Theory of Dyeing-F. Jones
Theory of Dyeing-F. Jones
Theory of Dyeing-F. Jones
16
change involving both enthalpy change and entropy change in the
dimerisation for any dye can be determined from the equilibrium
constant governing the reversible formation of dimer from two
monomeric species and its temperature dependence, the values
obtained in practice depend on the accuracy of the means by
which the equilibrium constant is obtained.
Thus, to a first approximation the dimerisation of a number of
ionised monosulphonated dyes and of some positively charged
basic dye cations is accompanied by standard entropy changes of
from - 10 to -20 cal deg-1 mole-1. This decrease is made up in
part by a loss in translationalentropy of the monomeric ion and in
part by a gain in entropy of the water. This gain of entropy by the
solvent is due to the probable decrease in the structural order of
the water promoted more effectively in the vicinity of a monomeric ion than in the region of a dimeric species. Conversely,
entropy values obtained for non-ionic dye vapours, which exist
mainly in the form of dimers (a), show that, under anhydrous
conditions, the decrease in entropy related to dimer formation is
only of the order of -1.0 to -2.0 cal deg-1 mole-1. This
decrease is therefore much less than that generally observed for
dimerisation in solution. It must, however, be pointed out that
association in the vapour is between molecules that, although
polarisable, do not possess a fully developed charge. It appears
then that the structural nature of water promotes association and
explains the large equilibrium shift towards monomer formation
at high temperatures, since the structure of the solvent is strongly
dependent on temperature. If association of dye molecules were
dependent only on the forces of interaction contributing to
hydrophobic bonding, then the phenomenon would also be
observed in other solvents. Since association is much less marked
in organic solvents of low dielectricconstant, it can be concluded,
at least for basic dyes possessing a non-localised positive charge
(9), that increased water-water interactions overcome the
repulsion forces acting between dye ions of similar charge.
The possibility that dye ions associate in solution is very real
and, if this is not taken into account, errors in determining such
parameters as ionisation constants can be considerable. The
problem can be overcome to some extent by using very dilute dye
solutions, where the probability of collision may reasonably be
expected to be low. Even so, self-associationoccurs at concentrations as low as one milligram of dye anion per litre of solution
(10). In determining ionisation constants for a number of
monosulphonated 00'-dihydroxyazo mordant dyes, it was
necessary to use mixtures of dioxan and water to overcome
association effects and extrapolate the ionisation constants to
values for pure water. It was then possible to compare the effect
of association on the ionisation constant related to the ionisation
of the first hydroxyl group in these dyes. This is increased when
association occurs. Under more alkaline conditions both
hydroxyl groups are ionised and association is minimised or
eliminated since the repulsion forces between the trivalent fully
ionised entities are much larger.
The influence of additives such as urea ( I I ) , formamide (12),
N-alkylacylamides (13) and alcohols (9) on the structure and
properties of dye solutions has recently been studied. It is
generallyaccepted that additives of this type induce disorientation
of the water structure in the vicinity of the dye ion, thereby
reducing aggregationattributed to loss of hydrophobic interaction.
It has been pointed out (14) that this mechanism has not been
conclusively proved, although no doubt a decrease in dye-dye
interaction by the action of urea on dye solutions does occur, and
leads to increased rates of dyeing. The swelling action on protein
substrates and reduction of hydrophobic interaction in the
substrates by urea also contribute to an increase in the rates of
dyeing, thus illustrating the interdependence of parameters
mentioned earlier.
Non-ionic disperse dyes possess very low solubilitiesin aqueous
dispersions at the dyeing temperature, and association, which
REVIEW
.. . (3)
where S, is the mean solubility of a particle of radius r, y is the
free surface energy, p is the density of the solid and S is the
minimum solubilitywhen the particle size is increased. There must
be a maximum value of r for the condition Sr =S and this can be
shown (17) to be approximately 10-2 pm, which is much less than
the mean radius of disperse dye particles. Further, the anomalies
in rates of dyeing were inconsistent, and it is now suggested that
the inconsistency may be explained by the formation of different
structural modifications of the solid dye during dyeing. These
modifications could be verifiable from X-ray diffraction data.
That this possibility has not been put forward by the authors is
surprising, since in another context (18) it is stated that X-ray
diffraction data are obtained as a matter of routine.
Solid-state transitions and polymorphic changes occurring
through solution and recrystallisation mechanisms are well
established in non-ionic dyes and pigments. In azo pigments
transitions occur on heating the pigment in an aqueous environment (19), and Apperley (20) has recently studied the influence of
surface-active agents on the morphology of C.I. Disperse Yellow
3 at the coupling stage. If such changes are occurring in dyebaths,
then further research on specific systems from this aspect may
throw considerable light on anomalous results obtained in
dyeing research.
Jhetics of Dyeing
.. ..(4)
THE THEORY
OF DYEING
17
measured diffusion flow to take account of any hydrodynamic
transfer of the component under investigation. This could be
achieved by taking into account a frame of reference within
which the diffusion process is measured. The reference frame may
be delineated in several ways. By conducting diffusion experiments in pre-swollen fibres or films,it can be assumed that no
further change in volume occurs on dyeing, and here the reference
frame is fixed with respect to the surface of the fibre or film.
Under these conditions Ficks laws d o appear to apply and
reference-frame effects may become important only in carrier
dyeing and in dyeing fibres that have not been pre-swollen.
Irreversible changes in polyester structures have recently been
observed (25)in carrier dyeing with disperse dyes.
A method for determining concentration-distance profiles
without cross-sectioning and thereby standardising the frame-ofreference effects still further has been developed by Blacker and
Patterson (26). The method utilises the continuous changes in
transmitted monochromatic light when a dyed filament, of
circular cross-section, is scanned across its longitudinal axis by
moving the filament across a narrow slit. A microspectrophotometer is used for this purpose, the results being suitable for
computer calculation to determine the dye distribution across the
fibre. Changes in profile shape for a number of disperse dyeings
on polyester and nylon 6.6 filaments over a range of dyeing times
were obtained. The profile shape and the observation that in all
cases a time-dependent increasing surface concentration of dye
occurs showed that the rate of transport of dye to a boundary
just within the surface of the substrate is no higher than that at
which dye is transferred to the interior. It is also interesting to
observe that for nylon 6.6 this latter rate is extremely high, even
during the initial stages of dyeing, since horizontal profiles were
obtained. This behaviour is difficult to interpret unless it is
assumed either that the substrate is behaving like a liquid or that
the driving force for diffusion is a variation in activity and not
concentration of the diffusing species.
When the dye and the substrate possess charges of opposite
sign, which usually applies to the nylon-acid dye system under
acid conditions, the charge on the fibre becomes increasingly
negative during dyeing. This happens in the dyeing of nylon
with Orange I1 (C.I. Acid Orange 7), the surface potential
becoming increasingly more negative as dye concentrations both
within (27) and on the surface (28) increase. The initial surface
potential depends on the history of the substrate. Bell (29) has
found that rates of dyeing of acid dyes on nylon 6.6 are directly
proportional to the surface area and the saturation equilibrium
value of the dye on the substrate. The latter values are considered
to be directly related to amine end-group content, but, in contrast
with Suzawa and Saitos results (28), it is assumed that there is
no possibility of adsorption of dye on the surface. Bells conclusions must therefore be taken with some reservation, particularly when it is noted that dye concentrations in the fibre phase
were estimated solely on the basis of changes in dye concentration
occurring within the dyebath.
When the ion and the substrate are oppositely charged,
interaction between species can lead to additional factors in the
interpretation of molecular diffusion processes. Some attention
has been paid to this problem by Mayer (30) in the dyeing of
acrylic fibres (negative sites) with cationic basic dyes under
commercial conditions. Diffusion is satisfactorily achieved only
below a certain temperature and strict temperature control is
necessary to achieve a reasonable rate of dyeing consistent with
levelness. Above this maximum temperature, bond formation,
represented by salt linkage, inhibits the attainment of adequate
rates of diffusion. Information to investigate this problem in a
fundamental way is, however, lacking at present.
A generalised treatment for explaining non-Fickian behaviour
has been given recently (31). This type of diffusion, usually
attributed to substrate changes, can also occur when a second
18
independent process such as an immobilising chemical reaction
is superimposed with a comparable time scale. The presence of
blind pores acting as diffusant 'sinks' in a porous substrate can
also have this effect. Anomalous diffusion may also arise in
systems in which 'thermodynamic' diffusion coefficients, theoretically determined from practical diffusion coefficients and
diffusant solubility, depend both on activity and on penetration
distance in such a way that activity and distance variables cannot
be separately assessed. Solutions to this general problem require
a large amount of computation and are wcrthwhile only in
particular circumstances.
The molecular interpretation of diffusion of dyes in polymeric
systems is based on the strong dependence of the apparent
diffusion coefficients D A on temperature, which often follows a
simple Arrhenius equation, viz.
DA
Do exp( - E / R T )
.. . .(5)
ic
.lF
--TAT
. . . . (6)
lyer 'el a/. (34) have applied Eqn 6 to show that a relation
between A H ' and 4 3 does exist in the dyeing of cellulose with
Chlorazol Sky Blue FF (C.1. Direct Blue 1) and that 4Ecvalues
increase with increasing size of alkali-metal cations present
during absorption. Calculated values of activity of the dye in
solution were used together with a variable substrate-volume
parameter defined previously (35) as the product of the surface
area available for dye sorption and the thickness of the diffuse
double layer existing between the bulk dyebath phase and the
outer surface of cellulose. As A i r increases in this manner there
is a corresponding increase in the value of the entropy change
uhich is considered to be due to different packing arrangements
of dye molecules at the surface of the substrate. The interpretation of these results, however, in terms of a breakdown in water
structure in the vicinity of the cellulose in the presence of large
cations (as is done by the authors) must be treated cautiously,
since thermodynamic data are concerned only with differences
in initial and final states and can give no information on the
mechanism by which the final state is approached. It is interesting
in this connection to note that, in the dyeing of cellulose with the
leuco anion of a non-symmetrical vat dye-a process similar to
the application of direct dyes-stacking or association of the dye
anion occurs on the fibre, and this leads to an oxidised dyeing
in which associates are present before oxidation (36).
More attention has been paid recently to research on the
dyeing of wool and nylon with acid dyes. Interaction has generally
been considered as electrostatic bonding between dye anion
and positively charged sites such as protonated amine groups
existing in the substrate under acid conditions. This conclusion
has been deduced from studies of sorption isotherms where no
further increase in dye sorption beyond the value equivalent
to the number of charged sites has been obtained. The possibility
that van der Waals forces arising from dipole-induced dipole
interaction and dispersion forces also operate must not be excluded. Possible substrate changes, particularly when the attainment
of equilibrium is prolonged, leading to the exposure of sites at
which interaction with dye anions may occur, must also be considered
One approech to reduce the number of these parameters (37)
has been to study the absorption of dye anions that normally
have no substantivity for cellulose, by a cellulose substrate
modified by conversion of some of the hydroxyl groups to
8-aminoethyl groups. Any dye bonding occurring should therefcre be specific to the amino groups. Thermodynamic affinities
and heats of dyeing show that the dye anion has interacted with
the protonated amino group. Changes in accessibility compared
with unmodified cellulose are shown to be negligible, but the
modification reaction in which polyethyleneimines having
substantivity for the substrate (38) are formed may lead to a
substrate in which more than one type of adsorption site is
present. The assumption of lack of substantivity of these acid
dyes for cellulose and their precise mode of interaction with
amino groups have been called into question (39), but in a simpler
system (40), when the same dyes have been applied to aminopolypropylene under acid conditions, the correlation between
protonated amino groups and equilibrium sorption values has
been explained on the basis of a simple ion-exchange model.
Although Langmuir-type adsorption isotherms indicate a
probable stoichiometric relation, amounts of dye absorbed over
and above the limiting value (overdyeing) give rise to Freundlichtype isotherms. This phenomenon is attributed to the presence. of
associated dye species within the dyebath. Theoretical expressions
describing differences in the two types of isotherm for acid dyes
on nylon depend not only on the degree of association of dye in
the dyebath but also on the equilibrium established between
sorbed and mobile dye anions within the polymer phase (41).
This latter type of equilibrium behaviour has been considered
19
Rattee has recently reviewed (44) the chemistry of these
reactions from a kinetic standpoint. In view of the heterogeneous
nature of the dyeing process, the initial model system used has
been one in which a homogeneous reaction phase-soluble
reactive dye, soluble alcohol acting as the substrate and wateris considered. Reaction of dye with alcohol is analogous with
fixation of dye on cellulose. The fixation and hydrolysis reactions
are bimolecular, although the total reaction normally behaves as
a pseudo-unimolecular reaction because water and alcohol are
present in excess. It can be shown that, under conditions where
the alcohol is very slightly ionised, the ratio of the rate constants
of fixation and hydrolysis, i.e. the reactivity ratio, Z , must be
constant at any temperature and be independent of pH conditions.
At higher pH values, the ionisation of the alcohol may become
significant and the reactivity ratio in this case is no longer constant but depends on pH. When the model is extended to include
cellulose, which contains ionisable primary and secondary
alcoholic groups, the situation becomes more complex, since
reactions may proceed at different rates in the fibre and in the
aqueous phase. The distribution of dye between the two phases
assumes a greater significance under these conditions and the rate
of diffusion into the fibre also plays a part. Hydrolysis occurs
both in the dyebath and in the internal water phase, but for the
purpose of this discussion the latter effect can be shown to be
minimal. Simultaneous reaction of the dye with the fibre and
diffusion of the dye within the fibre can be accommodated by
applying a simplified Danckwerts equation (44) i,n which the
efficiency of fixation E, defmed as the ratio of the rate of reaction,
dfldr, to the rate of hydrolysis, dhldt, is given by
20
reactive dyes when hydrolysis is at a minimum. This occurs under
slightly acid conditions for reactive dyes on cellulose. If, now, the
dyeing behaviour of dyes containing non-reactive residues but
similar in structure to reactive dyes is observed over a range of
pH values, it can be assumed that the changes in affinity and
rates of diffusion of these inert dyes will be paralleled by similar
but theoretical changes occurring with the reactive dyes. The
affinity and diffusion coefficients of the latter can therefore be
determined over a pH range by extrapolation. For two out of the
three dyes examined in this way, calculated values of D increased
and values of [ D ] F decreased with increasing alkalinity. In
contrast, the third dye exhibited a minimum in its D values and
amaximum for [ D l ~ apH
t I 1 *5.
Hydrolysis in the dyebath of dichlorotriazine reactive dyes in
which the chromogen is linked to the reactive residue through an
imino group may not be a simple second-order reaction but may
be complicated by the presence of a deprotonated imino form
(-i;j:)Bxisting as a result of acid-base equilibrium between the
latter and the imino form (-NH-) itself (48). The products of
hydrolysis of each form will be identical, although the rate
constants for hydrolysis for each form will differ. These constants
and the acid-base equilibrium constant cannot be determined
without a knowledge of the activity coefficients of each species.
Products of activitycoefficientsand rateconstants can, however, be
approximated by computer processes. When this approximation
is carried out, the derived activation energies of hydrolysis are
found to depend on temperature with a maximum curvature at
30C. This illustrates a common feature either in the dye structures or in the system as a whole. The observation of a minimum
in the mean activity coefficient in solutions of Orange 11 at this
temperature (49) determined by differential vapour-pressure
manometry is relevant in this context and may indicate structural
changes in the aqueous solvent in the vicinity of the dye anion
at this temperature.
More recently, the emphasis in reactive-dyeing theory has
shifted towards protein substrates and the investigation of substructures within the protein that can react with the dye. The
elucidation of reaction mechanisms is more difficult than with
cellulose, since reactions are possible with a greater number
of sites of different types, the possibility of fibre degradation
is higher and fibre morphology is more complex. Very little
quantitative information was available until Shore, in an admirable series of papers (50) and adopting the approach previously
taken for the reaction of dyes with cellulose, examined the rate
of reaction of a monochlorotriazine dye with a number of model
compounds related in structure to the amino-acid residues in proteins. If it is assumed that the reactivities or dissociation constants
of the groups in the protein are unaffected by their neighbours
then their reaction rates and activation energies will be comparable with those of model compounds in aqueous solutions.
By such comparison the order of relative reactivity in watersoluble proteins is cysteine thiol > N-terminal amino > histidine
> imidazolyl, etc., down to lysine amino and serine alcoholic
groups. This assumes that the availability of the groups in the
protein to the reactive dye is equally as great as their availability
as model compounds in a homogeneous solution, but this is not
very likely. By extending the study (51) to include water-insoluble
proteins of known composition the most important groups to
react were again shown to be the cysteine thiol, the primary amino
groups of lysine and N-terminal amino-acid residues. It is
important to note that the thiol groups are reactive over the
whole pH range, whereas primary amino groups exert an influence only under alkaline conditions. Conditions with respect to
pH in kinetic and thermodynamic studies will differ from those
adopted in the reactive dyeing of cellulose. It is not possible then
to adopt comparative techniques such as those of Sumner and
Taylor (47), since the dye reacts readily under neutral or slightly
acid conditions.
21
22
dichroic orientation factor. Nakayama et al. (68) have shown
that, provided the amorphous polymer structure does not change
irreversibly, the orientation factor is in fact reversible. It is
concluded that, even if dye migration occurs at higher temperatures, the dye molecule reverts to the same type of absorption
site on cooling.
The view that disperse dyes are at least initially monomolecularly dispersed in hydrophobic fibres is favoured by Husy et al.
(69). In their more recent experiments they qualitatively show that
exposure to light of cellulose acetate dyed with an azo disperse
dye in which a trans+& rearrangement can take place is
accompanied by contractions in the dimensions of the substrate.
With dyes that d o not undergo this phototropic change, the
dimensions of the substrate remain unchanged. These results
indicate a close interaction between dye and substrate molecules
which is favoured more by a molecular dispersion than by an
associated state.
Conclusions
A reading of this review will show that no new theories of
dyeing have been postulated and that a comprehensive theory of
dyeing is still far from reality. In a recent survey, Valko (70)
suggests that, whereas thermodynamic studies of dyeing can
make useful contributions to the general theories ofintermolecular forces, diffusion processes and the influenceof parameters such
as concentration, temperature, electrolyte concentration and
polymer structure on these processes remain largely uninvestigated and would be of greater relevance to application methods.
As is shown in this review, however, when equilibrium studies are
carried out and assessed in conjunction with the growing amount
of information on the structure of water and aqueous solutions,
their relevance to dyeing theory should not be underestimated.
Dyeing theory has been previously retarded by lack of knowledge
about non-ideal behaviour, but it is now possible, e.g. by differential manometry or vapour-pressure osmometry, to determine the
mean activity coefficients of dyes in solution. This may be the
first step in determining activity coefficients of dyes in the
internal aqueous phase and inthesubstrate. Finally,muchresearch
is still needed on the heat stability of dye dispersions and solids
and on the thermodynamics and kinetics of heat-fixation
processes.
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51 Idem, ibid., 84 (1968)545.
52 Idem, ibid., 85 (1969)14.
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70 Valko, ibid., 39 (1969)759.
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30