Adsorption at the Gas/Solid Interface

BY D. NICHOLSON and K. S. W. SING

1 General Aspects of Physisorption

The results of a large number of studies of physisorption at the gas/solid interface were reported in 1975 and 1976. As in the past, a great deal of research effort was devoted to the study of physisorption isotherms, but also increased interest was shown in the role of adsorption in the transport of gases through porous media. For this reason, the present Report deals in some detail with adsorption and surface effects in the context of the flow and diff usion of gases.

The mechanism of adsorption in micropores is another major topic which has featured in many recent research publications. Much of this work has been concerned with molecular sieve zeolites, which possess regular pore structures within their crystalline framework. Zeolites are often regarded as model microporous solids, but it has also been shown that the slit-shaped micropores in some molecular sieve carbons are remarkably uniform and are therefore also suitable for fundamental studies of micropore filling.

Other important areas of research, which have been discussed in previous Reports, include different types of gas-solid interactions and interpretation of the adsorption isotherm. It would be impossible in the present Report to discuss in detail these and all other aspects of physisorption, but attention is drawn to a few areas in which notable advances have been made during the period under review.

The Potential Energy of Adsorption. - The adsorbate-adsorbent interaction is fundamental to all physisorption processes. Pairwise summation continues to be the most widely used method for the calculation of adsorption energies, but for some purposes this has been replaced by the approximation of integration over a solid continuum as a model for the adsorbent. In an important general treatment of the interaction of gases with solid surfaces, Steele has compared these two methods for the calculation of adsorption potentials of noble gas atoms and has shown that the potential from the continuum calculation is a comparatively poor approximation. This is especially the case when the adsorbate atoms are relatively small. A rather more satisfactory approximation is given 1 by treating each layer of the adsorbent parallel to the surface as a continuum and then summing the resulting contributions from the layers.

The method of pairwise summation itself is open to criticism, however, and there is little doubt that the true dispersion potential between an isolated pair of atoms is not given exactly by such frequently used forms as the (12:6) Lennard-Jones potential. Recent work on the computer simulation of liquid properties has added strong support to the view that the (12:6) potential fortuitously compensates for neglected three-body (and perhaps higher order) terms. It must be kept in mind that such compensation effects may not operate in quite the same manner with asymmetric interfacial systems.

The dispersion energy contribution, [empty set]D, to the adsorbent-adsorbate potential energy can be expressed as a sum of terms (each of which is itself a summation over pairs, triplets, or higher order groupings of atoms).

Here &8364;(2) is the pairwise term, &8364;(3)etc. represent the higher order interactions, and the locations of the force centres are given by the vectors rietc. Schmit has estimated the importance of the three-body contribution in equation (1) for an Ar atom over the (100) face of an Ar crystal. The pairwise interaction &8364;(2) was calculated from the London formula. The triple-dipole contribution &8364;(3), which is repulsive, was calculated from the Axelrod and Teller formula with the triangle of atoms ijk formed from the adsorbate atom and two atoms of the adsorbent. The contribution from the triple-dipole interactions for Ar self-adsorbed on the (100) face of an Ar lattice was found to be of the order of 5% of the pairwise dipole-dipole term.

A new and promising approach to the calculation of the adsorbate-adsorbent energy, which should also contribute to the understanding of the role of three-body forces, is based on the work of Gordon and Kim. Their method was originally applied with success to pairs of closed shell atoms. The interaction between pairs was calculated on the assumption that no rearrangement of the separate electron densities occurs when the atoms approach each other. As the first step in the calculation the electron densities, [??](r), of the atoms are found as the square of a set of Hartree-Fock wave-functions. These electron densities are then used to calculate the four terms which contribute to the interaction: (i) the direct Coulomb energy, (ii) the kinetic energy, (iii) the exchange energy, and (iv) the correlation energy. The last three terms are obtained with the aid of standard theory for a homogeneous electron gas. The method was found to be particularly successful in the hitherto difficult region around the potential minimum, although the potential at greater separations (where perturbational dispersion force theory is generally considered satisfactory) was less well described. The essential requirement for the application of the method is thus a knowledge of suitable wave-functions.

Bennett used the Gordon and Kim method to calculate the interaction of Ar over an Ar substrate. Pairwise summation was considered to be adequate for calculation of the direct coulombic contributions, which are linear in electron density. The kinetic, exchange, and correlation contributions, however, are non- linear in densities and were treated collectively over a limited region of the adsorbent in the vicinity of adsorbate atom. An adsorbate-adsorbent potential was also estimated in the conventional way by direct summation of Ar pair energies obtained from the Gordon and Kim method. According to these calculations the non-additive potential could be as much as 12% above that from pairwise summation. Even more significant was a 70% reduction in the barrier height between adsorption sites.

The Gordon and Kim method has been applied to noble gases over a graphite substrate by Freeman. The surface model was a single plane of hexagonally packed carbon atoms for which a band wave function was used. The results were considered to be in error in that they gave a much more shallow potential well than that found by Steele. Discrepancies were attributed to two causes; the use of a minimum basis set in the calculation of the graphite wave-functions, and the inadequate treatment of long-range dispersion forces which is inherent in the method . Freeman also studied 10 the adsorbate-adsorbate interactions over a graphite surface. It was found that when the...