Adsorption on nonuniform surface

The influence of the crystallite size of catalysts upon such reactions as hydrogenation or dehydrogenation over platinum or nickel has been investigated by Rubinshtein and others (376). Roginskil s school has applied mathematical statistics to systems formed by primary monocrystals of a catalyst the cracks and pores of varying dimensions created by these crystals predetermine the nature of the resulting porosity. The application of the statistical method to the theory of adsorption and catalysis was recently described by V. I. Levin (200) and an equation for adsorption on nonuniform surfaces derived by Ya. Zel dovich and S. Z. 

In addition to the theoretical studies of equilibrium adsorption, Roginskii has conducted extensive investigations of the kinetics of adsorption on nonuniform surfaces and has shown that the character of the kinetics of adsorption is dependent upon the presence or absence of surface migration. Migration of the adsorbate molecules brings about a redistribution which conforms with the values of the adsorption coeffi-... 

Jin X, Wang NHL, Tarjus G and Talbot J 1993 Irreversible adsorption on nonuniform surfaces the random site model J. Phys. Chem. 97 4256-8... 

Other types of isotherms are reported in the literature for multi-centred adsorption on nonuniform surfaces with inclusion of lateral interactions with an average energy e... 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

A plot of p/(x/m) versus p produces a straight line with slope of l/k2 and an intercept of 1/k k2. Deviations from linearity are attributed to nonuniformity leading to various types of adsorption on same surface, that is, nonmonomolecular adsorption on a homogeneous surface. 

X. Adsorption Equilibrium and the Kinetics of Reaching it on Nonuniform Surfaces... 

S. Z. Roginsky, Adsorption and Catalysis on Nonuniform Surfaces, Izd. Akad. Nauka SSSR, Moscow-Leningrad, 1948. 

Soviet physicists and chemists have been reporting research on the peculiarities of adsorption on solid surfaces and the apparent deviations from the derived laws expressing adsorption phenomena, e.g., deviations from the Langmuir laws. S. Z. Roginskil has treated the nonuniformity of the surface and adsorption under conditions of limited extent of coverage of the surface in a number of articles. 

The kinetics of catalytic reactions on nonuniform surfaces have been discussed by Roginskii (330,331) certain general features of his discussion will be presented here. The rate of a complex multistage heterogeneous catalytic reaction is controlled by the rate of the slowest step. The slowest step may be the adsorption of the reactants, the chemical reactions on the surface, desorption of the products or diffusion of reactants or products through the gaseous phase near the surface of the catalyst. 

Experimental and theoretical studies of H adsorption are mostly performed on idealized surfaces, that is single crystals. Adsorption on real surfaces is a more complex phenomenon, mainly because of the physical and chemical nonuniformity of the surfaces. Surface defects (steps, kinks, grain boundaries) and the presence of impurity atoms strongly affect the adsorption [53]. Surfaces of alloys and intermetal-lic compounds show additional phenomena related to the fact that the chemical composition at the surface may differ from that in the bulk [47]. 

The charge nonuniformity on the surface of colloidal particles may also significantly contribute to the electrostatic interactions. It can arise from selective ion adsorption on the surface of colloidal particles and distribution of C potential [45, 46]. The surface charge nonuniformity can lead to attractive electrostatic and hydrophobic interactions between particles and cause suspension instability [47-49]. An extension of the HHF model for the randomly charged surfaces gives the following Velegol-Thwar potential [46] ... 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

The energy of an adsorbed species is the same anywhere on the surface and is independent of the presence or absence of nearby adsorbed molecules. This assumption implies that the forces between adjacent adsorbed molecules are so small as to be negligible and that the probability of adsorption onto an empty site is independent of whether or not an adjacent site is occupied. This assumption usually implies that the surface is completely uniform in an energetic sense. If one prefers to use the concept of a nonuniform surface with a limited number of active centers that are the only points at which chemisorption occurs, this is permissible if it is assumed that all these active centers have the same activity for adsorption and that the rest of the surface has none. 

The notion of nonuniformity of catalytic surfaces has been originally advanced by Langmuir (20) and particularly by Taylor. The physical nature of nonuniformity is insufficiently clarified. To some extent, it results from the difference in properties of crystal faces, from dislocations, and other disturbances of crystal lattice. It is possible that admixtures of some foreign substances is of greater importance. The particles of admixtures change adsorption energy on adjacent surface sites. The model of nonuniform surface probably describes the overall result of the effect of particles of admixtures on adsorbed particles and of the mutual influence of adsorbed particles (i.e., to an approximation the model takes into account not only biographical, but also induced nonuniformity). 

The diversity of possibilities of the general picture of a nonuniform surface makes it indefinite and hence scarcely suitable for concrete applications. On the basis of experimental data on heat of adsorption, adsorption equilibria, adsorption and desorption kinetics, the kinetics of reactions and electrode processes, a special model of a nonuniform surface has been formulated (41) that describes the experiments satisfactorily and without excessive mathematical complexity. 

Thus q0 is the heat of adsorption on a uniform surface with adsorption coefficient a0. According to (125), nonuniformity exponent may be regarded as the ratio to RT of the slope of the straight line in the plot of q as function of 8. For strongly nonuniform surfaces/is much greater than 1. 

Equations (146) and (147) express the dependence of the rate of adsorption on the fugacity of the adsorbed layer, p. In order to obtain r+ as a function of 6, p should be expressed in terms of 6 by means of a corresponding adsorption isotherm. For an evenly nonuniform surface, (123) and (147) give... 

This equation holds for the contributions of each site of a nonuniform surface to adsorption and desorption rates, and hence, for total r+ and r values on a nonuniform surface. Therefore, (148) with n taken from (145) gives directly... 

Equation (186) means that the rate of adsorption of A from a mixture of A and A depends on the total coverage of the surface by both gases in the same manner as it depends on the coverage of the surface by gas A when only A is being adsorbed. Thus, in the case of adsorption of A and A on an evenly nonuniform surface we have for the rate of adsorption of A, instead of (150),... 

The further development of the theory of nonuniform surfaces in the U.S.S.R. was helped by the mathematical methods of Zel dovich and Roginskil (200,201,331). A. V. Frost analyzed some work on the subject (mostly Russian) in a recent review (10) and concluded that an equation derived by him on the assumption that the reactants are adsorbed on a uniform surface and that no significant interactions take place between the adsorbed molecules, satisfactorily described many reactions on non-uniform surfaces including cracking of individual hydrocarbons and petroleum fractions, hydrogen disproportionation, and dehydration of alcohols. From the experimental results it was concluded that the catalytic centers on the surface were not identical with the adsorption centers. The catalysts used consisted of different samples of silica-alumina and pure alumina. 

Roginskif suggested a simplified method of analysis for processes occurring on a nonuniform surface which made it possible to surmount these mathematical difficulties without excessive distortion of the physical model. The method has general applicability to statistical processes however, its application to adsorption equilibrium only will be discussed here. 

The adsorption isotherm (p) on a nonuniform surface was expressed b y Roginskii as a function of the pressure p in the form... 

In the application of this method it should be pointed out that mobility of the adsorbed phase on a nonuniform surface will yield results that are equivalent to those of a uniform surface. However, making use of information obtained from the kinetics of adsorption and from studies employing the differential isotopic method, these difficulties can frequently be resolved. 

In the case where the reaction velocity is determined by the activated adsorption of the reactants and no poisoning by the products occurs, the action of a nonuniform surface simulates the behavior of a uniform surface. A similar situation occurs if there is redistribution on the heterogeneous surface after adsorption, assuming that the rate of surface migration is much greater than the rate of adsorption. 

Another problem in model applications is the adsorption on a nonuniform adsorbent. The immobilization of polyclonal antibodies will lead to different populations of binding sites, and the measurements will only give an apparent adsorption rate constant [22], The properties of the adsorbent surface are also greatly affected by the procedure used for protein immobilization. It may be important to select coupling methods that orient the covalently attached protein... 

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