CH-440 Nanotechnology

CH-440 Nanotechnology
Particle Size Determination

There are several ways to measure dimensions of
nanomaterials. Transmission scanning electron, AFM and
scanning tunneling microscopy yield direct data on particle
size. Spectroscopic methods based on light scattering
phenomena are also used. Each method has its own set of
issues when it comes to size determination e.g. Artifiacts and
other systemic errors.
Light Scattering
These are analogous methods that measure particle size:
- Dynamic light scattering (DLS)
- Static light scattering (SLS)
- Photon correlation spectroscopy (PCS)
-Quasi-elastic light scattering (QELS)
Measurement of Surface area and porosity
Surface area, pore volume, pore size distribution and pore

density distribution are required to characterize nanoparticles.
The most popular methods of surface area calculation are those
based on gas adsorption. Most methods are based on the
isothermal adsorption of nitrogen. Many advances in surface
science have made the methods surface sensitive, i.e., they are
sensitive to the outermost atomic layers (depth of 2-3 atomic
layers) of the bulk solids. Other methods include:
Small angle X-ray scattering (SAXS), Small angle neutron
scattering (SANS), Electron and atomic force microscopy,
Nuclear Magnetic Resonance (NMR) methods and Mercury
porosimetry.
Adsorption is the attachment of atoms or molecules to the surface of a solid. The
reverse is called desorption. The adsorbent is a solid substrate of high surface
area upon which the adsorbate ( a liquid or a gas) is adsorbed.
Types of adsorption
1. Physisorption
2. Chemisorption
Physisorption is governed by van ser Waals forces and usually results in
multilayers of adsorbed atoms and molecules. Physisorption occurs at low
temperatures with low selectivity and heat of adsorption is usually small
( 10< ∆Habs< 40 kJ/mol)
Chemisorption occurs at high temperatures with higher selectivity and involves
stronger interactions between adsorbates and the surface with
∆Habs>40 kJ/mol.
Surface coverage is defined as the proportion of surface sites on an adsorbent
that are partially or completely covered by an adsorbate and is designated as Θ
– the fraction of adsorption sites occupied by an adsorbate at equilibrium.
There are generally accepted to be six adsorption isotherms (Figure 1). The BET
method is applicable only to adsorption isotherms of type II (disperse, nonporous
or macroporous solids) and type IV (mesoporous solids, pore diameter between 2
nm and 50 nm). The BET method cannot reliably be applied to solids which absorb
(as opposed to adsorb) the measuring gas.
Figure 1 — IUPAC classification of adsorption isotherms (typical BET range is

indicated in Types II and IV by the shaded areas) (after [3]) na=quantity of
absorbed gas, p/p0 is the relative pressure
Example : The volume of nitrogen gas at 1 atm and 273K required to cover 1g of the
silica gel is 0.129 dm3. Calculate the surface area of the gel, if each N2 molecule
occupies an area of 1.62*10-20 m2.
b) BET (after Brunauer, Emmett and Teller) Method (1938)
BET (after Brunauer, Emmett and Teller) equation is used to give specific
surface area from the adsorption data. The BET equation is used to give the
volume of gas needed to form a monolayer on the surface of the sample. The
actual surface area can be calculated from a knowledge of the size and
the number of the adsorbed gas molecules. Any gas may be used, provided it is
physically adsorbed by weak bonds at the surface of the solid (van der Waals
forces), and can be desorbed by a decrease in pressure at the same
temperature. Nitrogen is used most often to measure BET surface, but if the
surface area is very low, argon or krypton may be used as both give a more
sensitive measurement, because of their lower saturation vapor pressures at
liquid nitrogen temperature. The volume of gas (usually nitrogen) adsorbed to
the surface of the particles is measured at the boiling point of nitrogen (-
196°C). At this temperature the nitrogen gas is below the critical temperature
and so condenses on the surface of the particles. It is assumed that the gas
condenses onto the surface in a monolayer and so, because you know the size of
the gas atom/molecule, the amount of adsorbed (condensed) gas is correlated
to the total surface area of the particles including pores at the surface
(inaccessible pores are not detected). It is this correlation calculation, volume
absorbed to surface area, that BET theory gives you. The BET method is the most
widely used procedure for the determination of the surface area of solid
materials and involves the use of the BET equation.
1 1 C 1 P 
   
W ( ( P / P0 )  1 ) W mC W m C  P0 
z 1 1 (C  1)
OR   z
(1  z ) V VmC VmC
H  H 
C  exp  ads cond

 RT 
C is a constant that relates the heat of adsorption to for the first physisorbed layer
with the latent heat of condensation (additional layers). Once C is known, the
calculation of heat of adsorption is straight forward. This relation works well
except for cases of high relative pressure (> 0.35) or very low relative pressure (<
0.05). At relative pressure between 0.05 to 0.35, the main eqn is approx.
Proportional to relative pressure and readily transforms into the eqn of a line. A
plot of (P/Po)/[V(1-P/o)] versus P/Po yields a st. Line with slope m equal to [(C-
1)/(cVm)] and intercept b equal to (1/CVm). Specific area is calculated by;
 Po V m   Vm 
Ss  am  RT  N A  am   N A
   V gas 
Where, Ss is sp. surface area, m2/g
Am is arae of solid surface for adsorption of one gas molecule (0.162nm2 for N2)
Vgas is molar vol of gas in its std state (2.24x10^2 m3)
NA is Avogadro’s number( 6.022x10^23 per mol)
Here it is sufficient to show that the measured inputs to this equation are:
•the equilibrium (p) and the saturation (p0) pressure of adsorbates at the temperature
of adsorption.
•The adsorbed gas quantity (na) (for example, in volume units)
BET equation
The calculated quantities are:

the nm is the monolayer capacity
the BET constant, C.
Finding nm:
Finding C :
To calculate these values the BET equation is plotted as an adsorption isotherm
typically at a relative pressure (P/P0) between 0.05-0.35. In this range BET theory
suggests it should form a straight line (see Figure 2). The value nm can then be found
from the gradient and from that the surface area can be calculated using the molecular
cross-sectional area.
Total surface area [7]
Where N is Avogadro’s number, s the adsorption cross section of the adsorbing species,
and V the molar volume of the adsorbate gas. The exact form of this equation will vary
depending on the units being used for alternative treatments).
The BET constant (C) is also calculated from the intercept and gradient and is related
to the energy of adsorption in the first adsorbed layer. Consequentl,y the value of C is
an indication of the magnitude of the adsorbent/adsorbate interactions. C is normally
between 100 – 200, if it is lower than around 20 there is significant adsorbent/
adsorbate and the BET method is invalid. Greater than 200 and the sample may
contain significant porosity.
The specific surface area is then calculated using the mass of sample.
Example : The data given below are for the adsorption of nitrogen on alumina at 77.3
K. Show that they fit in a BET isotherm in the range of adsorption and find Vmono
and hence surface area of alumina (m2/g). At 77.3 K, saturation pressure, P*or Po =
733.59 torr. The volumes are corrected to STP and refer to 1g of alumina.
Example: The following data refer to the adsorption of dinitrogen (N2) on a sample of
carbon black at 77 K.
Use the equation for the BET isotherm to calculate Vm, the volume of nitrogen adsorbed
which corresponds to a monolayer. If 1 g of carbon black was used in the experiment,
calculate the surface area assuming the area occupied by one nitrogen molecule to be
16.2 x 10-20 m2.
The surface area of this sample was estimated by electron microscopy to be 42 m 2 g-1.
Comment on the difference between the values obtained by the two techniques.
Solution
We can then work out the constant c and from that the value of Vm since:
We can then either use pV = nRT or the fact that at STP (which I'm assuming here to be
1 atm, 298 K) one mole of gas occupies a volume of 24000 cm3 to find the number of
moles of N2 that this volume corresponds to. This is 6.19 x 10-4 moles, which in turn will
occupy an area of 60.37 m2 (molar area x Avogadro's constant x 6.19 x 10-4). This is for 1
g of carbon black. This value is higher than the area estimated by electron microscopy
because electron microscopy doesn't take any account of the porosity of the material.
The process of BET measurement is shown in Figure 3. As all data are measured
relative to P0 this value must also be calculated. P0 is the saturation pressure of
adsorbate at the temperature of adsorption. It can either be measured initially for an
empty tube or it can be measured at the same time as the measurement described
below is occurring in a third tube (not shown in Figure 3). The following describe the
main steps in the process of BET measurement:
Degas: Prior to the determination of an adsorption isotherm over the BET region the
sample must be degassed, while avoiding irreversible changes to the surface. This is
generally done either using a vacuum system or by flushing the sample with a gas
(e.g. N2) often at elevated temperature. The temperature used depends on the
stability of the sample. A temperature of 110°C is quoted [8] for nitrogen isotherms
where the sample is stable to this temperature. Once cool the sample must be
reweighed to take into account any mass loss during degassing.
Evacuate: The sample and reference tubes are evacuated. The reference tube will be
treated in the same way as the sample tube throughout the measurement.
Volume: At this stage most BET methodologies will carry out a dead-volume
measurement using an inert gas such as He. This result is used to correct the
quantity of adsorbate adsorbed. It is important that the sample and reference tube
have similar dead volumes. A glass rod or glass beads are often used to reduce dead
volume and to give the two tubes similar dead volumes.
Evacuate: The dead-volume gas is then removed by vacuum.
Adsorption: The adsorbate gas is admitted to the two tubes either in doses or as a slow
continuous flow. Adsorption of the gas on to the sample occurs, and the pressure in the
confined volume continues to fall until the adsorbate and the adsorptive are in
equilibrium. The amount of adsorbate at the equilibrium pressure is the difference
between the amount of gas admitted and the amount of adsorptive remaining in the
gas phase. To calculate this the pressure, temperatures, and (dead) volume of the
system is required. The reference tube pressure is also used as a reference. This step
gives the adsorption isotherm over a selected range of P/P0.
Desorption: For the calculation of certain quantities (see Table 1) a desorption step is
also required where a vacuum is applied in the reverse of Step 5. This will give the
“desoption isotherm”
Normally, the determination of specific surface area requires at least 3 measurements
of adsorbed gas quantity (na) each at different values of P/P0. However, under certain
circumstances it may be acceptable to determine the specific surface area of a powder
from a single value of na measured at a single value of P/P0 such as 0.300.

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CH-440 Nanotechnology

Particle Size Determination

Surface area, pore volume, pore size distribution and pore

Figure 1 — IUPAC classification of adsorption isotherms (typical BET range is

The calculated quantities are:

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