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continues to be the most widely used method for the calculation of adsorption energies, but for some purposes this has been replaced by the approximation of integration over a solid continuum as a model for the adsorbent.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 adsorbate was at the equilibrium distance from the surface, these potentials were 12 to 20% more repulsive than for the corresponding gas phase pairs. These results are of the same order of magnitude as those calculated from experimental data and it was suggested that improved wave functions should bring theory and experiment into closer agreement.

The importance of contributions other than pairwise-additive to the potential has been emphasised by Mahanty and Ninham whose approach to the adsorption problem was along the lines originally developed for the prediction of dispersive interparticle attractions in colloid science. In this method the interaction is considered from the point of view of the electromagnetic field created by atomic dipole oscillators and the effect on its energy of the presence of polarisable interacting bodies. The methods and applications of the theory have been described in a recent book. In the context of physisorption, the solid adsorbent and layers of adsorbate were treated as dielectric continua. Allowance for incomplete filling of a layer was made through a 'mean field' type of approximation, which is consistent with the dielectric continuum model. The method incorporates higher order interaction terms in a natural manner. No numerical evaluation of the results was made, but it is interesting to note that the sole requirement for such an evaluation is knowledge of the frequency dependence of the various dielectric constants involved. In contrast to the Gordon and Kim method, this approach can account for long-range contributions to the dispersive force interactions. At the same time, no description of lateral periodicity in the vicinity of the adsorbent surface, nor of the repulsive side of the potential well, emerges from the method. As they stand, these two theories are therefore to some extent complementary. However, both agree on the weight of the theoretical argument in favour of the inclusion of higher order interaction terms in the calculation of adsorption potentials. The quantitative importance of these terms is a question which remains to be settled.

Until recently, calculations of adsorbate-adsorbent potentials have incorporated the assumption that the absorbent could be assumed to have the same structure at its surface as in the bulk material. In surface energy calculations, on the other hand, surface relaxation effects were taken into account many years ago and the subject was reviewed in some depth by Benson and Yun. An important conclusion which emerges is that relaxation due to asymmetry of the surface environment can cause considerable alteration of the lattice spacing in a direction normal to the interface. This effect is especially important in ionic lattices, but less so for noble gas crystals. Pisani, Ricca, and their co-workers found that layer relaxation in graphite has a negligible effect on the adsorbate-adsorbent potential for noble gas adsorbates. In a more detailed study of Ne adsorption on Xe crystals, the relaxation of different crystal planes and of edges was considered. The total energy of the ground state was calculated using a trial wave function and a variational procedure. Relaxation was found to be responsible for a decrease of about 1% over a (100) face and an increase by a similar amount over a (110) face. It is noteworthy that this effect raises the potential barrier which limits migration from one face to another.

The effect of relaxation on adsorption interaction with ionic lattices is apparently much more important. House and Jaycock found that the adsorption of Ar and Kr on a relaxed ( 100) surface of NaCl and KCl increases the depth of the adsorbate-adsorbent potential well over the cation by about 30% and 7%, respectively. The effect was much smaller for other sites and surface barriers are therefore considerably modified by relaxation effects. In the case of Kr on KCl the absolute minimum of the potential moves from a mid-cell position before relaxation to the cation position after relaxation. In a subsequent study considerable modification of the surface second virial coefficients was found to occur as a result of relaxation effects. Large changes in the calculated potentials for N2 and H2 over (100) NaCl were also found by Ben Ephraim and Folman, the increases in the adsorption energy over cation sites amounting to 20% and 25% for H2 and N2, respectively.

In the above studies of ionic solids, the potentials were calculated by using a single-charge model for the ions. A shell model, which allows for ion polarization, has not yet been investigated in the context of adsorption, but presumably would provide a more realistic approach. A further improvement would result from the consideration of relaxation in the adsorbate-adsorbent system taken as a whole.

Structure of Adsorbed Monolayers. - A number of newer physical methods (primarily particle scattering techniques) have been widely used for the study of chemisorption systems; many of these methods have received attention inter alia in the series of Specialist Periodical Reports on 'Surface and Defect Properties of Solids'. In recent years, some of these methods have been applied also to physisorption systems. For example, the application of LEED has been discussed in some detail by Webb and Cohen. A critical comparison of the application of LEED and Auger measurements in the study of krypton on graphite has been made by Kramer and Suzanne. Dash and his co-workers have used neutron scattering to study the structure of adsorbed argon and nitrogen on graphite (Grafoil). An interesting modification has been introduced by Venables and his co-workers, who have employed the technique of transmission high energy electron diffraction (THEED) for the study of xenon adsorbed on a thin single crystal of graphite. These scattering methods are capable of providing more direct and detailed information about the structure of the adsorbed layer than can be obtained from the classical analysis of thermodynamic adsorption data.

Graphitized carbon surfaces have been studied extensively for a number of years. Recently the emphasis in fundamental investigations has moved towards graphite-noble gas systems at low surface coverage and this work has involved the use of graphitized carbon blacks and exfoliated graphites of high surface purity. These materials offer the great advantage that at the present time they appear to provide the best available approximation to a uniform homogeneous surface.

Much of the recent work has been concerned with the adsorption of Xe. A combination of techniques has enabled a phase diagram to be constructed for the Xe-graphite adsorption system over a wide range of temperature and pressure (Figure 1). The monolayer region itself may be sub-divided into the two dimensional gaseous, liquid, and solid co-existence regions with a triple point at 99 K and a critical temperature of 117 K. As a result of LEED studies, it was established that the solid Xe phase has a hexagonal ([square root of 3] x [square root of 3]) structure and it has been generally assumed that this indicates that the Xe atoms are located in a regular array and occupy one third of all the potential wells at the centre of the carbon hexagons. However, the investigations of Venables and his coworkers have shown that it is possible to determine a 'misfit parameter', m(T,p), which is defined in terms of the nearest neighbour distance, a, between Xe atoms;

a = 0.4258[1 + m(T,p)], (2)

where 0.4258 nm is the spacing between the available potential energy wells. It was found that condensation within the Xe monolayer takes place at m = 0.060 ± 0.005 nm.

The compression of a monolayer from the localized epitaxial state to a close- packed state has been suggested as the origin of the sub-steps which have been identified on the stepwise isotherms of Kr and Xe on graphitized carbon blacks. Sub-steps have also been noted in Ar and N2 isotherms on graphitized carbon black at 77 K, but at this temperature are more likely to originate as a result of the transformation from the liquid-like state to the close-packed solid.

The existence of the epitaxial structure for Kr on the basal plane of graphite has been confirmed by the application of LEED. In the work of Kramer and Suzanne, the Kr isotherm was measured at 60 K using both Auger spectroscopy and LEED and it was found that the transition step from two-dimensional gas to the solid state was not vertical - in contrast to the behaviour of Xe. This effect was attributed to compression of the condensed state during the phase transition rather than to surface heterogeneity, but this observation seems to merit further consideration. In this connection, the careful experimental work of Antoniou of Ne adsorption on graphitized carbon over the temperature range 1.5-30 K, has revealed a sharp fall in isosteric enthalpy at very low surface coverage. This effect appears to be associated with a small amount of surface heterogeneity. A similar conclusion was reached in the work of Goellner et.al. on helium adsorption on Grafoil.

A few recent studies have been made of the structure of noble gas monolayers on clean metal surfaces. In the work of Papp and Pritchard, new diffraction spots were identified in the LEED pattern when the close-packed monolayer of Xe was formed on Cu(311), corresponding to a Xe-Xe spacing of 0.445 ± 0.005 nm. In another study, Roberts and Pritchard 3 5 have reported the results of LEED studies of the adsorption of Kr and Xe at 55 and 77 K, respectively, on Ag ( 111) and Cu (211) surfaces. They conclude that the LEED results support the view that the monolayer structures of Xe and Kr on metallic surfaces are generally hexagonal close-packed. Webb and Cohen, working at 25 K, have suggested that the Xe-Xe spacing on Ag (111) is 1.8% larger than in the bulk, but is not in registry with the substrate. Adsorption data over a wide range of coverage were obtained by Carden and Pierotti for Kr on Cu (111) over the temperature range 78-108 K and it was concluded that with this system surface periodicity has a minor effect on the packing of the adsorbate atoms.