The adsorption of non-polar gases on alkali halide crystals

In recent years many important theoretical advances have been made in the application of quantum statistics to adsorption problems. Fowler (1935), adopting the Langmuir picture of a monomolecular adsorbed gas layer, derived from purely statistical considerations the equationp = (θ /1-θ ) ((2πm )3/2 (kT )5/2 )/h 3 (bg (T )/vs (T )e-x/kT , in which the undetermined constants of Langmuir’s original equation (1918) are given explicitly in terms of the partition functions, bg (T ) andv s (T ) belonging to atoms in the gas phase and in the adsorbed layer respectively andx , which is the difference in energy of an atom in the gas phase and in the lowest adsorption level on the surface. In subsequent developments the change in the energy of adsorption as a function ofθ (the fraction of the surface covered) has been introduced in the above equation using (a ) the Bragg and Williams approximations (Fowler 1936a ) and (b ) the Bethe method (Peierls 1936) to determine the configurational energy. Further applications and extensions of these methods to special adsorption problems have been carried through by Roberts (1937) and by Wang (1937), and Rushbrooke (1938) has examined the validity of the assumption, which is implicit in all this work, namely, thatv s (T ) is independent of the configuration. In addition, an approach to the solution of the statistical configuration problem when molecules condense in two layers simultaneously has recently been made by Cernuschi (1938) and developed by Dube (1938). In order to evaluate correctly the summationsv s (T ) occurring in equation (1), the Schrödinger equation for an atom moving in the three-dimensional potential field of the substrate should be solved, but this has so far proved prohibitively difficult. In the past it has been customary, and for practical purposes it is possibly generally sufficient, to substitute classical partition functions for these summations.