Adsorption on Heterogeneous Surfaces

BY W. A. HOUSE

1 Introduction

This Report is concerned with the surface heterogeneity of gas-solid and liquid-solid systems. It presents a historical development of the subject with particular emphasis placed on work published in the period 1970 to July 1981.

Properties of the solid/gas and solid/liquid interfaces are dependent on the chemical structure and topology of the solid surface. The chemical potential of the adsorbate, whether vapour, gas, or liquid, is dependent upon the nature of the surface and the spatial variation of the adsorption potential energy. Generally the development of physical adsorption theory has tended to con centrate on homogeneous surfaces, although the subsequent applications have been made in a haphazard manner to a wide class of absorbents commonly termed heterogeneous; since the details of surface heterogeneity are invariably unknown, the entire development and results derived there from are disputable.

In many instances the macroscopic surface topology may be examined using electron microscopy and such techniques as ultraviolet and X-ray photoelectron spectroscopy, Auger electron spectroscopy, secondary ion mass spectroscopy, and infrared spectroscopy;2 these are commonly adopted to investigate qualitatively and sometimes quantitatively, the chemical nature of the solid surface. Other methods using ultra-high-vacuum surface techniques such as RHEED and LEED u are available to probe the microscopic structure of the surface and have proved invaluable in elucidating the structure of metal surfaces with and without adlayers. Unfortunately these methods are not generally applicable to the macroscopic analysis of particulate surfaces.

It is interesting to reflect on the situation described over thirty years ago by Roginskii and Todes: 'The inhomogeneity of the surfaces of most solids is borne out by a number of independent facts. The achievement of electron microscopy justifies the hope that the time is not very far off when the peculiar structure of an active surface will probably be open to direct observation and measurement. At present however, only integral and indirect methods of studying surface inhomogeneity are at our disposal.' As yet no direct and quantitative method of assessing surface heterogeneity is available. The theoretical development and applications of physical adsorption to heterogeneous surfaces has been orientated to deriving information about surface heterogeneity of particular systems (i.e. gas/solid combinations) from gas adsorption isotherm data.

The Development and Early Solutions of the Integral Equation of Adsorption. — Langmuir derived the classical isotherm equation which bears his name by assuming the adsorbate to be localized on the surface without lateral interactions and that adsorption was on a homogeneous crystal surface exhibiting only one kind of 'elementary space' (i.e. a region of uniform adsorption energy, U). The fractional monolayer coverage of the total surface was expressed as:

θ = p/(K + p), (1)

where

K = Ao exp(-U/RT). (2)

Here Ao is a constant related to the partition function for the adsorbate and usually assumed to be temperature dependent and independent of the adsorption energy; this approximation will be discussed in Section 3.

Langmuir himself was the first to generalize his equation: 5 'Let us assume that the surface contains several different kinds of elementary spaces representing the fractions (β1, β2, β3, etc., of the surface so that (β1+β2+β3 + ... = 1'. This approach led to an equation describing the total adsorption, θT,on a heterogeneous surface:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where K1, K2 ..., are the constants governing adsorption on sites of types l, 2,... This equation was also written in an integral form to describe adsorption on a surface divided into infinitesimal fractions dβ (3. Equation (3) found limited application owing to the number of unknowns required to describe a real surface and the uncertainty of the effects of ignoring lateral interactions. In spite of this, the model was developed to describe multilayer adsorption on a surface with one elementary space producing the well known BET equation.

During the same period the analysis of experimental data, particularly at low adsorbate concentrations, led to the popular application of an empirical equation usualJy attributed to Freundlich:

θT = cp1/n, (4)

where c is a constant and n an integer (n> 1). The success of this equation for surf aces that were not expected to be homogeneous led a number of researchers to investigate what distribution of adsorption energies the overall isotherm equation (4) represented. Zeldowich in 1935 was perhaps the most successful; he adopted the Langmuir integral equation for adsorption in a form equivalent to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where F'(K) is the distribution function for the elementary spaces on the surf ace. Zeldowich was not able to solve equation (5) exactly for F'(K) but formulated an approximate method of solution by approximating the Langmuir equation for the individual 'elementary spaces' as shown in Figure l(a) i.e.

θ(p, K) = p/K 0<p : Henry's Law, θ(p, K) = 1 K<p: Surface completely covered. (6)

This method produced the result:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

which when applied to the Freundlich isotherm [equation (4)] gave:

F'(K) = AFK(l/n-1), (8)

where

AF = -c/n2 + c/n (9)

Equation (8) may be rewritten by substituting equation (2);

F'(U) = B exp(-α U/RT), (10)

where

B = AFAo(1/n-1), α = 1/n - 1 (11)

When this distribution was adopted to generate θT(P) using equation (5), the Freundlich isotherm at low pressures was obtained.

Although more exact solutions of equation (5) were not forthcoming until later years, much effort using approximate methods was spent, including formidable pioneering work by many Russian investigators (see Tolpin, John, and Field for a review of this work prior to 1952). Roginskii's 'control band method' was particularly enlightening but restricted to distribution functions that do not change rapidly between the limits of the adsorption energy. Once again the Langmuir equation was employed to describe adsorption on the 'elementary spaces' and led to the formulation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

Roginskii and Todes were fully aware...