Page 35 - Adsorption Technology & Design, Elsevier (1998)

32 Fundamentals of adsorption equilibria

3.1 FORCES AND ENERGETICS OF ADSORPTION

When a molecule having three degrees of freedom of translation approaches an
unsaturated surface, at least one degree of freedom of translation is lost as a
consequence of its attraction to the surface where it is constrained to movement
across the adsorbent surface. In principle, at least, the force fields associated
with gas phase molecules as they approach one another can be calculated by
means of the Lennard-Jones (1928, 1932) potential energy equation in-
corporating a term arising from molecular attractive forces (inversely propor-
tional to the sixth power of the separation distance between molecules) and a
repulsive force (inversely proportional to the twelfth power of the separation
distance). Constants multiplying each of these terms are derived from
molecular susceptibilities and polarizabilities deduced from spectroscopic data.
Clearly, when an adsorbate molecule approaches a solid adsorbent surface, the
molecule interacts with a large assemblage of atoms in the crystal lattice of the
adsorbent simultaneously. Despite such difficulties, the potential energies (and
hence heats of adsorption) of the vapours of non-polar substances on
graphitized carbon black have been calculated (Kiselev 1960) using semi-
empirical formulations of the potential energy function. Kiselev (1971) was also
successful in computing heats of adsorption of gases in the cages of zeolite
structures.
Although it is beyond the scope of this chapter to outline any of the detail of
force field calculations, it is instructive to see from Figure 3.1 how the potential
energy curves of an adsorbate-adsorbent system relate to experimental heats
of adsorption. The potential energy function U(r) (the sum of all interactions
between an adsorbate molecule and molecules in the lattice of the adsorbent)
passes through a minimum known as the potential well, the depth U (r0) of
which is the energy of adsorption at a temperature of absolute zero. The depth
corresponds to several kilojoules per mole. For a given adsorbate-adsorbent
system U (r0) equates closely with measured heats of adsorption. Such heats of
adsorption can be measured from calorimetric experiments or adsorption
isotherms and isobars. Physical adsorption is an exothermic process and heat is
always released when adsorption occurs. That this is always the case may be
justified thermodynamically. When any spontaneous process occurs (physical
adsorption of a gas at a porous surface is one such instance) there is a decrease
in Gibbs free energy (AG < 0). Further, there must also be a decrease
in entropy because the gaseous molecules lose at least one degree of freedom
(of translation) when adsorbed. It follows then from the thermodynamic
expression
A G = AH- TAS
that AH also decreases (that is, heat is released).