient, and they should remain
sorbed in the wax until most of the active ingredient has penetrated the cuticle.
In this chapter we deal with the mechanistic aspects of sorption and diffusion
of plasticisers in wax and in cuticles, and their effect on permeability. All other
205
206
effects of adjuvants which occur on the outer surface of the cuticle (spreading,
adhesion, inhibition of desiccation of the spray droplets, partitioning between the
deposit and the cuticle) will not be considered, although they can significantly affect
foliar penetration (Baur 1998, 1999; Baur et al. 1997b, 1999; Tadros 1987).
207
102
101
cmc
106
105
104
103
Aqueous concentration of C12E8 (mol/L)
102
Fig. 7.1 Wax/water partition coefficient (Kww ) of octaethylene glycol monododecyl ether (C12 E8 )
for the system reconstituted barley wax/water. Error bars represent 95% confidence intervals.
Redrawn from Schreiber (1995)
the wax when external concentration of 14 C-labelled C12 E8 was increased (Fig. 7.1).
Kww is calculated in the usual way as the ratio of the internal and external concentrations of C12 E8 (6.1). Above the cmc, the partition coefficient Kww is constant
and independent of the external concentration (Fig. 7.1). This is due to the fact that
above the cmc all additional surfactant molecules form micelles, and the concentration of free C12 E8 molecules dissolved in water remains constant. Adding more
surfactant increases the number of micelles, but there is no increase of C12 E8 sorbed
in the wax. Correct Kww values are only obtained when cmc is used as external
concentration, not total surfactant concentration.
The formation of micelles also affects the sorption of lipophilic solutes in wax.
The Kww measured with 14 C-labelled pentachlorophenol (PCP) is about 3,500
(Table 6.2 and Fig. 7.2). It is not affected by C12 E8 as long as the cmc is not reached
(Fig. 7.2). If the C12 E8 concentrations exceeds the cmc, micelles are formed and
apparent Kww of PCP decreases, because PCP dissolves not only in the wax but also
in lipophilic micelles (PCP is solubilised). Thus, above the cmc PCP is in equilibrium between lipophilic wax, lipophilic micelles and the aqueous phase. Increasing
the number of micelles results in increasing amounts of PCP solubilised in micelles,
and less is sorbed in wax. This leads to a decrease of the apparent Kww . This should
be taken into account when calculating partition coefficient of surface active compounds or of lipophilic compounds in the presence of micellar solutions of surface
active compounds.
Kww have been determined for a large number of monodisperse alcohol ethoxylates and reconstituted waxes from three different species (Table 7.1). Partition
208
104
103
102
cmc
101
105
104
103
102
Fig. 7.2 Wax/water partition coefficient (Kww ) of pentachlorophenol (PCP) for barley wax as
affected by increasing concentrations of octaethylene glycol monododecyl ether (C12 E8 ) in the
external solution. Error bars represent 95% confidence intervals. Redrawn from Schreiber (1995)
coefficients of the alcohol ethoxylates varied over a range of about six orders of
magnitude, while the variability between reconstituted waxes from different plant
species was only about one order of magnitude (Table 7.1). Kww of Stephanotis wax
were always significantly higher by a factor of nearly 10 than Kww of Hordeum and
Chenopodium waxes, the latter two being identical within experimental error. This
pronounced difference is attributed to differences in the degree of crystallinity of
the reconstituted waxes. Wax composition of Hordeum and Stephanotis has been
analysed by gas chromatography and mass spectrometry (Simanova et al. 2005).
Chemical composition of barley wax is very homogeneous, with nearly 90% of
the wax composed of primary alcohols. Stephanotis wax is heterogeneous because
seven different substance classes are present in about equal amounts. Therefore,
barley wax has a higher degree of crystallinity than Stephanotis wax and thus barley wax contains viewer sorption sites. Chenopodium wax apparently has a similar
degree of crystallinity and a similar molecular structure to that of barley wax. Kww
of barley wax and lipophilic solutes are also low (Table 6.2).
The large variability in Kww values of monodisperse alcohol ethoxylates
decreases when the number of the polar ethylene oxide units (Ey ) is increased, while
it increases with the number of the carbon atoms Cx in the alcohol:
log Kww = 2.73 + 0.54Cx 0.23Ey (barley wax)
log Kww = 2.43 + 0.53Cx 0.24Ey (Chenopodium wax)
(7.1)
(7.2)
(7.3)
209
Table 7.1 Wax/water partition coefficients Kww of monodisperse alcohol ethoxylates in reconstituted wax of Hordeum vulgare, Stephanotis floribunda and Chenopodium album. Cx gives the
number of carbon atoms of the fatty alcohol, and Ey refers to the number of ethylene oxide units
in the polar part of the alcohol ethoxylates
Compound
C4 E2
C6 E3
C8 E4
C10 E5
C10 E8
C12 E2
C12 E3
C12 E4
C12 E5
C12 E6
C12 E7
C12 E8
C14 E3
C14 E5
C14 E6
C14 E7
C14 E8
C16 E3
C16 E8
cmc(mol kg1 )a
0.589
0.06
0.0062
0.00063
0.0012
0.000028
0.000035
0.000043
0.000053
0.000066
0.000079
0.000098
0.0000029
0.0000044
0.0000054
0.0000066
0.0000081
0.00000024
0.00000068
Kww
H. vulgare
0.083d
0.83d
4.9d
35.7d
5.6e
2,000e
1,300e
670e
400e
201d
160e
104b
1,561d
1,200e
12,350d
S. floribundab
C. albumc
21,125
7,909
4,439
2,626
962
1,610
687
268
203
109
19,700
8,040
3,700
1,410
231,000
13,700
a Calculated
With all three wax samples, log Kww decreased by the factor of 0.23 to 0.24
for each additional ethylene oxide (E) unit. For barley (7.1) and Chenopodium wax
(7.2), log Kww increased by the factor of 0.530.54 for each additional C atom.
Equations for barley and Chenopodium wax are identical within experimental error
(Burghardt et al. 1998, 2006). With Stephanotis the number of C atoms was constant
(C12 ), and only Ey was varied (Simanova et al. 2005). Hence, (7.3) is only available
in a reduced form describing the influence of Ey units on Kww . These results are
consistent with data published for linear alcohols and fatty acids by Dunn et al.
(1986), from which it can be calculated that for each -CH2 group added log Kow
increased by a factor 0.550.52. Thus, the influence of the number of E and C units
on log Kww is similar for all three wax samples; however, the absolute values can
vary by a factor of 10 depending on plant species. Using (7.1)(7.3), Kww can be
estimated accurately for other monodisperse alcohol ethoxylates.
Cmc of surfactants and their lipophility (i.e., Kww ) are related (Table 7.1). With
increasing lipophility of the surfactants, micelles form at lower concentrations. The
maximum concentration (g kg1 ) of alcohol ethoxylates sorbed in reconstituted
210
(7.4)
A similar equation was obtained for Chenopodium wax (Burghardt et al. 2006).
max
logCwax
= 1.61 0.104Ey (Chenopodium wax)
(7.5)
Maximum amounts of surfactant molecules which dissolve in wax are given by the
product of the cmc and the Kww . In most experiments, concentrations of the alcohol
ethoxylates far above the cmc are used. The variability in maximum amounts of
alcohol ethoxylates sorbed in reconstituted waxes is much lower than is suggested
by the tremendous variability of Kww (Table 7.1).
These considerations are valid only for aqueous solutions of alcohol ethoxylates.
The situation changes when treatment solutions dry, which is the situation after
spray applications in the field. Structures of these neat surfactant residues on the
cuticle and penetration into the cuticle have not been investigated.
(7.6)
This equation resembles (7.1) and (7.2). For each C atom log Kmxw increases again
by a factor of 0.52, and for each E unit log Kmxw decreases by a factor of 0.17
(7.6). This is excellent evidence that the amorphous environments in cutin and wax
in which alcohol ethoxylates are sorbed have similar physicochemical properties.
Cutin and waxes are composed of methyl and methylene groups with small amounts
of oxygen (Chap. 1). Kmxw values for alcohol ethoxylates are highly correlated with
Kww values (Fig. 7.3), but the former are higher by about one order of magnitude.
Linear regression equations quantitatively account for this correlation.
Equation (7.7) applies to barley wax, and Citrus MX (Burghardt et al. 1998) and
(7.8) to Chenopodium wax and Prunus MX (Burghardt et al. 2006):
log Kww = 1.06 + 1.00 log Kmxw
log Kww = 1.04 + 1.05 log Kmxw
(7.7)
(7.8)
211
105
104
C16E8
C14E7
103
K ww
C12E8
C12E6
102
C10E5
C8E4
101
100
C4E2
C6E3
10
102
101
100
101
103
102
104
105
106
K mxw
Fig. 7.3 Correlation between wax/water partition coefficients (Kww ) and cuticle/water partition
coefficients (Kmxw ). Redrawn from Schreiber et al. (1996b)
Reconstituted waxes from barley and Chenopodium leaves are solid and partially
crystalline phases, and they offer fewer sorption sites for alcohol ethoxylates than
the amorphous MX of Citrus and Prunus; for this reason, Kww are lower than Kmxw .
A similar observation had been made with lipophilic solutes lacking surface actvity
(Sect. 6.1) where Kww and Kcw are compared.
These results are specific for barley and Chenopodium wax, and should not be
extrapolated to waxes of other species. With Stephanotis wax, considerably higher
Kww were observed (Table 7.1). Maximum concentrations (g kg1 ) of alcohol
ethoxylates sorbed in Citrus MX (7.9) are a function of Ey (Riederer and Schreiber
1995), as was previously shown for wax [(7.4) and (7.5)].
max
logCwax
= 2.07 0.044Ey
(7.9)
212
As observed with alcohol ethoxylates (Table 7.1), partition coefficients for n-alkyl
esters are again a factor of about 10 higher for Stephanotis wax than for barley
wax. With increasing number of C atoms of the dicarboxylic acids and esterified
alcohols, Kwrec increases and the following regression equations were obtained for
barley (7.10) and Stephanotis (7.11):
log Kwrec = 0.39Cx 3.79 (barley wax)
(7.10)
(7.11)
213
b
10 C
10 C
0 C
0 C
10 C
10 C
20 C
20 C
30 C
30 C
40 C
40 C
50 C
60 C
10 Gauss
10 Gauss
Fig. 7.4 ESR (electron spin resonance) spectra of 5-doxyl stearic acid measured between 10
and 60 C in reconstituted barley wax in (a) absence or (b) presence of the alcohol ethoxylate
triethylene glycol monohexyl ether (C6 E3 ) at a concentration of 10 g kg1 . Arrows indicate the
hyperfine splitting. Redrawn from Schreiber et al. (1996b)
the hyperfine splitting continuously lose intensity until they finally disappear completely at high temperatures. A homogeneous ESR spectrum is obtained at high
temperature (Fig. 7.4). This indicates that the molecular environment of the ESRspectrum is fluid, allowing free rotation of the label around its own axis without any
restriction.
The molecular environment in which the spin label is dissolved in barley wax is
rigid between 10 and 40 C (Fig. 7.4a). A transition occurs between 40 and 50 C,
and at 50 C the spin label can freely rotate around its own axis. Increasing the
temperature provides the energy for the wax molecules forming the amorphous wax
phase to become fluid. This microscopic transition in the amorphous wax phase,
where sorption and diffusion of lipophilic molecules takes place, is mapped by the
spin label.
If C6 E3 is present in the wax (1%), this transition from a rigid to a fluid environment takes place at much lower temperatures (Fig. 7.4b). At 10 C the spin label
is still restricted in free rotation, and the hyperfine splitting is visible. At 20 C
the transition from a rigid to a fluid environment can be seen in the spectrum, and
already at 30 C the molecular environment of the spin label is fluid and free rotation of the label is possible. The alcohol ethoxylate plasticises the amorphous phase
of the wax, and it is fluid already at room temperature. In the absence of the plasticiser, the temperature needs to be 2030 C higher for the same degree of fluidity.
Thus, adding an alcohol ethoxylate to cuticular wax mimics the effect of higher
temperatures.
A series of alcohol ethoxylates was tested using ESR spectroscopy, and all were
active as plasticisers compared to the control (Fig. 7.5). The plasticising effect on
214
10 C
65
2 A max (Gauss)
0 C
10 C
60
20 C
55
30 C
50
on
tro
16
14
12
E
10
8E
4
6E
3
4E
2
40 C
Fig. 7.5 The hyperfine splitting (2Amax ) as a function of temperature for alcohol ethoxylates
sorbed in barley wax at maximum concentrations varying from 10 to 5 g kg1 between C4 E2 and
C16 E8 . Redrawn from Schreiber et al. (1996b)
barley wax was different among the alcohol ethoxylates. As different concentrations
of alcohol ethoxylates in wax were present (7.4), intrinsic plasticising effects cannot
be deduced from Fig. 7.5. The relationship between the effect of plasticisers and
their concentration in the wax is presented in Sect. 7.3.
Direct observation of the plasticising effect of alcohol ethoxylates on reconstituted wax was also possible using 2 H-NMR spectroscopy (Schreiber et al. 1997). In
this approach, two different deuterated probes, stearic acid and dotriacontane, were
added to barley wax, and the molecular motion of the two probes in the absence
and in the presence of C6 E3 was observed by NMR. Most interestingly, mobility of
dotriacontane, which is a very lipophilic long-chain alkane of 32 carbon atoms, was
not affected by the plasticiser, whereas mobility of deuterium-labelled stearic acid
significantly increased when C6 E3 was added to barley wax. This is good evidence
that dotriacontane, which is very similar in size and structure to a typical long-chain
paraffin wax, is located in the crystalline phase of the reconstituted wax, which
is not accessed and modified by C6 E3 . Stearic acid is located in the amorphous
wax phase, which is modified by plasticiser. This is consistent with the observation that a much higher D (1.1 1018 m2 s1 ) is measured for radio-labelled
dotriacontane when loaded to the wax from an external solution, compared to the
D of 1.4 1022 m2 s1 , which is obtained when dotriacontane is recrystallised
together with the wax during reconstitution (Schreiber at al. 1997). This difference
was not observed with stearic acid. D was 4.0 1018 m2 s1 when stearic acid was
loaded to the crystallised wax from solution, and it was 3.6 1018 m2 s1 when the
radio-labelled probe was reconstituted together with the wax (Schreiber et al. 1997).
215
Thus, D did not depend on the mode of loading of the wax with the radio-labelled
stearic acid. This phenomenon is also discussed in Sect. 6.5.1.
216
0.05
C12E8
0.04
0.03
+ C12E8
0.02
0.01
0.00
12
15
18
Fig. 7.6 Desorption of tetracosanoic acid (C24 Ac) from reconstituted barley wax. Within the
first hour (blue symbols) C24 Ac was desorbed using inert borax buffer (pH 9.0) as desorption
medium. During the second hour (red symbols) C24 Ac was desorbed by borax buffer containing
C12 E8 (102 mol l1 ). During the final desorption period (blue symbols) borax buffer was used
again. Error bars represent 95% confidence intervals. Data redrawn from Schreiber (1995)
217
1.2
1.1
1.0
0.9
C12E8 sorption in wax
Mt / M0
0.8
0.7
0.6
0.5
C24Ac desorption
from wax with C12E8
0.4
0.3
0.2
C24Ac desorption
from wax without C12E8
0.1
0.0
0
8
12
16
Square root of time (min1/2)
20
24
Fig. 7.7 Sorption kinetic of 14 C-labelled C12 E8 (octaethylene glycol monododecyl ether) in reconstituted barley wax (blue symbols) and desorption kinetics of 14 C-labelled C24 Ac (tetracosanoic
acid) from barley wax using either borax buffer (pH 9.0) with C12 E8 (102 M) (red symbols) or
without C12 E8 (green symbols). All three kinetics were determined in independent experiments.
Error bars represent 95% confidence intervals. Data redrawn from Schreiber (1995)
Maximum C12 E8 concentrations in wax are obtained when the desorption media
contains C12 E8 at concentrations well above the cmc. The relationship between different C12 E8 concentrations and plasticising effects on diffusion of 14 C-labelled
solutes can be investigated using desorption media with increasing C12 E8 concentrations (Fig. 7.8).
Effects of C12 E8 on D of C24 Ac increased from three- to more than 40-fold when
C12 E8 concentrations in the external desorption medium were increased from 109
to 104 mol l1 (Fig. 7.8). At concentrations above the cmc of 104 mol l1 , effects
were independent on the external C12 E8 concentration, because sorption above the
cmc does not increase (Sect. 7.1.1). A similar correlation between increasing C12 E8
concentrations in the external desorption medium and effects on D has been shown
for the desorption of 14 C-labelled PCP, with the main difference that effects on D
only increased from 1.5- to less than five-fold, with C12 E8 concentrations in the
external desorption medium increasing from 109 to 104 mol l1 (Schreiber 1995).
218
Effect (D /Dcontrol )
40
30
20
cmc
10
0
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Fig. 7.8 Effect on diffusion coefficients (D/Dcontrol ) of C24 Ac (tetracosanoic acid) in reconstituted
barley wax as a function of C12 E8 concentrations in the external borate buffer. D/Dcontrol is 1 in
absence of C12 E8 (blue symbol). Results obtained with various C12 E8 concentrations are shown in
red. Error bars represent 95% confidence intervals. Data redrawn from Schreiber (1995)
219
C6E3
20
C4E2
16
C8E4
C10E5
C12E8
12
C16E8
24
C12E6
C14E7
10
11
Kwrec H. vulgare
Kwrec S. floribunda
3.1
5.9
31.2
503
1,821
15.5
55.7
447
5,319
28,590
220
8
7
6
5
4
3
n-alkyl esters in barley wax
n-alkyl esters in Stephanotis wax
alcoholethoxylates in Stephanotis wax
2
1
0
0
20
40
60
80
100
120
140
160
180
with n-alkyl esters than with alcohol ethoxylates (Fig. 7.10). Thus, there are specific
differences between the two different classes of plasticisers investigated.
221
1e-15
SA
2,4-D
TRI
MET
TB
1e-16
BIT
log D (m2/s)
C8E4
C12E8
1e-17
control
1e-18
100
120
140
160
180
Vx
200
220
240
260
(cm3/mol)
Fig. 7.11 Plots of the log D of lipophilic solutes as a function of their molar volumes Vx . D
was determined either using a phospholipid suspension as inert desorption medium (control; blue
symbols) or in the presence of the accelerators octaethylene glycol monododecyl ether (C12 E8 ;
green symbols) and tetraethylene glycol monooctyl ether (C8 E4 ; red symbols). Salicylic acid (SA),
2,4-dichlorophenoxyacetic acid (2,4-D), metribuzin (MET), triadimenol (TRI), tebuconazole (TB),
bitertanol (BIT). Error bars represent 95% confidence intervals. Data redrawn from Burghardt et al.
(1998)
Table 7.3 Slopes , y-intercepts D0 and coefficients of determination r2 of the regression
equations fitted to data of Fig. 7.11
Desorption medium
PLS
C12E8
C8E4
(mol cm3 )
log D0 (m2 s1 )
r2
0.0065
0.0023
0.0011
15.94
15.85
15.51
0.91
0.76
0.67
tortuosity and wax crystallinity were not affected by C12 E8 and C8 E4 . This result
is consistent with results of ESR experiments (Fig. 7.4) and reversibility of the
plasticising effect of C12 E8 on barley wax (Fig. 7.8) described in Sects 7.2 and 7.3.
Figure 7.11 also indicates that the plasticising effect of the alcohol ethoxylates is
larger with larger solutes having a lower D. This is also seen when the effect of the
plasticisers (D/Dcontrol ) is plotted against the reciprocal of Dcontrol (Fig. 7.12). The
largest effects are obtained with bitertanol (which has the lowest Dcontrol ) while
the smallest effect is obtained with salicylic acid (which has the highest Dcontrol ).
Thus, diffusion of small solutes having a large D is less affected by plasticisers.
All the above experiments were conducted using reconstituted cuticular waxes.
These data provide insights into the molecular architecture of waxes, and show that
plasticisers increase fluidity of amorphous waxes. Can these findings be extrapolated
to cuticles of intact leaves?
222
BIT
80
TB
60
SA
TRI
20
MET
40
2,4-D
C8E4
C12E8
0
0
10
20
30
40
50
60
1/ Dcontrol . 10
16 (m2 /s )
Fig. 7.12 Effects of the two accelerators octaethylene glycol monododecyl ether (C12 E8 ; black
symbols) and tetraethylene glycol monooctyl ether (C8 E4 ; red symbols) on diffusion (D/Dcontrol )
of lipophilic solutes in barley wax. Salicylic acid (SA), 2,4-dichlorophenoxyacetic acid (2,4-D),
metribuzin (MET), triadimenol (TRI), tebuconazole (TB), bitertanol (BIT). Data redrawn from
Burghardt et al. (1998)
223
Fig. 7.13 Stainless steel transport chamber used in steady state experiments studying the effect of
Brij 30 on 4-NP penetration across CM from Prunus laurocerasus leaves. The CM (yellow) separates the donor and receiver half-cells. Sampling ports permit exchange and removal of solutions.
During the experiment, the sampling ports were closed by greased metal cylinders. Redrawn from
Schreiber et al. (1995)
224
removal of Brij 30
6
5
addition of Brij 30
4
3
2
1
0
0
10
11
12
13
14
Time (days)
Fig. 7.14 Effects of the polydisperse alcohol ethoxylate Brij 30 on steady state diffusion of
4-nitrophenol across 4 individual Prunus laurocerasus CM. Arrows indicate the addition to and
the subsequent removal of Brij 30 from the receiver solution. Data redrawn from Schreiber et al.
(1995)
shows the time course of events. After the addition of Brij 30, it equilibrated with
the cuticle and the wax in the cuticle. During this time period, which takes several hours, 4-NP penetration rates (slopes of plots) continuously increased. After
equilibration, rates of 4-NP penetration became constant again. When Brij30 was
removed from the receiver, the CM still contained significant amounts of Brij 30,
and penetration rates decreased slowly. Only after about 12 days, with frequent
renewal of the receiver solution (this was necessary to measure 4-NP penetration
and remove Brij 30), rates of 4-NP penetration constantly decreased. This reflects
the removal of Brij 30 from the cuticle, and as a consequence the plasticising effect
decreased again. After 7 days, average penetration rates of 4-NP were by a factor of six lower than those measured in the presence of Brij 30. This experiment
demonstrates that the plasticising effects are reversible, but that they are established
much more rapidly than reversed. Penetration of Brij 30 is rapid because plasticising activity in the limiting skin increases progressively. During loading of CM with
Brij 30, the surfactant is in contact with the limiting skin; equilibrium concentration
is reached quickly, and penetration becomes steady. More Brij 30 now penetrates
the plasticised limiting skin, and the sorption compartment of the cuticle is equilibrated. This has no effect on rates of 4-NP penetration. When Brij 30 is removed
from the receiver, the accelerator departs from the limiting skin, D for 4-NP and
Brij 30 decrease and it takes some time before all Brij 30 has been removed from
the sorption compartment. Apart from these kinetic effects, it is clear that accelerator
effects in CM are reversible, as was previously shown for reconstituted wax.
225
22
20
C6E3
C10E5
18
C6E3
C10E5
16
14
C8E4
C8E4
C12E6
12
C12E6
10
8
6
C16E8
C14E7
C16E8
C12E8
50
60
70
80
90
Concentration (g/kg) of alcohol
ethoxylates in Citrus MX
C14E7
C12E8
4
10 11
Concentration (g / k g) of alcohol
ethoxylates in barley wax
Fig. 7.15 Correlation between the effects of monodisperse alcohol ethoxylates on mobility k of
2,4-D in Citrus CM with concentrations of alcohol ethoxylates in (a) Citrus MX (blue symbols)
and in (b) reconstituted barley wax (red symbols). Effects on mobility are taken from Schnherr
(1993a); data for alcohol ethoxylate sorption in Citrus MX were calculated using (7.9), and for
sorption in barley using (7.4)
226
be calculated from (7.9). A reasonable positive correlation between effects and concentrations of the respective alcohol ethoxylates sorbed in Citrus MX is obtained
(Fig. 7.15a). Unfortunately, partition coefficients Kww have not been determined for
Citrus wax. Citrus wax is largely amorphous, and we expect Kww to be smaller
than Kmxw . Using (7.4), concentrations of alcohol ethoxylates sorbed in barley wax
instead of Citrus wax can be calculated. A plot of the effects on mobilities in Citrus
as a function of the plasticiser concentration in barley wax gives a reasonable correlation as well (Fig. 7.15b). This confirms that intrinsic effects of these plasticisers
are similar, and that effects on solute penetration across cuticles are only a function
of the concentration of accelerators sorbed in the transport-limiting barrier of wax.
When comparing the effects of alcohol ethoxylates with those of n-alkyl esters
on diffusion in wax (Sect. 7.3.3), it was shown that n-alkyl esters were five times
more efficient in plasticising waxes at the same internal concentrations in the wax
(Fig. 7.10). A similar tendency can be observed with CM (Schnherr et al. 2001;
Shi et al. 2005b). This is not too surprising, since above we have presented evidence showing that transport properties of cuticles and effects of plasticisers can be
attributed to sorption and diffusion properties of wax.
Comparing intrinsic effects of alcohol ethoxylates with those of the n-alkyl
esters tributyl phosphate (TBP) and diethyl suberate (DESU) on 2,4-DB (2,4dichlorophenoxybutyric acid) mobility in Stephanotis cuticles shows that highest
effects were obtained with DESU, intermediate effects with TBP, and lowest but
still significant effects with alcohol ethoxylates (Table 7.4). At 15 C the n-alkyl ester
DESU is about 4.4 times more effective than alcohol ethoxylates in plasticising the
waxy transport barrier. This effect gradually decreases with increasing temperature
from 15 to 25 C. At 30 C the difference disappears completely (Table 7.4).
Activation energies for mobility of 2,4-DB in Stephanotis CM are 105 kJ mol1
in the absence of a plasticiser. They significantly decrease to 26 and 36 kJ mol1 in
the presence of DESU and of the alcohol ethoxylates respectively (Schnherr et al.
2001). TBP shows the same tendency of decreasing effects with increasing temperature (Table 7.4), and the activation energy decreases to 64 kJ mol1 (Schnherr et al.
2001). Effects of plasticisers are highest at low temperatures. Increasing temperature
or adding plasticisers have similar effects on fluidity of the waxy transport-limiting
barrier of cuticles. ESR experiments (Sect. 7.2) support this conclusion.
Table 7.4 Effect of alcohol ethoxylates (Cx Ey ), tributyl phosphate (TBP) and diethyl suber
ate (DESU) on 2,4-DB (2,4-dichlorophenoxybutyric acid) mobility k in Stephanotis CM at 4
different temperatures
Plasticiser
Cx Ey
TBP
DESU
Concentration in CM
(g kg1 )
Effect on k
15 C
20 C
25 C
30 C
85
90
90
11
35
48
9
17
25
9
17
15
9
14
9
227
228
iprovalicarb
methyl glucose
C12E2
C12E4
10
C12E8
C12E6
C12E6
C12E4
C12E8
1
control
control
C12E2
0.1
0
50
100
150
50
100
150
Fig. 7.16 Logarithms of the effects (k/kcontrol ) of monodisperse alcohol ethoxylates on rate constants of penetration k across Stephanotis CM of iprovalicarb (blue symbols) and methyl glucose
(red symbols) as a function of the concentration of the alcohol ethoxylates in Stephanotis wax.
Dotted lines represent 95% prediction intervals for the regression lines. Data from Shi et al. (2005a)
diffuse in the amorphous wax phase, where diffusion of lipophilic solutes such as
iprovalicarb takes place. They act as plasticisers, and accelerate their own diffusion
and the diffusion of other solutes which can access the waxy pathway.
The fact that DESU and TBP, which are very lipophilic compounds lacking surface activity, do not enhance penetration of methyl glucose indicates that these
plasticisers are spatially separated from methyl glucose during penetration of the
cuticle. The plasticising effect of DESU and TBP on wax cannot affect diffusion
of methyl glucose in aqueous pores. Kww values measured with Stephanotis wax
(Table 7.1) are 692 and 2,626 for C12 E8 and C12 66 respectively. Hence, these alcohol ethoxylates are primarily sorbed in wax and cutin and only traces will be in the
aqueous pores. If methyl glucose does not dissolve in wax and cutin, C12 E8 and
C12 66 should not enhance rates of penetration of methyl glucose in CM. Yet they
do, and C12 E8 is more effective than C12 66 even though its concentration in wax
is lower. An effect on aqueous pores can be ruled out, because the overwhelming
majority of these surfactant molecules are in lipid phases and not in water. How can
this be explained?
Alcohol ethoxylates are surfactants, with a lipophilic and a polar domain in the
same molecule, and this distinguishes them from DESU and TBP. With increasing
degree of ethoxylation their polarity increases, and statistically significant accelerating effects on methyl glucose penetration have been observed only with the more
polar C12 E6 and C12 E8 representatives. This indicates that C12 E6 and C12 E8 must
at least partially diffuse in the same phase as methyl glucose, such that diffusion of
methyl glucose can be increased by C12 E6 and C12 E8 to some extent.
229
230
Problems
1. What is the cmc and how does it affect the sorption of surfactants and lipophilic
solutes to wax?
2. Alcohol ethoxylates have the general formula Cx Ey . Cx indicates the number of
C atoms or lipophilic CH2 groups of the alcohol. Ey refers to the number of
the polar ethylene oxide units. How is the wax/water partition coefficient Kww
affected by Cx and Ey ?
3. What is the Kww of C12 E8 in barley wax?
4. How much C12 E8 is sorbed in barley wax when equilibrated with an aqueous
solution above the cmc?
5. What is the Kww for a solute in barley wax when the Kmxw of this substance is
250 in Citrus MX?
6. Which property of waxes is studied by ESR and NMR? How is wax structure
affected by alcohol ethoxylates?
7. Mobility of lipophilic solutes in wax and cuticles is increased by the addition
of alcohol ethoxylates. The effect can be reversed when alcohol ethoxylates are
desorbed from wax. Is this observation consistent with solubilisation of waxes?
8. Diffusion coefficients in reconstituted waxes can be estimated from molar volumes of solutes using (6.23). For C12 E8 , a D of 5.74 1020 m2 s1 is calculated.
This value is 150 times higher than D measured by desorption which is 8.5
1018 m2 s1 . Can you explain this difference?
9. The n-alkyl esters DESU and TBP have pronounced accelerating effects on cuticular penetration of the lipophilic solute iprovalicarb, but they were ineffective
with the polar compound methyl glucose. Can you explain this?
Solutions
1. The cmc is the maximum aqueous concentration of a surfactant. If surfactant
concentration is increased beyond the cmc, micelles are formed and the concentration of free surfactant molecules does not increase. The maximum amount
of surfactant molecules sorbed in wax is reached at the cmc. Lipophilic solutes
which are sorbed in wax are also sorbed in micelles.Hence, apparent partition
coefficients (Kww ) decrease when the surfactant concentration is increased above
the cmc, and micelles are formed which compete as sorbers with the wax.
Solutions
231
2. According to (7.1), (7.2) and (7.3), log Kww of an alcohol ethoxylate increases
by an increment of 0.530.54 with each additional C atom, and it decreases by a
decrement of 0.230.24 with each additional ethylene oxide group.
3. Using (7.1), a Kww of 81 is obtained for barley wax.
4. According to (7.4), the maximum amount of C12 E8 sorbed in barley wax is 4.5 g
surfactant per kg wax. This corresponds to 0.45 weight percent.
5. According to (7.7), log Kww for barley wax is 1.34; thus, Kww is 21.8.
6. ESR and NMR experiments provide information regarding the molecular architecture of wax. ESR and NMR probes directly map their environment in the
wax. The main finding from ESR and NMR experiments was the observation
that alcohol ethoxylates plasticise the amorphous wax phase. In the presence of
sorbed alcohol ethoxylates ESR and NMR, probes in the amorphous wax phase
are in a liquid environment at room temperature. In the absence of the plasticisers, the same fluidity of wax is obtained only at higher temperatures. Alcohol
ethoxylates sorbed in wax mimic the effect of higher temperatures.
7. A rapid increase in solute mobility after addition of alcohol ethoxylates, and
reversion of the effect after removing the plasticiser, indicate reversible changes
in fluidity of the waxy pathway. Waxes are not solubilised and lost.
8. Equation (6.23) for estimating D is only valid for solutes lacking plasticising
activity. C12 E8 is a plasticiser, and increases solute mobility in wax. C12 E8 also
increases its own mobility in wax, and thus the measured D is much higher than
the D value estimated for a passive solute.
9. In cuticles, an aqueous pathway and a lipophilic waxy pathway are arranged
in parallel. The lipophilic iprovalicarb preferentially diffuses in the lipophilic
pathway which is plasticised by DESU and TBP. Methyl glucose is not soluble
in amorphous waxes, and its penetration is limited to aqueous pores. Diffusion in
aqueous pores is not affected by lipophilic plasticisers.
Chapter 8
233
234
Cinternal = kCaqueous
(8.1)
1
logCinternal = log k + logCaqueous
n
(8.1a)
or in logarithmic form
Freundlich isotherms are frequently encountered when solutes interact with heterogeneous substrates. At low concentrations the parameter n is not far from 1.0, but at
higher sorbate concentrations the plots become increasingly convex to the Caqueous
axis. At low sorbate concentrations this type of isotherm can be classified as constant partitioning, while at higher concentrations (>103 mol kg1 ) it resembles a
Langmuir type isotherm. Linear isotherms are obtained under the following conditions: (1) the substrate consists of flexible molecules and has regions of differing
accessibility to the sorbate, (2) the solute has a higher affinity to the substrate than to
the solvent water, and (3) the solute is able to penetrate into initially less accessible
(highly ordered) regions of the solid.
At all concentrations and temperatures, partition coefficients (K) and the
Freundlich parameter k were >1. K ranged from about 15 to 250 (Fig. 8.1), and
k varied between 14 and 190 (Riederer and Schnherr 1986a); that is, 4-NP is better
soluble in CM and MX than in water. At low internal concentration, K is greater
with the MX than with the CM. The only lipid compartment of the MX is cutin,
235
0.139
1.39
13.9
139
6.0
403
Lycopersicon
5.5
245
5.0
148
4.5
90
30
4.0
55
50
3.5
33
3.0
20
2.5
Partition coefficient
ln Partition coefficient
15
12
5
3
2
1
log Internal concentration (mol / kg)
Internal concentration (g / k g)
0.014
0.139
1.39
139
13.9
6.0
403
Ficus
5.5
245
148
20
4.5
4.0
90
55
35
3.5
33
3.0
20
2.5
Partition coefficient
ln Partition coefficient
5
5.0
12
5
3
2
1
log Internal concentration (mol/ kg)
Fig. 8.1 Partition coefficients of 4-nitrophenol for CM (red) and MX (blue) from Lycopersicon
esculentum fruits and Ficus decora leaves as functions of temperature and concentration of sorbed
solute. (Redrawn from data of Riederer and Schnherr 1986a)
236
(8.2)
237
partition coefficients was exclusively due to a temperature effect on solute activity in the aqueous phase, that is, on water solubility of 4-NP. With increasing
temperature water solubility increased, and as a consequence partition coefficients
decreased. Sorption in tomato fruit MX differed. Here, k increased with temperature
from about 5 to 14, showing that the number of available sorption sites increased
with temperature. The plot k vs T has plateaus at 722 C and 2232 C. A gradual increase occurred between 22 and 47 C (Riederer and Schnherr 1986a). This
indicates structural changes in the cutin matrix, and the step character can be interpreted as phase transitions which lead to a loosening of the polymer chains, with a
concomitant increase in number of sorption sites.
(8.3)
(8.4)
Hs Ss
+
RT
R
(8.5)
Plotting ln K vs T 1 (in Kelvin) results in a straight line having the slope Hs /R,
and the y-intercept is Ss /R. A large entropy is characteristic for sorption on solid
substrates, which leads to a higher degree of order. For Gsorption to be negative, the
large T Ss term must be overcompensated by the heat of sorption (Hs ). This was
the case at all temperatures and concentrations (Riederer and Schnherr 1986a).
With both species, a striking difference between CM and MX exists for the
effect of sorbate concentration on Hs . At low concentration the heat of sorption
of CM was constant, and decreased only if the internal concentration exceeded
102 mol kg1 (Fig. 8.2a). Sorption sites in the CM seemed to be energetically
homogeneous as long as the internal concentration was <1.39 g kg1 . With MX
membranes the enthalpy varied from the beginning, indicating that sorption sites
available in the MX are more heterogeneous. With Ficus MX, Hs increased from
the beginning, because sorption sites evolving higher amounts of heat became
238
0.139
1.39
13.9
139
15
CM
20
Lycopersicon
MX
25
CM
Ficus
30
MX
35
40
45
50
4
20
40
Ssorption (kJ mol1Kelvin1)
3
2
1
log Internal concentration (mol/ k g)
60
Ficus MX
Ficus CM
Lycopersicon MX
Lycopersicon CM
80
100
S = 3.78 x H + 47.1(r2 = 0.995)
120
140
50
45
40
35
Hsorption (kJ
30
25
20
15
mol1)
Fig. 8.2 (a) Change in molar enthalpy due to transfer of 4-NP from the aqueous to the cuticle
phase. HS for various concentrations was calculated at 25 C. (b) Entropyenthalpy relationship
at 25 C and internal concentrations shown in (a)
239
available by an opening up or swelling of the polymer cutin once the low energy
sorption sites of about 30 kJ mol1 had been saturated. With tomato fruit MX,
the opposite effect was observed. Heats of sorption decreased initially until the
internal concentration reached about 18 kJ kg1 . All sorption sites seemed to be
equally accessible, but those providing higher heats of sorption were being saturated
first. At higher internal 4-NP concentrations heats of sorption increased strongly,
and this phenomenon can be explained by a cooperative effect between sorbate
molecules inside the cuticle. After all sorption sites in cutin have been saturated,
additional sorption occurs on the surface of 4-NP molecules already sorbed on
the polymer. In other words, initially solutematrix interactions dominate, while at
high internal concentration sorbatesorbate interactions become important and solid
4-NP precipitates between the polymer chains, which are forced apart. The polymer
swells.
The partial molar entropy measured for transfer from aqueous solution to the
cuticles has a negative sign (Fig. 8.2b). This loss of entropy can be attributed to
reduced mobility of 4-NP molecules and increased degree or order on sorption
on a solid substrate. The good correlation between enthalpy and entropy at all
concentrations, with both species and for CM and MX, indicates that the same
entropyenthalpy relationship prevails for both species and for MX and CM. Sorption sites having a low enthalpy result in lower order of sorbed molecules and vice
versa. Larger amounts of heat are evolved when solutes are sorbed at higher order
and reduced mobility. Whenever solutesolute interactions dominate, multilayers of
sorbate molecules may arise between the polymer chains of cutin.
It is tempting to extrapolate these data to the formation of embedded wax, that
is, to the generation of wax plates in cutin. Enthalpies of transfer to cutin are
very high when compared to the octanol water system, for which HS between
5 and 8 kJ mol1 were measured for substituted resorcinol (1,3-benzenediol)
monoethers (Sangster 1997). Sorption of 4-NP is driven by very high enthalpies, and
dipoledipole interactions are important. It is unfortunate that we have no comparable data for fatty acids, alcohols esters or alkanes. With these lipophilic solutes, van
der Waals forces are probably more important than dipole-dipole interactions. For
these reasons, extrapolation of the above data to formation of intracuticular waxes
should be looked at with extreme caution. These highly lipophilic compounds were
not included in this study because of their extremely low water solubility. Mixtures
of ethanol and water would have to be used to overcome this problem.
240
D = Do exp RT
(8.6)
where ED is the activation energy of diffusion, R the gas constant, T the Kelvin
temperature and Do is the pre-exponential factor. In diffusion across polymer membranes, the activation energy is a measure of the energy expanded against the
cohesive forces of the polymer in forming gaps through which solutes can diffuse. This concept assumes that vacancies, holes or void volumes must be formed
between polymer chains by thermal motion, which can accommodate solutes. These
voids or holes must be large enough to accept the penetrant, and they must form
very close to the original position of the solute, such that they can be reached in
a single jump. Frequency of hole formation and the size of these holes determine
rates of diffusion, not the jumping frequency of the molecules themselves, which is
much larger. Both increase with temperature, and this is the reason why D increases
with temperature and why the increase is much larger in membranes than in solutions. Based on the argument that the activation barrier in membrane diffusion is
the energy necessary to form a hole of proper dimensions, Glasstone et al. (1941)
proposed the transition state theory, and derived an expression for diffusion:
D = 2
G
T
exp RT
h
(8.7)
where is the mean free path of the solute in the solid, is Boltzmanns constant,
h is the Blanck constant and G is the Gibbs free energy of activation, which is
G = H T S
(8.8)
where H and S are the enthalpy and entropy change per mole during formation
of the transition state. The enthalpy of activation H is related to the Arrhenius
activation energy (ED )
H = ED RT
(8.9)
and substituting (8.9) and (8.8) into (8.7) we obtain
D = 2
ED
S
T
exp R exp RT
h
(8.10)
S
T
exp R .
h
(8.11)
241
This shows that Do is proportional to the square of the jump distances, temperature
and of some physical constants. The entropy enters as an exponent.
Temperature dependence of diffusion is usually described using (8.6). D is measured at various temperatures, and ln D is plotted versus T 1 . If the slope is a
straight line ED can be calculated from the slope, and the y-intercept is equivalent
to ln Do . With Do and activation energy known, D can be calculated for any other
temperature (8.6).
These equations can be used to investigate dependence on temperature of solute
mobility in CM and MX. Using the UDOS method (Sect. 6.3), rate constants k
are obtained which are proportional to diffusion coefficients. In CM, their magnitude depends on properties of the waxy barrier. Temperatures studied, ranged from
15 to 70 C, and internal solute concentrations were in the order of mg kg1 . At
these concentrations, solutemembrane interactions predominate and solutesolute
interactions in cuticles are improbable.
(8.12)
where kinfinite is the pre-exponential factor and ED is the activation energy of diffusion. This equation is similar to (8.6), except that D was replaced by the UDOS
rate constant k . In the original publications by Baur et al. (1997a), Buchholz and
Schnherr (2000) and Buchholz 2006, the symbol for pre-exponential factor was ko
similarly as for Do in (8.6). However, ko was previously used for rate constants for
solutes having zero molar volume (Buchholz et al. 1998, Sects. 6.3.2.2 and 6.3.2.3);
we now define the symbol kinfinite for the y-intercept of Arrhenius plots. This
y-intercept kinfinite is the solute mobility at infinite temperature. By plotting log k
vs the reciprocal of the Kelvin temperature, a straight line is obtained and ED can
be calculated from the slope:
ED = 2.3 slope R
(8.13)
The factor 2.3 is included in the above equation because published Arrhenius plots
are on log scale, rather than ln scale as in (8.6) and (8.12).
Figure 8.3a shows Arrhenius plots for seven individual Citrus CM/2,4-D combinations. Slopes are linear, and log k increases with decreasing values of T 1 . With
increasing temperature, solute mobility k increases by almost two orders of magnitude. Regression equations for the CM having highest and lowest rate constants are
shown in the graph, and it can be seen that plots tend to converge at higher temperatures. CM having high k values have lower y-intercepts and smaller slopes than CM
having low k values. Differences in k among membranes decrease as temperature
242
40
35
Temperature (C)
25
30
20
15
13
- 4.5
- 5.0
y=
- 6.0
y=
- 90
log k (s-1)
- 5.5
88
- 6.5
x+
23
- 76
50
x+
.8
19
.6
6
5
4
3
2
- 7.0
- 7.5
1
- 8.0
3.20
3.25
3.30
3.35
T
84
72
60
-1 x
1000
3.40
3.45
3.50
40
30
21
(K-1)
Temperature (C)
50
-2
y=-8500x+21.2
y=-6460x+15.5
y=-9910x+25.2
y=-8020x+20.4
-3
-5
log k (s-1)
-4
-6
Hedera / bifenox
Hedera / IAA
Hedera / c holesterol
Ilex / b ifenox
-7
-8
-9
2.8
2.9
3.0
3.1
3.2
3.3
3.4
T -1 x 1000 (K-1)
Fig. 8.3 Arrhenius plots of log k vs T 1 for CM of selected species/solute combinations. (a)
Arrhenius plots for seven individual Citrus CM. (b) Arrhenius plots obtained with Hedera helix and
Ilex aquifolium CM and the solutes bifenox, cholesterol and indoleacetic acid (IAA). Arithmetic
means of k for 710 CM were plotted. Regression equations for the linear portions of the plots
are given in the upper right corner. (Replotted from data by Baur et al. 1997a)
243
increases. This general feature has been observed with CM of all species and solutes
(Baur et al. 1997a).
When the logarithms of average k values are plotted over a wider temperature
range, these plots are often linear up to 70 C, as with the combinations Hedera/IAA
and Hedera/bifenox (Fig. 8.3b). With some CM/solute combinations, plots departed
from linearity at temperature above 50 C, when the melting points of the waxes
were approached and the diffusion was no longer totally determined by properties of
the limiting skin (Sect. 6.3.2). When rate constants for the limiting skin and the sorption compartment are similar, diffusion in the sorption compartment can become
rate-limiting, as was shown for the combination Citrus MX/PCP (Fig. 6.20). Further,
flattening of slopes is often observed with homogeneous rubbery polymers where it
indicates the onset of viscous flow of polymer chains (Schlotter and Furlan 1992).
For these reason, most studies have been limited to temperatures below 50 C, which
is the range experienced by most plant species under natural conditions. Generally,
only linear portions of Arrhenius plots were utilised for data analysis, as shown for
the combinations Ilex/bifenox and Hedera/cholesterol. In the upper right hand corner of Fig. 8.3b, regression equations for the linear portions of the Arrhenius plots
are given. Slopes vary between 6,460 and 9,910, and using (8.7), ED in the range
of 123.5185.5 kJ mol1 can be calculated.
As seen in Fig. 8.3b, differences in rate constant among species also tend to
decrease with increasing temperature, and above 60 C differences have practically disappeared. Thus, differences among individual CM and differences between
species/solute combinations decrease with increasing temperature, and above
5060 C they are small or nil. These observations are the consequences of the
fact that size selectivity , which amounts to 0.095 mol cm3 at 25 C (Table 6.8),
decreases with temperature. Buchholz et al. (1998) measured k for ivy leaf CM
and the solutes IAA and tebuconazole, which had molar volumes of 130 and
1
241 cm3 mol respectively. The ratios of the two rate constants decreased with
temperature, and amounted to 24.5 at 25 C, 10.5 at 35 C and 2.2 at 55 C.
244
From Arrhenius plots as shown in Fig. 8.3, y-intercepts (pre-exponential factor kinfinite ) and the slopes (ED /R) were obtained for individual CM, and results
were plotted (Fig. 8.4). Data obtained with four species and the smallest and least
lipophilic solute IAA (Appendix B) are depicted in Fig. 8.4a. There is an excellent
correlation between kinfinite and the Arrhenius slopes (ED /R). CM with steep slopes,
that is, high energies of activation, have large y-intercepts and vice versa. With all
species, kinfinite varied among individual CM. For instance with Citrus CM, kinfinite
varied between 10 and 20 and (ED /R) between 11 103 and 19 103 Kelvin.
Large variability in permeance and solute mobility is a typical property of CM. In
Fig. 8.4b, all available species/solute combinations are plotted for individual CM.
An excellent linear correlation was again obtained, and both y-intercept and slope
are very similar to those in Fig. 8.4a. This linear free energy relationship is good evidence that in CM from all species all solutes diffuse in a similar environment. This
is astounding, since wax amounts and composition differ greatly among species
(Tables 1.1 and 4.8) and partition coefficients ranged from 14 to 108 .
The results characterise the lipophilic or waxy pathway, which in CM consists of
methylene groups donated by amorphous waxes and cutin environment. The most
polar solute included in the study is IAA; it is 14 times more soluble in CM than
in water, and is still sufficiently soluble in cutin and waxes. Its solubility in water
is smaller than in membrane lipids, and since water content of fully swollen CM is
below 8% (Fig. 4.7) the concentration of IAA in lipid compartments is much larger.
IAA exclusively diffused in a lipophilic matrix, otherwise these data would not have
fallen on the straight line seen in Fig. 8.4b, and slopes and y-intercepts in Fig. 8.4a
and 8.4b would have differed.
It was not possible to include highly water soluble solutes in these studies,
because the UDOS method does not work with them (Sect. 6.3). However, there
is no reason why results should not apply to more polar non-electrolytes, as long
as they are not ionised and soluble in amorphous waxes. As shown in Sect. 4.6,
water can penetrate cuticles using two parallel pathways, in aqueous pores located
between polar polymers and in cutin and in amorphous waxes. ED /R and
y-intercepts for the fraction of water which diffuses in cutin and waxes most probably would fit the regression equation shown in Fig. 8.4b, but data are not available
(see below).
There are a few data available for MX membranes. Extraction of waxes greatly
increases solute mobility (k ) and activation energies are much lower. Plots log k
vs ED /R have similar slopes than shown in Fig. 8.4 for CM, but y-intercepts were
higher, that is, they had smaller negative numbers (Fig. 8.5). With the combination
Hedera/IAA, this parallel displacement amounted to a factor of 1.97 (log scale), that
is, with the MX entropy was higher by a factor of 94. With Strophanthus/IAA the
factor was 50, and with Schefflera/IAA entropy was 5,011 times higher with MX
than with CM. With Pyrus/bifenox, the MX had a 25-times higher entropy than the
CM (Buchholz 2006; Buchholz and Schnherr 2000). These y-intercepts represent
the entropy, when ED /R is zero (Fig. 8.5), that is when there is no free energy and
no driving force for diffusion.
245
22
20
Citrus aurantium
Hedera helix
Prunus laurocerasus
Strophantus gratus
16
log k infinite
18
14
12
10
8
8
10
12
14
16
Enthalpy of diffusion x 103 x R 1 (Kelvin)
18
20
35
30
log k infinite
25
20
15
log kinfinite = 3.61+2.8ED 1.0 3 / R
10
5
5
10
15
Enthalpy of diffusion x
20
103
xR
25
30
1 (Kelvin)
Fig. 8.4 Correlation between y-intercepts and slopes of the Arrhenius graphs for individual CM.
(a) Data for IAA and leaf CM from four species are plotted. (b) Data for 297 leaf CM from 14
plant species (including varieties) and five test compounds (IAA, NAA, bifenox, tebuconazole,
cholesterol) are plotted. (Redrawn from Buchholz et al. 1998 and Buchholz and Schnherr 2000)
246
15
CM
log kinfinite
10
MX
0
log kinfinite = - 5.24 +(1.37ED 10-3/R)
-5
Hedera helix /IAA
-10
0
10
12
14
16
18
Fig. 8.5 Dependence of Arrhenius y-intercepts (log kinfinite ) on slopes (ED /R) measured with
IAA and ivy CM or MX membranes
Theoretically, the mean free path of diffusion can be calculated using (8.11), but
our y-intercept is not Do but rather log kinfinite . In order to convert k to D we would
need the thicknesses of the membrane compartments involved, which are not known
and would have to be assumed (Sect. 6.3.2). This would result in arbitrary estimates
of . Still, the y-intercept increased when waxes were extracted, and this increase is
proportional to 2 and to entropy [exp(S/R)]. Flexibility of the cutin polymer may
well be higher than in amorphous waxes, allowing for a more frequent formation of
larger voids in cutin than in amorphous waxes. This might have contributed to the
differences in y-intercepts after extraction of waxes. However, an effect of extraction
on S cannot be precluded, and a separation of the two factors is not possible at
this time. It is clear, however, that the micro-environment in which diffusion took
place was not affected by extraction of waxes. The slopes, that is, the free energy
relationship were not affected; only the free energy involved in diffusion was lower
(Fig. 8.5). As in waxes, diffusion across MX membranes of lipophilic solutes takes
place in the methylene group environment of cutin, but this differs structurally.
Buchholz and Schnherr (2000) suggested that the difference in y-intercepts
between CM and MX might be due in part to a much higher tortuosity in CM.
From the difference in y-intercepts between MX and CM, tortuosity factors ranging
from 25 to 5,000 can be calculated. Factors of 25100 might be plausible, but a factor of 5,000 is incomprehensible. Waxes are expected to decrease the length of the
diffusion path, because wax crystallites embedded in cutin represent excluded volume and solutes must diffuse around them. This concept of a barrier membrane was
introduced by Riederer and Schreiber (1995). It is plausible, but some of the assumptions can be questioned (Fowler 1999). In some thin cuticles (e.g. Citrus) there is
simply not enough space in the limiting skin to accommodate many superimposed
247
crystalline wax layers, which are separated by layers of cutin. A wax monolayer
composed of a C40 hydrocarbon is 5 nm thick and has a mass of about 0.5 g cm2 .
Total wax in Citrus CM is about 12 g cm2 , and about one third of it is crystalline,
i.e. 4 g cm2 . This would be enough for eight superimposed wax monolayers. It is
not at all obvious how they could be accommodated in cutin as large continuous
platelets. Waxes also occur in cuticular layers and as surface waxes (Chap. 1).
There is good evidence that waxes in the cuticular layers have very little effect on
water permeance and solute mobility (Chaps. 4 and 6). When discussing effects of
waxes on water permeability (Sect. 4.6), some evidence was discussed showing that
one or two monolayers on top of the limiting layer could account for the effect of
waxes on water permeability. A similar effect on solute mobility of superficial wax
monolayers cannot be ruled out.
(8.14)
The effect of temperature on Pwv or Pwv can be analysed using Arrhenius plots
such as
Pwv = Po exp(EP /RT )
(8.15)
where Po is the pre-exponential factor and EP is the Arrhenius activation energy of
permeability or permeance. As long as EP is constant and sorption isotherms are
linear, we can further write
D = Do exp(ED /RT )
(8.16)
which is identical to (8.6), and for the partition coefficients we can write
Kwv = Ko exp(HS /RT )
(8.17)
(8.18)
where HS is the heat of sorption as explained in Sect. 8.1. EP has been determined for cuticles of a number of species. Later we shall take a look at the
248
Temperature (C )
72
60
50
40
30
21
13
-7
-8
-8
Hedera k (bifenox)
-9
-10
ln Pw (m / s)
-11
-12
-12
-13
Citrus k (IAA)
-14
-14
Citrus MX (Pw)
-10
-15
Citrus CM (Pw)
-16
-16
-17
-18
-18
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Fig. 8.6 Arrhenius plots showing the effects of temperature on water permeance (Pw ) of Citrus aurantium CM and MX. The membranes separated aqueous buffers at pH 6 containing
CaCl2 (0.01 mol l1 ) and water fluxes were measured using tritiated water. For comparison rate
constants (k ) determined with Hedera/bifenox and Citrus IAA were included. Water permeance
data were taken from Schnherr et al. (1979). Rate constants were taken from Fig. 8.3
249
The same approach was used with onion bulb scale epidermis (non-isolated CM).
The kink occurred around 47 C, and EP below and above the kink were 58 and
177 kJ mol1 respectively (Schnherr and Mrida 1981). Schreiber (2001) also used
tritiated water, and compared temperature effects on Pw of isolated CM and leaf
disks (Vinca major, Prunus laurocerasus, Forsythia intermedia, Citrus aurantium,
Hedera helix). All Arrhenius plots exhibited a kink in the range of 3039 , and no
significant differences between CM and leaf disks were observed. Below the kink
EP ranged from 26 (F. intermedia) to 61 kJ mol1 (H. helix). Above the kink, EP
was higher and ranged from 67 (V. major) to 122 kJ mol1 (F. intermedia). EP was
higher with species having low Pw , and with increasing ln Pw the kink temperature
increased. Clearly, the occurrence of the kink and the differences in EP below and
above the kink is a natural property of the CM and not an artifact related to isolation
and storage of the CM. Additional data can be found by Riederer (2006), who used
the cup technique to study temperature effects on Pwv of isolated CM of 14 species
in the range of 1055 C. In contrast to the above methods, partial pressure at the
morphological outer surface of the CM was practically zero and the CM were not
fully swollen. With most species the kink occurred around 35 C, and below the kink
EP ranged from 21 to 38 kJ mol1 , while above the kink EP was again higher and
ranged from 52 and 117 kJ mol1 .
High temperatures above the kink irreversibly changed permeance. With the
MX in Ca2+ form, Arrhenius plots obtained with increasing temperatures showed
decreasing slopes when heated above 45 C (Fig. 8.7). When Pw was studied using
descending temperatures beginning at 65 C, a straight Arrhenius plot was obtained
with a slope similar to the initial slope (535 C) of the ascending temperature
run. At all temperatures, Pw of MX membranes measured with descending temperatures were significantly lower than before heating the MX. The opposite was
observed with CM. The Arrhenius plot obtained with decreasing temperatures starting at 65 C had significantly higher Pw values, and the kink occurred around 35 C
(Fig. 8.7). After heating the CM once to 65 C, the descending and ascending temperatures runs were superimposed and the system became reversible. What causes
the kink in the Arrhenius plots for Pw with the CM and its absence with the MX?
The kink in the Arrhenius plots of the CM and its absence with the MX has
been interpreted as solid/liquid phase transition of cuticular waxes (Schnherr et al.
1979; Eckl and Gruler 1980). Differential scanning calorimetry (DSC) of moist CM
and MX at a rate of 0.1 C min1 revealed a number of first-order phase transitions,
while with dry CM no phase transitions were observed between 0 and 200 C. At
low temperatures a phase transition with a latent heat of 4.7 J g1 cuticle at 16.3
and 17.6 C was observed with MX and CM respectively. The transition at 38 C
occurred only with CM. Its latent heat was about 0.4 J g1 CM. Above 40 C, three
additional first-order phase transitions at 41, 46 and 49 C in MX and CM were
observed. Latent heat was around 0.3 J g1 MX for each transition (Eckl and Gruler
1980). Between 35 and 40 C, a sudden change in volume of the Citrus CM was also
observed (Schnherr et al. 1979). The only phase transition which can be attributed
to waxes is that observed at 38 C, while all others were observed with MX and CM
and can be assigned to the polymer matrix.
250
60
50
40
30
21
13
9
Citrus MX ascending from 5 C
10
11
ln Pw (m/ s)
12
Citrus CM descending T
from 68 C
Citrus MX descending T
from 65C
13
14
15
ascending from 10 C
16
17
Citrus CM ascending from 5 C
18
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
1 / T (Kelvin1)
Fig. 8.7 The effect of heating Citrus CM and MX on water permeance and on Arrhenius graphs.
The same methods and experimental conditions as in Fig. 8.6 were used. (Redrawn from data of
Schnherr et al. 1979)
In CM and MX we have two parallel pathways for water, the lipophilic cutin/wax
pathway and the aqueous pathway formed by pores associated with polar polymers
(Sects. 4.5 and 4.6). Diffusion of lipophilic solutes in the cutin and in the waxy pathways did not reveal any phase transition (Sect. 8.2), as Arrhenius plots were linear at
least up to 50 C. At higher temperatures Arrhenius plots occasionally became convex to the abscissa, as seen in Fig. 8.6 for Citrus/IAA. A sudden increase in slope
and ED above 35 to 40 C was never observed. Hence, a phase transition of waxes
can be ruled out. The transition at 38 C observed with Citrus CM certainly had no
effect on solute diffusion in waxes. With this in mind, the kink in the plots ln Pw vs
1/T cannot be attributed to changes in wax structure. All evidence (DSC, thermal
expansion) points to changes in structure of the polymer matrix, that is, temperature
affected the aqueous rather than the waxy pathway. Above the kink, the aqueous
pathway underwent a phase transition or a new aqueous pathway opened up. The
aqueous pathway had been studied and characterised only at 2025 C (Sect. 4.5). It
appears that at temperatures below the kink the bulk of the water diffuses along the
waxy pathway. Co-permeation of lipophilic solutes and water are excellent evidence
(Sect. 4.6.2.3). Above the kink, an increasing fraction of water uses the aqueous
pathway(s).
High temperatures irreversibly decreased Pw of the polymer matrix in Ca2+ form
(Fig. 8.7), while in Na+ form Pw decreased only slightly (Schnherr et al. 1979).
251
Table 8.1 Thermal expansion coefficients for the temperature range 2565 C
Polymer
PTT
C
Citrus CM
Citrus MX
Citrus cutin
Ficus CM
Ficus cutin
Capsicum CM
Capsicum cutin
Lycopersicon CM
Pyrus CM
Nerium CM
Olea CM
PEMAa
Polyvinylacetata
PVA-Cl copolymera
PETP amorpha
17 and 42
21 and 44
none
18 and 50
none
42
none
46
46
39
55
65
32
30
67
K1 )
below 42 C
above 42 C
above/below
0.53
0.50
0.95
0.55
0.96
0.56
0.82
0.57
0.62
0.39
0.45
0.275
0.24
0.20
0.19
0.74
0.65
0.95
1.40
1.30
1.0
1.73
0.60
0.69
1.41
0.62
0.70
0.27
0.45
0.24
0.80
1.07
1.0
1.21
2.27
1.59
1.56
0.98
1.88
1.20
4.21
252
253
254
Temperature (C)
60
50
40
30
-9.0
21
13
-3
Polystyrene
PVC-Ac
-9.5
PVC-Ac
-10.0
PVC
PE
-10.5
PE
-11.0
Rubber hydrochloride
-11.5
Polyvinylidene chloride
-12.0
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
1/ T x 1000 (Kelvin-1)
Fig. 8.8 Arrhenius plots showing the effect of temperature on water vapour permeability (Pwv in
m2 s1 ). Two lots of polyvinyl chloride-acetate copolymer (PVC-Ac) and polyethylene (PE) were
used. PVC is polyvinyl chloride. Data from Doty et al. (1946) were re-calculated and re-plotted
255
Temperature (C)
60
50
40
30
21
13
-3
2.6
-9.5
-10.0
x - 8.15 (r 2 =0
.94)
2
7
60
4
3.5
x-
-11.0
K
log
-11.5
wv
(r
2.2
=1
2.0
log Kwv
log Pwv or D
-10.5
2.4
8)
0.9
1.8
-12.0
log D
= -1
918
-12.5
-13.0
3.0
3.1
3.2
3.3
x -5.
3.4
49 (r 2
3.5
= 0.9
1.6
9)
3.6
3.7
1.4
1 /T x 1000 (Kelvin-1)
Fig. 8.9 Temperature dependence of Pwv , D, und Kwv for polyvinyl chloride. Data taken from
Doty et al. (1946)
For polyvinyl chloride, D was also determined by Doty et al. (1946) using the
hold-up time method (2.5). With increasing temperature (1 to 55 C), D increased
slightly (7.8 101117 1011 m2 s1 ), while Pw increased from 2.2 1013 to
54 1013 m2 s1 (Fig. 8.9). The partition coefficient Kwv can be calculated from
these data using (3.17). Kwv decreased with increasing temperature from 246 to
31 cm3 vapour per cm3 polymer.
From the slopes given in Fig. 8.9, the energies of activation can be calculated.
For EP and ED 10.3 and 36.7 kJ mol1 are obtained, and by difference (8.18) the
enthalpy of sorption or the heat of solution HS of 26.4 kJ mol1 is obtained. The
enthalpy change for transfer of water into PVC is negative, indicating it to be a
spontaneous process, but with increasing temperature decreasing amounts of water
are sorbed (c.f. Sect. 8.1). For the other polymers in Fig. 8.8, D was not measured
and ED remains unknown. With polystyrene EP is zero, and this implies that ED and
HS are numerically equal but have opposite sign.
In Table 8.2, some additional data including rather polar polymers (EC, CA,
PEMA) have been collected. At 25 C, some of the polymers are in the glassy state
(PET, Nylon, PVA, EC and PEMA). In this collection, Pwv was highest with cellulose acetate (which is used for desalination membranes) and lowest with polyvinyl
acetate. They differ by a factor of 251. PVA has the lowest diffusion coefficient
of 5.1 1015 m2 s1 . For the other polymers, D varies from 1.1 1011 (EC) to
1.2 1012 m2 s1 (nylon, rubber HCl) by a factor of 9. Partition coefficients (Kwv )
in the range of partial pressures where sorption isotherms are linear (3rd column)
ranged from 7,255 (PVA) to about 8 for PE.
256
Table 8.2 Pwv , D, and Kwv at 25 C and EP , ED and HS for selected synthetic polymers
cellulose acetate (CA), polyvinyl butyral (PVB), polyethylene (PE), polyethylene terephthalate
(PET), rubber hydrochloride (rubber), polyvinyl acetate (PVA), ethyl cellulose (EC) and polyethyl
methacrylate (PEMA)
Polmer
Tg C
p/po
Pwv m2 s1
D m2 s1
Kwv
EP
kJ mol1
ED
kJ mol1
HS
kJ mol1
CAa
PVBa
PEa
PEb
PETb
PPb
Nylona
Rubbera
Rubberb
PVAa
PVCc
ECd
PEMAe
67
30
50
65
0.10.6
0.10.6
0.40.8
0.11.0
0.11.0
0.11.0
0.10.5
0.10.6
0.10.5
0.10.9
0.20.5
0.10.5
9.3 109
1.5 109
5.4 1011
3.3 1010
5.4 1011
3.7 1011
9.8 1011
1.9 108
2.9 109
3.1 1012
1.3 1012
6.8 1012
1.2 1013
1.2 1013
5.1 1015
1.1 1012
1.9 1011
1.1 1011
3,000
1,153
8
2,750
450
7,269
89
1,000
264
0
8.8
33.4
11.7
26.4
962
10.2
6.3
2.1
50.2
45.5
80.2
59.5
43.5
68.7
55.6
72.0
58.6
59.8
36.7
26.3
36.4
50.2
54.3
46.8
43.9
45.6
50.2
31.0
32.6
34.3
Tg is the glass transition temperature, p/po partial water vapour pressure used for measurements
a Hauser and McLaren (1948)
b Yasuda and Stannett (1962). Original data (P ) were converted to SI units as explained in
Hg
Chap. 3. Hauser and McLaren (1948) determined sorption gravimetrically and calculated D as
Pwv /Kwv : The other diffusion coefficients were obtained from the hold-up time and HS was calculated as ED EP
c Doty et al. 1946
d Wellons et al. (1966)
e Stannett and Williams (1965)
EP ranged from 8.8 to 33.4 kJ mol1 . Negative values indicate that permeance
slightly decreased with increasing temperature. EP for CA was zero, that is, ED
and HS were 52 and 52 kJ mol1 respectively. With this data set, which includes
relatively polar polymers, high permeability was again associated with low EP and
vice versa, but the correlation between log Pwv and EP (log Pwv = 0.06 EP
8.78) was much weaker than with the data set of Fig. 8.6. ED and Hs varied much
less than EP . (Fig. 8.10).
ED increased with increasing EP , but the correlation is too weak to use the linear regression equation shown in Fig. 8.10 for the purposes of prediction. Pwv was
determined at relatively low partial pressure, when water content of the polar membranes increased linearly with partial pressure. Water content of EC, PEMA and EC
greatly increases when partial pressures are higher than 0.50.6. Hence, the data
should not be extrapolated to 100% humidity.
The enthalpy of sorption (HS ) was very similar for all polymers, and did not
depend on either ED or EP . The mean enthalpy was 47 kJ mol1 . It is negative
and in the vicinity of the heat of evaporation or condensation, which at 25 C is
44 kJ mol1 . Again, it should be remembered that these values characterise sorption
Problems
257
100
rubber
ED (kJ /mol)
80
PVC
60
PVB
CA
40
PVA
PEMA
20
EC
ED =
0
DHS (kJ /mol)
PE
NY
42.3
5 EP
+ 1.0
)
0.71
2
(r =
20
40
60
80
20
10
EP (kJ /mol)
20
30
40
Fig. 8.10 The relationship between ED and HS with EP . Data from Table 8.2 were plotted
of water at low partial pressures, where clustering of water and swelling of the polar
polymers are not involved.
The above data obtained with homogeneous polymers leave little doubt that
temperature effects on water permeability of cuticles cannot be analysed if only
activation energy for penetration (EP ) is known. The problem cannot be solved by
analogy, because cuticles are heterogeneous, and data on temperature effects on
water vapour sorption in waxes, cutin and MX have not yet been determined. Sorptive properties of polar polymers in the MX can be obtained by comparing sorption
in cutin and in MX. Some of these aspects have been discussed when dealing with
sorption of 4-nitrophenol in CM and MX (Sect. 8.1), but comparable data for water
vapour sorption as affected by temperature are not available. Such measurements
can be made. They may be difficult, but there are no insurmountable obstacles. As
long as these data are not available, speculations concerning the magnitudes of ED
and HS in CM should be avoided.
Problems
1. What is the difference between the partition coefficient K and the parameter k
of the Freundlich isotherm? For n = 1 calculate k when K = 90.
2. When all sorption sites are occupied K = 1. What is Gibbs free energy change
in this situation?
3. How large are H and T S when G = 0?
4. Given the data of Fig. 8.2b, what is S when H = 30 kJ mol1 ?
258
5. Using the Arrhenius equations given in Fig. 8.3a for the CM number 1 and 6,
calculate the rate constants k at 10 C and 50 C?
6. Calculate the energy of activation for the species/solute combinations shown in
Fig. 8.3b.
7. Why does ED with ivy leaves increase in the order IAA, bifenox, cholesterol?
8. What is the difference between Do and Po ?
9. Water permeance of Citrus CM at 5 and 35 C is 1.36 108 and 1.17
107 m s1 respectively. For MX, the respective values for Pw is 6.14 106
and 3.04 105 m s1 (Fig. 8.7, ascending T ). How much larger is Pw of the
MX at 5 and 35 C? What are the Arrhenius equations for CM and MX?
10. From the slopes given in Fig. 8.9, ED and EP can be calculated and 10.3 and
36.7 kJ mol1 respectively are obtained. HS = 26.4 kJ mol1 can be calculated by difference (10.336.7) as specified in (8.18). If HS is calculated from
the slope of the plot log Kwv vs 1/T we obtain 30.7 kJ mol1 . How do you
explain this difference between the two HS values?
Solutions
1. K is the slope of a plot internal vs external concentration, while k is obtained
when the logarithms of the two variables are plotted. When n = 1, then
K = k = 90.
2. G = 0.
3. H = T S.
1
4. S = 66 kJ mol1 K .
5. For CM 6, we obtain 3.7 108 (10 C) and 8.2 05 s1 (50 C) respectively.
For CM 1 we have 4.9 109 (10 C) and 4.61 105 s1 (50 C). With CM 6
having the initially highest k , the increase with T was 2,216-fold. With CM 1
the increase was even 9,408-fold. The k ratio between the two CM is 7.55 at
10 C and 1.78 at 50 C.
6. ED is 123.5 kJ mol1 (Hedera/IAA), 162.5 kJ mol1 (Hedera/bifenox), 189.5 kJ
mol1 (Hedera/cholesterol) and 153.4 kJ mol1 (Ilex/bifenox).
1
7. Because solute size increases from 130, 216 to 349 cm3 mol (Appendix B)
and the activation energy is larger when larger holes must be formed in the
membrane matrix.
8. Eo depends on jump distance within the polymer chains and entropy (8.11). Po
depends in addition on thickness of the cuticles and on sorption of water in the
polymer and in waxes.
9. The ratio of Pw is 451 at 5 C and 260 at 35 C. The Arrhenius equation for CM
is Po = 3.986,142 1/T, and for the MX Po = 4.44 4,571 1/T.
10. The individual data points for log Kwv were obtained from individual data of log
D and log Pw at the respective temperatures. The difference is due to rounding
errors.
Chapter 9
In this book, we have focussed on the physical meaning of transport parameters such
as permeance (P), rate constants (k ) and diffusion coefficients (D) measured with
plant cuticular membranes. Experimental methods and statistics have been kept to
a minimum, as we felt this might distract the reader from the arguments regarding
chemistrystructureproperty relationships. This does not imply that we consider
methods and statistics to be matters of minor importance. They are of importance,
and during the course of our investigations new methods had to be devised. We had
to overcome problems related to the variability inherent to biological materials.
Anyone trying to study permeability of plant cuticles has to cope with a discouraging problem. Permeability among individual cuticles, leaf disks and leaves varies
tremendously. Differences between lowest and highest rates often amount to one or
even two orders of magnitude, and the problem increases with decreasing permeability. How can such data sets be characterised, and how can treatment effects be tested
for statistical significance? A normal symmetric distribution of data is the prerequisite for calculating arithmetic means, standard deviations and confidence intervals.
The distribution of data must be established using large populations, and it must be
known to justify elimination of outliers. In most of our investigations, we have used
isolated cuticular membranes to study the effects of humidity, temperature, adjuvants, and solute properties on permeability. With this approach, the permeability
of a large population of 50100 CM can first be characterised and treatment effects
can be established using the method of paired observation. The same CM is used
for various treatments, and it can be tested whether the treatment effect depends on
initial permeability of the CM. If this approach is used, it must be established that
treatments do not change properties of cuticles.
259
260
261
After 120 days most leaf discs are digested, and the upper astomatous cuticles can
be selected from the slurry. It is better to use a blunt pair of tweezers, as this avoids
puncturing the cuticles accidentally. Cuticles are collected in deionised water, which
is changed carefully a couple of times to remove enzymes and cellular debris.
The cuticles of some species contain epoxy fatty acids which covalently bind
lipophilic organic chemicals with carboxyl groups. Treating the isolated cuticles
with 1 mol l1 aqueous HCl converts these epoxy groups to vicinal diols and eliminates binding (Riederer and Schnherr 1986b, 1988). There are no indications that
any other property of cuticles is affected, and for this reason treatment with HCl
for a day, followed by washing with deionised water until free of chloride ions, is a
good routine.
During disintegration of the leaf tissue, fatty acids and phenolic compounds are
liberated from cells and sorbed in the cuticles. Most of the sorbed phenolic compounds can be removed by repeated washing with deionised water or with aqueous
borax buffer (pH around 9.0), but some C16 and C18 fatty acids cannot be removed.
These sorbed materials have no effect on permeability of cuticles, but if waxes are to
be extracted from isolated cuticles, identified and quantified by GC-MS it should be
kept in mind that some of the short-chain fatty acids detected may have been sorbed
during isolation (Schnherr and Riederer 1986).
Isolated clean cuticles must be flattened and dried for storage and better handling.
Cuticles floating in water are pulled on small pieces of Teflon and flattened with a
stream of pressurized air. Initially the stream must be directed to the centre, and
from there it is slowly moved towards the edges. This takes care and some experience. Cuticles dry quickly when exposed to ambient air. When dry, thin cuticles stay
reasonably flat, and they are collected into vessels which are covered to protect them
from exposure to chemicals in the air of the laboratory. Thick fruit cuticles (pepper,
tomato, apple) tend to roll up when dry, and it can be difficult to unroll them in order
to insert them into the transport apparatus.
It is also essential to distinguish the physiological outer side from the physiological inner side of the isolated cuticle. With some species the outer side appears
more shiny, whereas the inner side is more dull. However, this is not the case with
all species. In case there are difficulties in identifying the two sides of an isolated
cuticle, as an unambiguous test a small drop of water (1020 l) can be added on
the surface of the cuticle. Water will spontaneously spread when added on the physiological inner side (due to carbohydrates present), whereas water forms droplets
with finite contact angles on the outer side (due to the presence of lipophilic cutin
and wax).
262
263
total permeance may be acceptable. But holes larger than that, and more numerous
ones, may contribute significantly to Ptotal , and this may go unnoticed if hold-up
times are not determined. This is the case when foliar penetration is measured with
only one time point.
In some studies, k was determined using UDOS (Sect. 6.3), and with many
species k was as low as 107 and 108 s1 (Fig. 6.21). These rate constants can
be converted to permeances P by multiplying k by membrane thickness (6.16).
If k is 1 108 s1 and is 3 m, P is 3 1014 m s1 . P can be obtained by
multiplying P by the partition coefficient (6.17). For bifenox log K is 4.4, and
we obtain P equal to 7.5 1010 m s1 . This calculation shows that with lipophilic
chemicals small holes in the CM result in few problems, as long as the partition
coefficient is very high. With polar non-electrolytes or with ionic solutes having
a K < 1, P values as small as 1015 m s1 or lower are obtained. Such CM are
essentially impermeable to these solutes when penetration is restricted to the waxy
pathway.
From the data of Table 6.8 and (6.21), k for Pyrus communis can be calculated. When the molar volume is 100 cm3 mol1 we obtain 3.5 106 s1 , and a
calculation similar to that above yields a permeance P of 1.05 1011 m s1 if
is 3 m. For ionic solutes K is at least 0.01 or smaller, and this results in a P
of 1.05 1013 m s1 . A hole in this CM having a permeance of 7 1012 m s1
would be a disaster, as the flux across the hole would be 67 times larger than the
flux across the CM. This calculation assumes that aqueous pores are absent from
this CM. In this case, almost the total ionic flux observed would be the flux across
the hole. With pear CM, ionic solutes penetrate across the aqueous pathway, having
rate constants in the range of 1 1051 106 s1 (Fig. 5.7). Hence, P ranges
from 3 1011 to 3 1012 m s1 . This is of the order of the permeance of the hole
of 7 1012 m s1 , and by no means negligible.
Extremely low diffusion coefficients (Chap. 6) in the range from 1015 to
20
10 m2 s1 or even lower are typical for CM. As a consequence [cf. (2.5)], very
long hold-up times in the order of hours or even days are observed (Fig. 6.2). If
plots amount diffused vs time intersect the origin or even the positive part of the
ordinate, this is an indication for membrane defects, resulting in waterwater continuity between donor and receiver. D of water in water is about 2.5 109 m2 s1 ,
and with a 3 m-thick CM the hold-up time for a water layer of this thickness would
be 6 104 s. If cuticular or foliar penetration is studied using only one sampling
interval, the hold-up time is not known and cannot be used as an integrity criterion.
264
Population size ranged from 50 to 750 CM. With MX membranes distribution were
normal, and arithmetic means, standard deviations or confidence intervals can be
used to characterise these MX membranes. With CM from all species, histograms
of frequency distributions of k or P were always skewed and had a pronounced
tail at high values. Skewness tended to be more pronounced with small populations.
After log transformation, symmetrical histograms with normal distributions were
obtained. If populations are skewed, arithmetic means are higher than geometric
means obtained by log transformation of the data. For this reason, it is a good practise to use large sample sizes of 50100 CM and to subject data to log transformation
for calculating geometric means and confidence intervals. Log transformation of
normal distributions presents no problems, as in this case arithmetic and geometric
means are numerically identical.
9.6 Cutin and Wax Analysis and Preparation of Reconstituted Cuticular Wax
265
Fig. 9.1 Experimental setup used for measuring sorption or diffusion coefficients. An aluminium
disk covered with reconstituted wax was affixed with a needle to the screw cap of a glass vial.
The aluminium disk was immersed in an aqueous solution for either loading the wax with a radiolabelled compound (determination of Kww ) or for desorption of a radio-labelled compound from
wax (determination of D)
Aluminium disks (diameter 8 mm) affixed to stainless steel needles were immersed
in a chloroform solution of wax (2050 mg ml1 ). After evaporation of chloroform, the aluminium disks were uniformly covered with microcrystalline wax
(150250 g per 100 mm2 ). However, when immersed in an aqueous desorption
medium the wax crystallites were rapidly detached from the aluminium disks. This
was overcome by heating them for 5 min to 100 C in an oven. The wax melted, and
at room temperature it solidified and formed a uniform smooth layer of reconstituted
wax, which adhered to the aluminium disk during subsequent experimentation.
In most cases, radio-labelled solutes were added directly to the chloroform/wax
solution and were reconstituted together with the wax. These samples can be used
for the determination of D by desorption experiments. This type of loading of wax
is called internal loading. For the determination of Kww , wax samples were reconstituted, and loaded with radio-labelled solutes by immersing them in solutions with
266
Fig. 9.2 A stainless steel transpiration chamber consisting of donor chamber and lid. The area
of the orifice in the lid is 1.13 cm2 . The chamber is filled with 800 l water (blue colour inside
the chamber). An isolated CM ( yellow) is mounted between lid and donor chamber using silicon
grease. Chambers are placed in boxes containing silica gel beads, boxes are closed and incubated
at constant temperature. Water loss from the chamber is determined using a balance (accuracy
0.1 mg)
267
temperature equilibrium and steady state are established before weighing is started.
Depending on water permeability, chambers are weighed at intervals of hours or
even days to get a significant loss of mass. These intervals are too long for detecting
extrapolated hold-up times in the range of 415 min (Table 4.10).
When we used the cup method, the CM were inserted such that the morphological
inner side of the CM was in contact with water while the outer side was exposed
to dry air. In this arrangement, driving force was maximum (aw = 1.0; Cwv =
23.05 g m3 at 25 C). With most plant species, swelling of cuticles and permeance
depend on partial vapour pressure (Fig. 4.6). When in equilibrium with silica gel the
limiting skin is not or very little swollen, and the cup method results in minimum
permeances. Humidity in the box does not have to be zero. If constant humidity
saturated salt solutions (cf. Greenspan 1977; Kolthoff et al. 1969; Appendix B) or
glycerol/water mixtures (Slavik 1974) are used instead of silica gel, humidity can be
varied and effects of humidity on permeance can be studied. We have not tried this,
however. The cup method has been used extensively because it is simple, cheap,
and very accurate, and large sample sizes can be handled (Geyer and Schnherr
1990; Mrida et al. 1981; Riederer and Schnherr 1990; Schnherr and Bauer 1992;
Schreiber and Riederer 1996a, b).
The cup method resembles the situation in nature, except that in the field humidity is rarely close to zero. It has some other limitations. Water fluxes at 100%
humidity cannot be measured, because driving force is zero and no net flux occurs.
In this situation, tritiated water (THO) was used as tracer (Schnherr and Schmidt
1979). An aqueous buffer containing THO served as donor in contact with the morphological inner surface of the CM. Air of constant humidity obtained by the dew
point method was blown over the outer surface of the CM. The moisture containing the THO which had penetrated was trapped in a dry-ice cold trap (70 C),
and radioactivity in the cold trap was assayed by scintillation counting (Figs. 4.6
and 4.8). Schreiber et al. (2001) also studied the effect of water activity of the
receiver using a slightly different approach. The stainless steel transpiration chamber, with THO as donor solution facing the morphological inner side of the cuticle,
was attached upside down to a scintillation vial (Fig. 9.3). Humidity of the receiver
(the scintillation vial) facing the morphological outer side of the CM was varied
using 100 l glycerol (2% RH), pure water (100% RH) or mixtures of glycerol and
water having humidities between 2 and 100% RH (Slavik 1974). The surface of
the CM was in contact with the equilibrium vapour pressures of the glycerol/water
mixtures, but not with the solutions themselves, which were on the bottom of the
vials (500 l). THO which penetrated the cuticle was absorbed in the glycerol, water
or glycerol/water mixtures, and after adding scintillation cocktail, radioactivity was
determined by liquid scintillation counting.
The effect of cations and pH on water permeability of CM or MX membranes
was studied using the system buffer/CM or MX/buffer and tritiated water as tracer
(Schnherr 1976a, b). If a fine capillary is attached to the receiver containing an
osmotic solute, this system can be used to measure osmotic water transport in MX
membranes (Fig. 4.9), but it is not sufficiently sensitive for CM (Schnherr 1976a;
Schnherr and Mrida 1981).
268
Fig. 9.3 Experimental setup used for measuring the effect of humidity on water permeability.
Stainless steel transpiration chambers containing radio-labelled water were mounted upside down
on scintillation vials. Inside the vials, various humidities were established using glycerol (2%
humidity), glycerol water mixtures (humidity between 2 and 100%) or pure water (100% humidity)
269
Sects. 6.1 and 9.5. During our studies of permeability of plant cuticles, a number of
new methods have been developed, some which proved useful and are summarised
here. Further details not mentioned in Chaps. 18 are also provided.
Mass flow can be studied either in the steady (Sect. 6.2.1) or in the transient state
(Sect. 6.3). Detached leaves or conifer needles can be studied using the submersion
technique (Sect. 6.2.2). The well technique is more convenient with leaf disks from
broad-leaved plants (Sect. 6.2.3). Merits and drawbacks associated with the above
methods are discussed in Chap. 6, and need not be repeated here.
Our analysis of barrier properties of cuticles draws heavily on data collected
using isolated cuticular membranes (CM). This makes it possible to measure penetration in the transient state (Sects. 2.5, 6.3 and 6.4). Solute mobility in the limiting
skin and in the sorption compartment of the CM can also be studied quantitatively.
These methods are very powerful for analysing the reasons for differences in permeability among species and solutes (Sect. 6.3.2). The role of accelerators (plasticisers)
in cuticular penetration also relies on these methods (Chap. 7). This warrants a closer
look at these new methods. All of them rely on radio-labelled solutes.
The CM are equilibrated with an aqueous solution containing the radio-labelled
solute. Solutions must be buffered if the solute is a weak acid or base. After equilibration most solutes are contained in the sorption compartment, which has also the
largest mass (Sect. 1.4). The limiting skin is very thin, and only a small percentage
of the total amount sorbed is located there (Fig. 9.5). Solutes sorbed in the CM can
be desorbed using an apparatus shown in Fig. 9.4. For simultaneous bilateral desorption (BIDE) the CM is inserted into the apparatus, and the two compartments
are filled with the desorption medium (water, buffer or phospholipid suspension,
depending on properties of solute). The receiver solutions are withdrawn periodically and exchanged for fresh ones. Radioactivity of receiver solutions is determined
by scintillation counting. Typical results are shown in Fig. 6.15. From the desorption
kinetic, the average rate constants (6.13) and diffusion coefficients in the limiting
skin and the sorption compartment can be estimated [(2.33) and (2.35)]. Desorption from the inner surface is very rapid, and samples must be taken in very short
intervals.
If desorption media are added only to the half-cell facing the morphological inner
surface of the CM, the process is called unilateral desorption from the inner surface
(UDIS). Diffusion of solutes into the sorption compartment (soco) of the CM is very
rapid,and sampling intervals of 13 min are necessary to estimate diffusion coefficients from the initial rates of desorption (Fig. 6.20). These methods are depicted
schematically in Fig. 9.5.
Solute mobility in the limiting skin is measured using unilateral desorption from
the outer surface (UDOS). A simpler method of loading the CM with solutes is
used. The CM are inserted in a simple apparatus (shown in Fig. 6.17). A droplet
(200 l) of aqueous donor solution is added to the inner surface of the CM exposed
in the orifice of the cover and allowed to dry. During evaporation of water at ambient
temperature and humidity, the solute is driven into the sorption compartment of the
CM, as solute concentration in the droplet increases during evaporation of water.
An experiment with 14 C-labelled solute and THO showed that the ratio 14 C/3 H
270
Fig. 9.4 Apparatus made of stainless steel used for unilateral or bilateral desorption (UDIS or
UDOS). The CM (yellow) loaded with radio-labelled solute is inserted between the two halves of
the apparatus, desorption media are added through the sampling ports and solutions are stirred for
mixing. Desorption media are withdrawn periodically and fresh ones are added. The apparatus in
maintained at constant temperature
271
Fig. 9.5 Schematic drawing showing initial distribution of solutes (red dots) in CM consisting of
the limiting skin (ls) and the sorption compartment (soco). In BIDE, UDIS and UDOS experiments,
most of the solute molecules are initially in the soco and very few in the limiting skin. In SOFP,
the solutes are added to the outer surface of the limiting skin and they form a concentrated solution
when they deliquesce. The effect of adjuvants (green dots) is studied by adding the adjuvant to
the desorption medium. The directions of solute (red arrow) and adjuvant flows (green arrow) are
indicated by arrows
272
decreased during droplet drying (data not shown). If the solute was sufficiently soluble in cutin, the solute disappeared from the droplet faster than water evaporated.
Accumulation of solutes on the inner surface of the CM was observed only with
highly water soluble solutes. These are not suitable for UDOS studies, and SOFP
is the method of choice (see Sects. 5.2 and 7.4.3). Once the water had evaporated
the orifice was closed with transparent sticky tape (Tesafilm). This maintains 100%
humidity over the CM and prevents a radioactive spill should a CM break. Desorption is started by adding 500 l desorption medium, which is periodically withdrawn
quantitatively and replaced by fresh medium.
Quantitative sampling of the receiver requires that the length of needle of the
syringe is adjusted such that it almost touches the CM without actually puncturing it.
Holding the chamber slightly inclined towards the port causes the sorption medium
to collect under the sampling port. During desorption, the chambers were positioned
in wells of a thermostated aluminium plate (Fig. 5.4a). Our plate had 100 wells, and
it was lightly rocked at 6080 rpm for mixing of desorption media. During UDOS all
solutes sorbed in the sorption compartment must diffuse through the limiting skin, as
there is no desorption medium on the inner side of the CM (Fig. 9.5). Rate constants
(k ) of desorption (Fig. 6.18; 6.13) characterise solute mobility in the waxy limiting
skin (Sect. 6.3.2), and may be converted to diffusion coefficients (6.20).
Penetration of highly water soluble non-electrolytes (sugars) or ionic solutes
(amino acids, glyphosate salts, inorganic salts) can be studied using the same chambers and experimental setup. However, the CM are inserted into the chamber such
that the morphological outer side is exposed in the orifice of the lid. Solutes penetrating the limiting skin are desorbed from the inner surface of the CM. They do
not accumulate in the sorption compartment, because their partition coefficients
are <1 and solute mobility in the soco is much higher than in the limiting skin.
Small droplets (25 l) of aqueous solutions containing the radio-labelled solute are
placed on the centre of the outer surface of the CM. The water evaporates quickly,
and the chambers are placed into the wells of the thermostated aluminium plate
(Fig. 5.4). The plate is rocked for mixing, and air of constant humidity is blown on
the salt residue on the CM (Schnherr 2000). If humidity is higher than the point of
deliquescence (POD) of the salt, the salt deposit sorbs water and deliquesces. Penetration into the CM occurs from a concentrated donor of unknown concentration.
For this reason, rate constants of penetration (k) must be calculated from amounts
(M) of salt rather than concentrations (5.1). If humidity of the air stream is below
POD, the salt remains solid and there is no penetration (Fig. 5.7).
This type of experiment is called simulation of foliar penetration (SOFP) because
it resembles the situation after spray application to the foliage. These rate constants
(k) characterise permeability of the limiting skin. They are proportional to permeance (P) rather than D because the effect of the partition coefficient is not known
and cannot be corrected for (6.14)(6.17). In these experiments, temperature control is critical because humidity of the air stream depends on temperature of the
aluminium plate. When POD of the salt is close to 100%, the donor side can be
closed with Tesafilm and humidity over the salt residue quickly reaches 100% due
to penetration of water from the receiver. In SOFP experiments, area after droplet
273
drying is not known exactly. As the area is not needed to calculate rate constants
(5.1), this is no problem. Adding a surfactant to the donor solution improves contact
between the aqueous solution and the lipophilic waxy cuticle. This greatly increases
rate constants (Fig. 5.6).
Surfactants and other adjuvants affect partition coefficients (Sect. 7.1) of
lipophilic solutes. If surfactants and solutes are both contained in the donor, data
interpretation can be difficult, because adjuvants affect both partition coefficients
and solute mobility in the limiting skin. These effects can be separated by adding
the adjuvants to the desorption media. When solutes are desorbed, the adjuvants
penetrate the CM from the outer surface and quickly accumulate in the limiting skin
and the sorption compartment. They accumulate in the CM, from which they cannot
escape (Fig. 9.5). There is no effect of adjuvants on driving force, because solute
concentration in the soco is the driving force (Fig. 9.5). The adjuvant concentration
in the CM can be calculated from the partition coefficient and the concentration in
the receiver (Schnherr et al. 2001; Shi et al. 2005a, b). If solute mobility in the control (no adjuvant) is smaller than in the treatment (adjuvant), the adjuvant is called
accelerator (Chap. 7).
Appendix A
SI unit
Symbol
Magnitude
Energy
Force
Pressure
Electric potential
Joule
Newton
Pascal
Volt
J
N
Pa
V
kg m2 s2
kg m s2 = J m1
N m2
J A1 s1
Fundamental constants
Constant
Symbol
SI unit
CGS
Avogadros
constant
Boltzmanns
constant
Molar gas
constant
Faraday constant
Plancks constant
N0
1.381 1023 J K1
8.314 J K1 mol1
Abbreviations
Abbreviation
Description
CA
CL
Cellulose acetate
Cuticular layer(s), layer composed of cutin, cutan and polar
polymers located between CM and cell wall
Isolated cuticular membrane
CM
(continued)
275
276
Appendix A
Abbreviations
(continued)
Abbreviation Description
cmc
CP
CU
DSC
EC
ESR
GC
MS
MX
NMR
PE
PEMA
PET
PMA
POD
PP
PVA
SCL
SOFP
TLC
UDIS
UDOS
Symbols
Symbol
Quantity
Magnitude
a
aw
awv
A
C
Cs
Cw
Cwv
polymer
Cw
D
d
Activity
Activity of liquid water
Activity of water vapour
Area
Concentration
Solute concentration
Concentration of water
Concentration of water vapour
Concentration of water in polymer
Diffusion coefficient
Ratio of D of water in a helium and nitrogen
atmosphere (DwH /DwN )
Density
Density of water vapour at standard
temperature (0 C) and pressure (105 Pa)
Energy of activation of diffusion
Energy of activation of permeance
Flow
Activity coefficient
Change in Gibbs free energy
m2
mol m3 or mol l1
mol m3
kg m3 or g cm3
kg m3 or g cm3
kg m3 or g cm3
m2 s1
(STP)
ED
EP
F
kg m3 or g cm3
8.03104 g cm3
kJ mol1
kJ mol1
mol m2 or g cm2
kJ mol1
(continued)
Appendix A
277
Symbols
(continued)
Symbol
Quantity
Magnitude
J
Jv
Js
Jw
Jwv
K
KHg
Enthalpy change
viscosity
Mass flux
Volume flux of gas or vapour
Solute flux
Mass flux of water
Mass flux of water vapour
Partition coefficient
Water partition coefficient calculated as
PHg /D
Water partition coefficient
Solute partition coefficient between CM, MX,
or wax and aqueous solutions
Water vapour partition coefficient
Octanol/water partition coefficient
CM/water partition coefficient
MX/water partition coefficient
Cutin/water partition coefficient
Wax/water partition coefficient
Mass transfer coefficient
UDOS mass transfer coefficient
UDOS mass transfer coefficient of a solute
having zero molar volume
Pre-exponential factor of the Arrhenius
kJ mol1
Pa s
kg m2 s1
m3 (STP)m2 s1
mol m2 s1
kg m2 s1
kg m2 s1
Kw
Kwrec
Kwv
Kow
Kcw
Kmxw
Kcuw
Kww
k
k
ko
kinfinite
k
k
m
M
N
P
Pw
Pwv
P
PHg
Pw
Pwv
s1
s1
s1
s1
m
m
kg
mol
m2 s1
m2 s1
m2 s1
m s1
cm3 vapour (STP) cm2 s1
m s1
m s1
(continued)
278
Appendix A
Symbols
(continued)
Symbol
Quantity
Magnitude
p
pKa
Pa or cm Hg
pKb
p/po
R
Swater
S
S
te
t
T
V
V
Vx
y
z
s m1
mol kg1 or mol l1
kJ mol1
mol cm3
mol cm3
S
eq/F
C or Kelvin
m3 or l
cm3 mol1
cm3 mol1
Appendix B
Vxb
log Kcw
1912-24-9
65-85-0
107-43-7
42576-02-3
55179-31-2
57-88-5
94-75-7
216
122
117
342
337
387
221
162
93
88
216
267
349
138
2.16c
1.71d
4.44e
3.87f
8g
2.61c
2,4-DB
94-82-6
249
205
3.05g
DEHP
2,4,5-T
117-81-7
93-76-5
390
255
340
166
7.69c
3.16c
HCB
IAA
IPRO
LIN
M-Gluc
MET
NAA
4-NP
C12 H14 N2
PCP
PER
TB
SA
118-74-1
87-51-4
140923-17-7
58-89-9
13224-94-7
21087-64-9
86-87-3
100-02-7
4685-14-7
87-86-5
189-55-0
107534-96-3
69-72-7
285
175
320
291
194
214
186
139
186
266
252
308
138
222
130
296
158
153
162
144
95
157
139
263
241
99
5.77c
1.16g
3.18h
3.80i
0.87e
1.48d
2.25f
1.87c
4.56c
6.36c
3.54g
2.03d
Name
Abbreviation
CAS
Atrazine
Benzoic acid
Betaine
Bifenox
Bitertanol
Cholesterol
2,4-Dichlorophenoxyacetic
acid
2,4-Dichlorophenoxybutyric acid
Diethylhexylphtalate
2,4,5-Trichlorophenoxyacetic
acid
Hexachlorobenzene
Indoleacetic acid
Iprovalicarb
Lindane
Methyl glucose
Metribuzin
1-Naphthaleneacetic acid
4-Nitrophenol
Paraquat
Pentachlorophenol
Perylene
Tebuconazole
Salicylic acid
AT
BA
C5 H11 NO2
C14 H9 Cl2 NO5
BIT
CHOL
2,4-D
(continued)
279
280
Appendix B
Abbreviation
CAS
Octadecanoic acid
Tetracosanoic acid
Triadimenol
Urea
C18 AC
C24 AC
TRI
(NH2 )2 CO
57-11-4
557-59-5
55219-65-3
57-13-6
MWa
Vxb
284
369
296
60
272
356
219
47
log Kcw
8.20j
11.33j
3.37f
2.11k
a Molecular
weight (g mol1 ); b Equivalent molar volume (cm3 mol1 ); c Kerler and Schnherr (1988a); d Kirsch et al. (1997); e Baur et al. (1997b); f Sabljic et al. (1990); g Buchholz
et al. (1998) and Buchholz and Schnherr (2000); h Shi et al (2005a); i Schreiber and Schnherr (1992b); j log Kow calculated from data by Dunn et al. (1986); k log Kow from Sangster (1997)
Abbreviation
CAS
FeC6 H8 O7 NH3
BS
C5 H11 NO2
Ca(H3 C2 O2 )2
CaCl2
Ca3 (C6 H5 O7 )2
C12 H22 CaO14
C10 H16 CaN2 O8
C14 H26 CaO16
Ca(OH)2
C6 H10 CaO6
(C12 H21 O12 )2 Ca
Ca(NO3 )2
C18 H32 CaN2 O10
(CH3 CH2 COO)2 Ca
FeC6 H8 O7
FeCl3 6H2 O
FeEDTA
FeIDHA
Natrel
HgCl
IPA-GLY
K2 CO3
KCl
KNO3
KH2 PO4
C5 H9 NO2
C4 H12 N2
FeEDDHA
AgCl
a Estimated
d
MW (g)
POD (%)
1185-57-5
633-66-9
107-43-7
62-54-4
10043-52-4
5785-44-4
299-28-5
19238-49-4
10030-53-2
1305-62-0
41372-22-9
110638-68-1
35054-52-5
137-08-6
4075-81-4
2338-05-8
7705-08-0
15708-41-5
254
769
117
158
111
499
430
332
490
74
218
755
164
477
186
263
162
367
100a
<50b
>80a
29c ; 32a
100a
100a
100a
100a
>80a
100a
50c ; 56a
100a
90d
100a
44d
100a
7487-94-7
38641-94-0
584-08-7
7447-40-7
7757-79-1
7778-77-0
609-36-9
110-60-1
7783-90-6
393
507
272
228
138
75
101
136
115
88
368
143
100a
100a
<50a
45c
85c
94c
95d
70d
78d
100a
Appendix B
281
MW a
Vxb
c
log Kww
112-34-5
25961-89-1
19327-39-0
23244-49-7
24233-81-6
3055-93-4
3055-94-5
5274-68-0
3055-95-6
3055-96-7
3055-97-8
3055-98-9
26826-30-2
92669-01-7
5157-04-0
40036-79-1
27847-86-5
4484-59-7
5698-39-5
162
234
306
379
511
274
318
363
407
451
495
539
347
435
479
523
567
374
595
141
213
266
332
430
254
288
322
356
390
424
458
316
384
418
452
486
328
515
1732-09-8
2050-23-9
110-40-7
16090-77-0
109-43-3
202
230
258
286
314
167
194
213
241
269
1.08
0.08
0.69
1.55
0.75
3.30
3.11
2.82
2.60
2.30
2.20
2.02
3.19
3.08
4.09
d
log Kwrec
1.19
1.75
2.65
3.73
4.46
Abbrev.
CAS
C4 E2
C6 E3
C8 E4
C10 E5
C10 E8
C12 E2
C12 E3
C12 E4
C12 E5
C12 E6
C12 E7
C12 E8
C14 E3
C14 E5
C14 E6
C14 E7
C14 E8
C16 E3
C16 E8
DMSU
DESU
DES
DBSU
DBS
weight (g mol1 )
molar volume (cm3 mol1 )
c Partition coefficient barley wax/water K
ww (Schreiber et al. 1996b; Burghardt et al. 1998)
d Partition coefficient Stephanotis wax/aqueous solution containing 100 g l1 propane-1,2-diol
Kwrec (Simanova et al. 2005)
b Equivalent
Appendix C
Index of Plants
Botanical name
Common name
Organ
Family
Silver fir
Korean fir
Onion
Tea-plant
Needle
Needle
Bulb scale
Leaf
Pinaceae
Pinaceae
Liliaceae
Theaceae
Bell pepper
Seville orange
Lemon
Kaffir lily
Cucumber
Evergreen euonymus
Benjamins-tree
Indian rubber plant
Fruit
Leaf
Leaf
Leaf
Fruit
Leaf
Leaf
Leaf
Solanaceae
Rutaceae
Rutaceae
Amaryllidacea
Cucurbidaceae
Celastraceae
Moraceae
Moraceae
Golden bells
Leaf
Oleaceae
Maidenhair tree
Ivy
Barley
English walnut
Prim, privet
Tulip-tree
Tomato
Leaf
Leaf
Leaf
Leaf
Leaf
Leaf
Fruit
Gingkoaceae
Araliaceae
Poacea
Juglandaceae
Oleaceae
Magnoliaceae
Solanaceae
(continued)
283
284
Appendix C
Index of Plants
(continued)
Botanical name
Common name
Organ
Family
May lily
Leaf
Convallariaceae
Apple
Breadfruit-vine
Oleander
Olive
Philodendron
Rosaceae
Araceae
Apocynaceae
Oleaceae
Araceae
White spruce
European plum
Cherry laurel
Grey poplar
Needle
Leaf
Leaf
Leaf
Pinaceae
Rosaceae
Rosaceae
Salicaceae
Pear
Leaf
Australian umbrella-tree Leaf
Rosaceae
Araliaceae
Eggplant
Madagascar jasmine
Fruit
Leaf
Solanaceae
Asclepiadaceae
Lilac
English yew
Vanilla
Big periwinkle
Leaf
Needle
Leaf
Leaf
Oleaceae
Taxaceae
Orchideaceae
Apocynaceae
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Index
2,4-D, 46
2,4-Dichlorophenoxyacetic acid, 41
abscisic acid, 142
accelerator, 205, 273
activation energy, 226, 240, 241, 257
diffusion, 241
adjuvants, 192, 205, 273
agriculture, v
agrochemicals, 205
alcohol ethoxylates, 206, 209, 210, 218, 223
amino acids, 3
amorphous wax fraction, 148
amorphous wax phase, 196, 213, 215, 228
amorphous waxes, 246
analysis
cutin, 264
wax, 264
anticlinal walls, 126
aqueous pathway, 125
aqueous pores, 77, 78, 83, 85, 87, 88, 90, 94,
98, 105, 106, 125, 126, 135137, 227,
244
aqueous solubility, 159
Arabidopsis, 4, 117, 121
aromatic compounds, 7
Arrhenius equation, 240, 254
Arrhenius plots, 241, 243, 244, 247250, 253,
254
astomatous leaf cuticle, 137
asymmetry, 94, 178, 191
atomic force microscopy, 14
autoradiography, 175
barley, 160, 161, 209
barley wax, 213
barrier membrane, 246
296
composite membrane, 1
enzymatic isolation, 259
heterogeneity, 1
isoelectric points, 71
isolation, 1
cuticle proper, 15, 87
cuticle/water partition coefficients, 146
prediction, 149
cuticular layer, 15
cuticular ledges, 126
cuticular transpiration, 96
cuticular uptake, 31
cuticular wax
sorption of water, 100, 117
cutin
biosynthesis, 22
expansion coefficients, 252
fine structure, 22
specific volume, 251
volume expansion, 251
cutin synthesis, 26, 27
desorption, 180
outer surface, 179
desorption analysis, 167
desorption experiment, 165, 176, 179
dicarboxylic acids, 212
differential scanning calorimetry, 249
diffusion, 241
rate constants, 241
thermodynamics, 243
diffusion coefficient, 36, 38, 44, 48, 49, 98,
100, 107, 109, 110, 155, 158, 160, 179,
185, 193, 198, 216, 220
temperature, 239
dissociable fixed charges, 73
Donnan exclusion, 68
Donnan potentials, 65, 66
driving force, 57
droplet radii, 172
droplet sizes, 172
Ecotoxicologists, v
ecotoxicology, vi
effect of plasticisers
polar solutes, 227
electrical potential, 65
electron spin resonance, 212
enthalpy, 239, 255, 256
entropy, 237, 239, 243
enzymes
cellulase, 260
pectinase, 260
epicuticular waxes, 14
Index
esters, 12
ethyl cellulose, 54
extrapolated hold-up time, 33
fibrillar network, 23
Ficks law, 31, 35
first-order process, 46, 132
fixed charges, 65, 66
flavonoids, 72
flow
diffusional, 78
viscous, 78, 83
flux, 35
fractional pore area, 81
free energy, 246
Freundlich isotherm, 234
gas chromatography, 4, 11, 12
gibberellic acids, 142
Gibbs free energy, 237, 240
glyphosate, 140
guard cells, 118, 127
half time, 46
heats of sorption, 237, 239
hold-up time, 36, 43, 64, 107, 108, 154, 155
homogeneous polymers, 257
humidity, 104, 106, 130, 134, 191, 192, 267,
272
rate constant, 135
hydrostatic pressure, 79
indolacetic acid, 142
infiltration of stomata, 171
intracuticular waxes, 14
inverse micelles, 229
ion exchange properties, 72
ion selectivity, 74
ionic solutes, 125
isoelectric points, 66
isolated cuticle
defects, 261
integrity, 263
physiological inner side, 261
physiological outer side, 261
isolated wax
diffusion, 198
isolation of CM, 1, 259
isotherm, 234
KMnO4 , 20, 21, 24, 25
lamellae, 24
lateral heterogeneity, 15
Index
leaf disks, 130
leaf surface
microorganisms, 171
limiting barrier, 94, 108
limiting skin, 87, 94, 178, 183, 184, 190, 199,
269
surface wax, 190
thickness, 108
lipophilic compartments, 145
lipophilic matrix, 88, 89
lipophilic pathway, 106
lipophility, 209
mass, 3
mass spectrometry, 4, 11
mass transfer, 46
membrane
asymmetry, 178
heterogeneity, 156
homogeneous, 64, 156, 176
membrane potentials, 66
membrane thickness, 35, 64, 108
methyl glucose, 227
methylation, 104
micelle, 206, 216, 222, 229
MnO2 , 21
mobility
effect of plasticisers, 225
model
cuticular transpiration barrier, 120
molar volumes, 158, 159, 189, 197, 220
molecular size, 197
monodisperse alcohol ethoxylates, 207, 208,
225
monolayer, 114, 120, 121, 169, 170, 247
water barrier, 115
monolayers, 114
multilayers, 239
n-alkyl esters, 211, 218, 226
Naringinin, 72
NMR spectroscopy, 6
non-electrolytes, 153
nuclear magnetic resonance, 212
octanol/water partition coefficient, 145
Ohms law, 37
organic salt residues, 135
osmotic pressure, 79
OsO4 , 20
paraffin, 112
crystals, 113
water vapour transmission, 112
297
paraffin wax, 111, 112, 252
parallel paths, 94
partial pressure, 56
partial vapour pressure, 74, 75, 92
partition coefficient, 40, 44, 58, 59, 64, 146,
147, 151, 152, 156, 159, 234, 264
alcohol ethoxylates, 210
degree of ionization, 151
lipophilic solutes, 151
plasticisers, 206
polar compounds, 152
temperature effect, 236
water, 117
path length of diffusion, 200
pavement cells, 118
pectinase, 2
penetration, 173
biphasic, 163
CaCl2 , 136
droplets, 172
leaf surface, 173
leaves, 160
needles, 160
salt, 134
pentachlorophenol, 162, 207
permeability, 53
dark, 139
diffusional, 85
light, 139
viscous, 85
permeability coefficient, 36, 57
permeance, 43, 53, 153156, 198
distribution, 263
histogram, 264
hole, 262
prediction, 158
pesticides, 205
phase transition, 233, 249, 251, 252
phenols, 3
plant nutrition, vi
plant protection, v, vi
plasmalemma, 38
plasticiser, 213, 223, 226
plasticisers, 158, 192, 205, 220
plasticising effect, 212, 214, 215, 217, 218,
224
cuticular transpiration, 229
reversibility, 221
point of deliquescence, 130, 134, 272
polar aqueous pores, 121
polar non-electrolytes, 129
polyethylene, 32
polyethylene terephthalate, 55
polymer
298
homogeneous, 62
matrix, 61
polar, 62
synthetic, 61, 62
polymer membranes
viscosity, 240
polymethacrylate, 49
polypeptides, 7
polysaccharides, 75
pore
diameter, 86
pore area, 81
pore radii, 80, 85, 87, 90, 137
pore size, 78, 85
pores, 89
porometry, 262
potassium permanganate, 15
precipitates, 129
precipitation of AgCl, 106
projected surface area, 169
radio-labelled solute, 269
radioactivity, 267, 269
rate constants, 37, 132, 136, 164, 181, 183, 191
rates of cuticular penetration
optimising, vi
predicting, vi
reconstituted cuticular wax, 98, 197
reconstituted wax
preparation, 264
reconstituted wax samples, 194
resistance, 37
resistivity, 37
salt penetration, 132
scanning electron microscopy, 18
self-diffusion, 78
silylation, 4
simulation of foliar penetration, 191, 192
size of pores, 81
size of solutes, 158
size selectivities, 199, 200
size selectivity, 137, 139, 188, 198, 220
SOFP, 130, 272
solubilisation, 229
solute
molecular weight, 84
solute diffusion
accelerating effects, 215
solute mobilities, 188
solute mobility, 180, 184, 186, 189, 269
solute permeability, 153, 268
solute radii, 83
solute size, 137
Index
sorption, 49
cuticle, 165
temperature, 233
wax, 165
sorption compartment, 178, 180, 182, 184
sorption isotherm, 58, 77, 104
sorption site
4-nitrophenol, 236
specific gravity, 3
specific surface areas, 169
spin label, 213
state flow rates, 154
steady state, 32, 43
steady state diffusion, 38, 41
StokesEinstein relationship, 86
stomata, 118, 126
stomatal infiltration, 162
structureproperty relationships, v
submersion technique, 159, 191, 269
Sudan III, 15
surface tension, 134
surfactant, 133, 205, 207, 273
swelling, 92
synthetic polymers
water vapour permeability, 254
thermal expansion, 251
thermodynamics
water permeability, 247
thickness of CM, 93
thin-layer chromatography, 11
titration, 68, 69
titration curves, 71
tortuosity, 64, 86, 99, 220, 246
transesterification, 3
transmission electron microscopy, 20
transport limiting barrier, 200
transport-limiting barrier, 193, 225
transversal heterogeneity, 15
trichomes, 126, 127
triterpenoids, 14
tritiated water, 267
UDIS, 186, 269, 271
UDOS, 272
unilateral desorption, 180, 185
urea, 32, 33
Van der Waals forces, 233
vapour pressure, 54, 74
vapour pressures, 54
vapour sorption, 92
volume expansion, 7
Index
water
molar volume, 110
plasticiser, 8
sorption, 77
water activity, 56, 57
water barrier
waxes, 94
water permeability, 97, 247
abaxial CM, 119
adaxial CM, 119
cup method, 266
method, 96
Wax amounts, 96
wax composition, 96
water permeance, 98
water solubility, 150
water vapour, 55, 57
water vapour pressure, 104
wax
amorphous, 99
analysis, 11
biosynthesis, 10
crystalline, 18, 99
crystalline phase, 214
crystallinity, 208, 221
desorption experiment, 193
diffusion, 201
diffusion coefficient, 195
299
diffusion of water, 253
extracting, 93
extraction, 2, 8, 94
fluidity, 221
gravimetric determination, 13
reconstituted, 193, 211
sorption, 201
sorption of water, 253
stripping, 9, 19
wax amounts, 97, 111
wax barrier
thickness, 111
wax coverage, 111
wax film, 19
wax films, 8, 14
wax layer, 94
thickness, 110, 194
wax reconstitution, 195
wax structure, 98
wax/water partition coefficients, 148, 199
waxy barrier
diffusion, 193
Sorption, 193
thickness, 111, 116, 117
well technique, 171
wetting agent, 133
xenobiotics, v, 145