Adsorption at the Gas/Solid Interface

BY K. S. W. SING

1 Introduction

Numerous studies of gas/solid interfacial systems were reported in the years 1970 and 1971, with much attention given to the physisorption of gases on carbons, oxides, clays, and zeolites and to chemisorption on metal and oxide catalysts. The main objective of much of this work has been to elucidate the surface structure and texture of porous and finely divided materials of industrial importance (e.g. catalysts, desiccants, and pigments) and various experimental techniques were developed for this purpose. Advances were also made in the application of the principles of statistical thermodynamics and quantum mechanics to both chemisorption and physisorption.

It would be impossible to deal adequately in this Report with all of these areas of research. By restricting the scope of this chapter to physisorption and its role in the characterization of solid surfaces, an introduction is provided to certain of the later chapters in this first volume and also to the more specialized aspects of the gas/solid interface to be surveyed in subsequent volumes. This approach should avoid any appreciable overlap of subject matter with the series of Specialist Periodical Reports on 'Surface and Defect Properties of Solids', which deals inter alia with various aspects of chemisorption and catalysis.

Physisorption occurs whenever a gas (the adsorptive) is brought into contact with an evacuated solid (the adsorbent). The phenomenon is thus a general one and is dependent on those intermolecular attractive and repulsive forces which are responsible for the condensation of vapours and the deviations from ideality of real gases. In physisorption (as distinct from chemisorption) there is no electron exchange between the adsorbed species (the adsorbate) and the adsorbent.

In the least complicated cases (the adsorption of a non-polar molecule on a homopolar surface), dispersion forces provide the main attraction between the adsorbate molecule and the assembly of force centres in the adsorbent. In other cases (the adsorption of a polar molecule on a heteropolar surface), various types of specific adsorbent-adsorbate interactions may contribute to the adsorption energy. The importance of specificity within the context of physisorption has only been fully appreciated in recent years and increasing attention is being given to its assessment. It seems appropriate therefore to discuss this aspect of physisorption in some detail.

Most adsorbents of high surface area are porous; to discuss the effect of porosity on physisorption it is helpful to classify pores into three groups on the basis of their effective width. The narrowest pores, of width not exceeding about 2.0 nm (20 Å) are called micropores; the widest pores, of width exceeding about 50 nm (0.05 µm or 500 Å) are called macropores. The pores of intermediate width, which were for a time termed intermediate or transitional pores, are now referred to as mesopores.

The whole of the accessible micropore volume may be pictured as adsorption space, since in pores of these dimensions the adsorption fields of opposite walls overlap. The micropore volume is thus filled by adsorbate molecules at fairly low relative pressure (i.e. within the region of the adsorption isotherm below the conventional 'monolayer capacity'). The filling of micropores may therefore be regarded as a primary physisorption process. On the other hand, capillary condensation in mesopores is always preceded by the formation of an adsorbed layer on the pore walls and is consequently a secondary process; this aspect of the problem is dealt with in Chapter 4.

Although a clear distinction may be drawn in principle between the processes occurring in micropores and mesopores, in practice it is difficult to specify this difference in terms of the characteristic features of a real system. There are two underlying problems: first, the adsorbent properties of a solid are determined both by its texture (area and porosity) and by the adsorbent-adsorbate and adsorbate-adsorbate interactions, which occur in a unique way in each adsorption system; secondly, the pores in a real solid are generally distributed over a wide range of both size and shape. In view of these difficulties, it is hardly surprising that the interpretation of isotherms, in terms of monolayer-multilayer adsorption and micropore filling, has been the subject of much debate over the past few years.

With the growing awareness of this complexity of physisorption has come the appreciation of the need for the determination of standard adsorption data on carefully prepared and well-characterized solids. Graphitized carbon blacks probably represent the best examples of adsorbents with uniform (homotattic) surfaces. Certain low-temperature isotherms (e.g. of Ar or Kr) on graphitized carbon blacks exhibit a stepwise character indicating well-defined layer-by-layer adsorption. Oxide surfaces are generally energetically heterogeneous; they are hydrated (hydroxylated) unless they have been heated to a high temperature. The effect of the surface dehydroxylation of silica on the physisorption of a number of vapours has been studied in great detail and the results have revealed the sensitivity of the adsorption heats and isotherms to the change in the character of the adsorbent-adsorbate interactions.

In this Report, current theories of physisorption are discussed in relation to the adsorption potential and to the adsorption isotherm, with a final section devoted to empirical methods of isotherm analysis. Emphasis is thus placed on the interpretation of adsorption data, rather than on any theoretical treatment per se. Reference is made to a wide range of gas-solid systems, but the surface properties of particular adsorbents are left for detailed consideration in a subsequent Report.

2 The Adsorption Potential

Adsorbate-Adsorbent Interactions on Non-porous Solids. — The importance of a priori calculations of the potential energy (φ)of an atom or molecule in the force field of a solid surface has long been recognized, and a considerable literature dealing with this subject has accumulated. The earlier work has been discussed in some detail by Young and Crowell, and more recent developments have been reviewed by Crowell, Steele, and Pierotti and Thomas.

The potential energy depends both on the distance, z, of the atom from the surface and on the location relative to the lattice of the solid. If the position of the foot of the normal from the atom to the surface is defined in terms of a vector τ in the plane of the surface, relative to some chosen point in the lattice, then

φ=φ(z,τ). (1)

In the earlier work concerned mainly with adsorption by ionic crystals, the values of φ were calculated for certain specific values of τ, ITL(e.g.) over the centre of the lattice cell and the midpoints of the lattice edges. Recently, various attempts have been made to express φ(z, τ) as a periodic function of τ. Attention has been confined mainly to simple adsorptives such as the noble gases, which in the case of He, requires that account be taken of quantum mechanical effects. Studies of the adsorption of He on Kr and Xe crystals are of special interest because they may be expected to improve our understanding of energetic heterogeneity in physisorption.

The Lennard-Jones (12:6) potential is generally used to give the single pair He-substrate atom interaction, ε(r):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where r is the distance between the two interacting particles, and r0 is the equilibrium distance corresponding to the minimum potential energy ε0. In the case of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], as calculated by the usual combination rules for unlike pairs. Ricca and his co-workers carried out their calculations of potential energy as follows: for each point of co-ordinates x, y, z (x]-ITL and (y -axis lying in the plane of surface atoms, z-axis outwards), the potential energy φ(x, y, z) was calculated as the discrete summation over all atoms of solid contained within a sphere centred at point x, y, z with radius equal to three times the edge, a0, of the unit cell of the solid together with integration for uniform density outside the sphere.

The potential energy of adsorption is generally expressed in the topographical form, i.e. φ0(x,y) at z0 as defined by the conditions [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. For convenience the potential energies are often normalized or referred to the minimum value for single pair interaction. Maps of such potential energy surfaces have served to identify the adsorption sites. For example, in the case of a He atom on the (110) face of solid Xe, the adsorption site is located at the centre of the elementary surface cell, directly above an atom in the underlying layer. Two saddle points of different energies connect adjacent sites.

An alternative method of representing the variation of potential energy in three dimensions, adopted by Ricca and Garrone, is to plot the iso-potential contours on the three orthogonal planes intersecting at the point of minimum potential. Such a representation provides a clearer picture of the gradients of potential energy in various directions.

The closely spaced contour lines on the x-y co-ordinates (i.e. the plane parallel to the adsorbing surface) indicate the steep increase in potential as the adsorbed He atom moves across the surface towards the surface atoms of Xe. This lateral movement is equivalent to the penetration of the adsorbed atom into the crystal structure of the adsorbent since the point of minimum potential is at a distance of only 0.134 nm from the surface plane. This analysis also showed that the probability of migration from one site to another is very different in the directions parallel to the two normal edges of the surface cell.

The other maps referring to the vertical planes containing the two different saddle points revealed the importance of the role played by atoms in the second layer of the solid. Ricca and Garrone concluded that the shape of the potential hole, which is particularly flat near the minimum, as well as the strong asymmetry normal to the surface, exclude any possibility that the adsorbed atom may be satisfactorily treated as a harmonic three-dimensional oscillator centred at the point of minimum potential energy.

Studies of He adsorption on the (110) and (100) faces of Xe have confirmed that the minimum potential energies are close in the two cases [-349.1 x 10-23 J on the (110) face, and -339.9 x 10-23 J on the (100) face]. Quantum mechanical calculations, however, indicated that the energies for the fundamental state differ by about 20% (-252.3 x 10-23 J and -210.4 x 10-23 J, respectively), the (110) face providing the more stable adsorption. This result was taken to confirm the need for an adequate quantum mechanical treatment to provide a satisfactory evaluation of the effect of surface heterogeneity on the adsorption energy.

Brown calculated the enthalpy of adsorption of He atoms on the basal plane of a graphite surface and included quantum corrections in the zero-point energy by adapting the Zucker approximation for condensed inert gases. The effect of including the quantum corrections was found to shift both the lattice spacing and the potential energy, i.e. to increase z0 by about 6% and to decrease the enthalpy of adsorption by about 30–50%.

Avgul, Kiselev, Lygina, and Poskus have calculated the interaction energy of a large number of simple and complex molecules with the basal plane of graphite. The basis for these semi-empirical calculations was the relation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where rij is the distance of the centre of either the adsorbed molecule i(or for a complex molecule, its atom or group i) from the centres of the carbon atoms in the graphite lattice j, and z is the distance of the centre i from the plane that passes through the centres of the outer layer of carbon atoms.

The (6:8:10) function (first three terms) arises from the induced dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole interactions. The dispersion force constants Cij1, Cij2, and Cij3 were calculated with the aid of the Kirkwood-Müller equation and analogous equations derived by Kiselev and Poskus. It was estimated that the dipole–quadrupole and quadrupole–quadrupole terms contributed about 10% and 1%, respectively, to the total value of the dispersion interaction; the latter was therefore ignored in most cases.

The fourth term in the expression for Ψ(z) allows for the interaction between permanent dipoles of adsorbate molecules with induced dipoles in the graphite lattice. The induction interaction constant, Aij, was estimated by means of the equation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where αj is the polarizability of the graphite and µi the dipole moment of the adsorbate molecule. The fifth term in equation (3) allows for the short-range repulsion, and the constant Bi was adjusted to satisfy the condition [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The summations of r-6ij, r-8ij, r-10ij and were made over 100–250 centres j and of e-rij/ρij over 40–50 j; the remaining interaction was estimated by integration. In the case of complex molecules, the interaction energy of the whole molecule was estimated by summation over i groups, taking into account the possible spatial arrangements of the molecule. The value of the potential energy of adsorption at 0 K, φ0, was given as the minimum of the curve. This corresponds to adsorption at zero coverage.

The enthalpy data obtained by Kiselev and his co-workers for the adsorption of many different molecules on graphitized carbon are plotted in Figure 1 as a function of the molecular polarizability, α. The experimental values of q]st0 (minus the differential enthalpy of adsorption at zero surface coverage) were obtained by the calorimetric, isosteric, and gas-chromato-graphic methods. The agreement between the calculated values of -φ0 and the experimental values of q]st0 is remarkable, as is the linear dependence on α. This holds true not Only for the noble gases and saturated hydrocarbons, but also for polar molecules which have lone electron pairs or π-bonds and those containing various functional groups (OH and NH). It is evident that the basal plane of graphite interacts in an essentially non-specific manner with all types of adsorbate molecules.

The somewhat higher values of -φ0 as compared with those of q]st0 (e.g. for n-C6H14 and n-C7H16 in Figure 1) are accounted for by the fact that these values of q]st0 were determined at higher temperatures. The direct measurement of the heat capacity of certain adsorption systems has revealed that the enthalpies of adsorption generally decrease with increasing temperature (over 100 °C this may amount to a 5–10% change in q]st0). This also explains the small difference in q]st0, as determined by calorimetry at room temperature and gas chromatography at elevated temperatures.

It is clear that no allowance has been made by Kiselev and his co-workers for electrostatic interaction between a polar molecule and the graphite surface. Avgul and Kiselev have suggested that Crowell's calculation gives too high a value for the electrostatic interaction energy term for a simple dipole interacting with its image in the graphite. Crowell has now extended this calculation to the case of a nearly spherical molecule possessing a significant classical quadrupole moment, Q. It was assumed that interaction with graphite can be represented as the sum of the pairwise (12:6) potential and the interaction of Q with its image formed by the graphite conduction electrons, i.e.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

According to Crowell, the image interaction energy ΨQ(z, φ) is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)

where δ is the distance of the image plane from the basal plane and θ is the angle of the linear quadrupole with the normal to this plane. The maximum contribution was assessed for nitrogen by assuming θ = 0 and taking δ = b/2 (b, the interlaminar spacing, is 0.335 nm). The inclusion of the quadrupole term had the effect of displacing the minimum potential from z0=0.348 nm to z0 =0.341 nm. At the uncorrected minimum, φ12:6= 8.8 kJ mol-1 compared with φ(z0)= -9.5 J mol-1.