Non-uniform surface

Figure 16.23 presents the alumina-coated ceramic membrane. There were opportunities to fabricate a crack-free ceramic membrane coated with y-alumina. The supported zirconia-alumina membrane on the ceramic support shows an irregular surface. The non-uniform surface of ceramic support causes the irregular surface on the top layer of the membrane. Some of the membrane sol was trapped in the porous ceramic support during coating, and caused the irregularity of the membrane surface. 

Structure and mobility of adsorbed molecules may exhibit a wide spectrum of features. As a general view it is commonly accepted that layers are formed on increasing abundance. The mobility of molecules in the first layer depends strongly on interactions present in a given case. Local domains of adsorbed molecules may be formed in the case of non-uniform surface. Analysis of deuteron spectra for a series of molecules adsorbed on neutral alumina led to the conclusion that while the exchange of molecules between layers in a given domain is fast, the diffusion rate between domains is slow [5],... 

Let the gas pressure that corresponds to adsorption equilibrium be denoted as p. The value of p for the standard state of a site is denoted as b and is called desorption pressure of the site (Section IV). Each site of a non-uniform surface is characterized by a certain b value or by an adsorption coefficient, a = l/b (for a given temperature). At adsorption equilibrium, the probability that a site is occupied... 

Non-uniformity of catalytic sites A characteristic of a catalytic surface is that its sites may differ in their thermodynamic and kinetic properties. In the kinetic description of catalytic reactions on non-uniform surfaces, a parameter a is frequently used to connect changes in the activation energy of activated adsorption with the enthalpy of the adsorption... 

In this connection, it is interesting to consider questions of the heat of adsorption on a non-uniform surface, of the fraction of the specific heat of the adsorbed gas related to redistribution of the gas on the surface for a change in temperature, and so on—both for the general case and for a distribution of the form (17). The elaboration of these problems, however, at present would necessarily be nothing more than a mathematical exercise. We note only that for the distribution equation (17), the smaller the value of q, the sharper is the maximum of the specific heat near T = 7, while the differential heat of absorption at T = 0 obeys the equation... 

In conclusion, I would like to emphasize that the main object of this part of the paper has not been a quantitative theory of adsorption on non-uniform surfaces, but a struggle for the correct qualitative interpretation of a specific set of experimental data. 

An integral equation for adsorpt ion on non-uniform surfaces is derived and an approximate method for its solution T is given. 

This work was carried out independently of and simultaneously with Temkin s work on adsorption on non-uniform surfaces (performed at the L. Ya. Karpov Physico-Chemical Institute). The difference in methods, objectives and, partly, results justifies the separate publication of our articles. 

This paper by Ya.B. was translated and published, with a few changes, in the collection Statistical phenomena in heterogeneous systems, 1 which was devoted especially to the theory of non-uniform surfaces and to statistical phenomena in adsorption and catalysis. In the review article by V. I. Levin in this collection the priority of Ya.B. s article in statistical research on the theory of adsorption and catalysis is emphasized. The article also cites articles by other authors who came to similar conclusions, but later than Ya.B. The significance of Ya.B. s work for the theory of catalysis is elucidated in detail in S. Z. Roginskii s book, Adsorption and Catalysis on a Non-Uniform Surface. 2 After this a summary of this paper by Ya.B. has entered into the majority of monographs and textbooks on catalysis. Thus, in the course of Thomas and Thomas3 the derivation of the adsorption isotherm on a non-uniform surface is given in full and referred to as classical. 

Roginskii S. Z. Adsorbtsiia i kataliz na neodnorodnoi poverkhnosti [Adsorption and Catalysis on a Non-Uniform Surface]. Moscow, Leningrad Izd-vo AN SSSR, 643 p. (1948). 

An unusual dependence for adsorption on a uniform surface arises when it is assumed that the rate of change of the surface is considerably slower than the rate of adsorption (see figure). If adsorption and desorption occur rapidly, the state of the surface remains practically unaltered and we then get an adsorption isotherm corresponding to a non-uniform surface with a distribution p(E, 0) of the heat of adsorption (curve 1) [3]. However, when the time interval is considerable, slow adsorption accompanies changes in the properties of the surface, and the amount of gas adsorbed approaches that given by the Langmuir isotherm (curve 2, point B), which describes a state of complete equilibrium (see above). 

What functions to describe a distribution of adsorption centers on non-uniform surfaces are needed for calculation of adsorption isotherm, the adsorption and desorption rates of dissociating molecules, for allowing the lateral interaction between the nearest neighbors ... 

The electronic conductivity of the substrate can also be probed by SECM. In the case of finite conductivity, a non-uniform surface potential profile develops at the surface. Liljeroth et al. [80] developed the theory for probing the film resistivity with the SECM in a feedback mode. The electrochemical mass-transport equation in this case was... 

In order to solve (25) a change of variables is introduced which simplifies the equation and allows the construction of the solution for a non-uniform surface concentration from that valid for a uniform surface concentration by means of Duhamel s theorem. Since u and v are functions of x. Duhamel s theorem cannot be directly applied to (25)."0... 

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. 

On the other hand, if E and Q vary conversely to one another then the controlling band shifts with coverage toward higher values of E and the kinetics will coincide practically with the kinetics of adsorption on a non-uniform surface without redistribution discussed previously. 

Employing the approximate theory of non-uniform surfaces developed by Roginskil the distribution function p(E) of activation energies E was determined to be... 

Roginskil, S. Z., Adsorbtsiya i kataliz na neodnorodnykh poverkhnostyakh (Adsorption and Catalysis on Non-uniform Surfaces). Acad. Sci. U.S.S.R. 1948. 

In this respect it can be mentioned that several authors have derived rate expressions for non-uniform surfaces. In Ref. [4], Boudart and Djega-Mariadassou... 

Halsey, G.D. Physical adsorption on non-uniform surfaces. J. Chem. Phys. 1948,16, 931-937. 

Goodman AL, Underwood GM, Grassian VH (2000) A laboratory study of the heterogeneous reaction of nitric acid on calcium carbonate particles. J Geophys Res 105 29053-29064 Gorbimov BZ, Kakutkina NA (1982) Ice crystal formation on aerosol particles with a non-uniform surface. J Aerosol Sci 13 21-28... 

Reaction step (1) in Fig. 3.1 is an adsorption step. Under equilibrium conditions, the net rate is zero and the equilibrium is then described by Eqn. (3.14). This does not mean per se that Ki is constant. It may vary with surface occupancy in the case of a non-uniform surface, due to the interaction of adsorbed species with each other. In conventional catalytic kinetics it is generally assumed that one is dealing with a homogeneous surface. Under the assumptions that ... 

The predominance of kinetic studies have assumed uniform sites on the catalyst surface. However, it has long been recognized that many catalyst surfaces exhibit non-uniform sites. Boudart and Djega-Mariadassou [3] have discussed the kinetics of non-uniform surfaces and conclude that "a non-uniform surface behaves catalytically. .like a uniform surface..", and that "rate equations are similar for a given mechanism on a uniform or non-uniform surface". This result justifies "the common practice of neglecting non-uniformity of catalytic surfaces in kinetic studies". However, it appears that uniform catalyst sites catmot adequately explain catalyst deactivation phenomena. The objective of the present study was to explain deactivation in terms of a model based on a variable activation energy site distribution on the catalyst. 

Dubinin, M.M. (1960). The potential theory of adsorption of gases and vapors for adsorbents with energetically non uniform surfaces. Chem. Rev., 60, 235-41. 

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