Page 30 - Adsorbents fundamentals and applications

BASIC CONSIDERATIONS FOR SORBENT DESIGN 15

in Chapter 4 for calculating pore size distribution from a single isotherm. The
results in Table 2.4 exhibit the remarkable attraction forces acting on the adsor-
bate molecule due to the overlapping potentials from the surrounding walls. The
same carbon atom density on the surface was assumed for all geometries, i.e.
2
3.7 × 10 15 1/cm . The experimental data on two molecular sieve carbons agreed
with predictions for slit-shaped pores. Scarce or no experimental data are avail-
able for cylindrical pores and spherical pores of carbon. Data on these shapes
may become available with the availability of carbon nanotubes and fullerenes
(if an opening to the fullerene can be made).
As expected, the total interaction energies depend strongly on the van der
Waals radii (of both sorbate and sorbent atoms) and the surface atom densities.
This is true for both HK type models (Saito and Foley, 1991; Cheng and Yang,
1994) and more detailed statistical thermodynamics (or molecular simulation)
approaches (such as Monte Carlo and Density Functional Theory). By knowing
the interaction potential, molecular simulation techniques enable the calculation
of adsorption isotherms (see for example, Razmus and Hall, 1991; Cracknell
et al., 1995; Barton et al. 1999).

NOTATION
A constant in the 6–12 potential
B constant in the 6–12 potential; dispersion constant
c speed of light
C dispersion constant; average number of sorbate molecules per
cage in zeolite
E interaction energy
F electric field strength
G Gibbs free energy
h Planck constant
H enthalpy
k Boltzmann constant
m mass of electron
P total pressure
saturation vapor pressure
P 0
q electronic charge of ion or surface
Q heat of adsorption; linear quadrupole moment
r distance between centers of pair; pore radius
r i ionic radius
R gas constant
T temperature
V molar volume

α polarizability
γ activity coefficient
ε potential energy field over surface; emittivity