Adsorption uniform surface

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

Effects of Flooding and Redox Conditions onfs. I know of no published data on this. Bnt it is likely that the natnre of particle surfaces in intermittently flooded soils wonld restrict snrface mobility. For ions to diffuse freely on the surface there must be a continuous pathway of water molecules over the surface and uniform cation adsorption sites. But in intermittently flooded soils the surface typically contains discontinuous coatings of amorphous iron oxides on other clay minerals, and on flooding reduced iron is to a large extent re-precipitated as amorphons hydroxides and carbonates as discussed above, resulting in much microheterogeneity with adsorption sites with disparate cation affinities. 

Figure 14. Simple model demonstrating how adsorption and surface diffusion can co-Urnit overall reaction kinetics, as explained in the text, (a) A semi-infinite surface establishes a uniform surface coverage Cao of adsorbate A via equilibrium of surface diffusion and adsorption/desorption of A from/to the surrounding gas. (b) Concentration profile of adsorbed species following a step (drop) in surface coverage at the origin, (c) Surface flux of species at the origin (A 4i(t)) as a function of time. Points marked with a solid circle ( ) correspond to the concentration profiles in b. (d) Surface flux of species at the origin (A 4i(ft>)) resulting from a steady periodic sinusoidal oscillation at frequency 0) of the concentration at the origin.

The assumption implicit in equation (4.8) is that the adsorption energy E is constant, which implies an energetically uniform surface. 

Consider a uniform surface with a number no of equivalent adsorption sites. The ratio of the number of adsorbed atoms or molecules, n, and no is defined as the coverage, d = n/no. The coverage in the monolayer is usually less than or equal to unity for a uniform surface. For a heterogeneous surface that exhibits multiple binding sites, i.e., more than one site per substrate unit cell, small adsorbate atoms may build up coverages somewhat greater than unity. We shall, however, ignore this possibility for the present. 

It has to be noted that the adsorption of reactants is generally not uniform across the catalyst surface. Adsorption, and therefore catalysis, takes place mainly at certain favorable locations on a surface called active sites. In environmental chemistry, catalysts are essential for breaking down pollutants such as automobile and industrial exhausts. 

The surface adsorption of tritiated PMCG was studied as a function of its bulk concentration (Figure 7). In the absence of brain lipid the surface adsorption increased sharply as the concentration approached 10"4M, reaching a maximum at 5 X 10 3M. When brain lipid (5 X 10 9 moles, as phospholipid) was added, the surface adsorption of PMCG was significantly reduced. If the solutions were allowed to dry, the concentration-radioactivity curve was essentially parallel to that obtained for PMCG in solution. When brain lipid was present as the samples were dried, the radioactivity increased twofold. Since the residue could not be dried as a uniform layer, it is not possible to make any reasonable estimation of the amount of PMCG adsorbed to the dried lipid film. 

The heterogeneous nature of polycrystalline solid electrodes invalidates the approximation of uniform surface or one-dimensional model used for the mercury electrode. Variations of pzc occur with surface structure. Study of single crystal sp metal electrodes has shown structural effects on adsorption [99]. 

Langmuir equation for a uniform surface, but by the Zel dovich and Rogin-skii equation or by the Bangham equation. Adsorption equilibrium is described not by the hyperbolic Langmuir isotherm, but by the Freundlich isotherm or the logarithmic isotherm (40). 

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... 

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 for desorption rate, r, could be obtained by calculations similar to those used for adsorption rate, r+, but there is a simpler method based on the following considerations that are analogous to those developed in Section VIII. On a uniform surface at gas pressure P and fugacity of the adsorbed layer p, adsorption rate is... 

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... 

We mentioned above the general agreement on the linearity of the initial sector of the adsorption isotherm on a uniform surface. The isotherms derived by Chakravarti and Dhar, g = Cp1 /( + p1/ ), and by Zeise, q = [ap/(p + )]1/2, are interesting in that, together with the nonlinearity of the isotherm at the beginning (q p1/" g y/p), they also reflect the tendency of adsorption towards saturation for p — oo. 

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). 

The concept of a uniform surface is widely used in theoretical work on adsorption. A closer examination of this concept, and of the unexpected conclusions to which it may lead upon suitable selection of the various possibilities, may therefore be of some interest. 

Analogously, one can imagine a uniform surface as a collection of identical potential holes only at 0°K. As a result of thermal agitation at T 0°, sectors with heats of adsorption differing from the mean will be continuously formed and destroyed on a surface which was originally ideally uniform. A uniform surface may be defined as one on which p(E) is the same for all surface elements, where p E) dE is the probability that the heat of adsorption on a given element lies between E and E + dE. 

Assuming that the second process is rapid, we obtain the following standard picture of adsorption on a uniform surface the equilibrium concentration q, which depends on the pressure of the gas, is determined by the Langmuir isotherm. The only difference from the standard picture is that the statistical sum for all states of the adsorbed molecule in a potential hole must be replaced by a combination of two statistical sums for all states of the adsorbed molecule and for all possible states of the surface element. This, of course, has no effect on the form of the Langmuir equation. Under very simple assumptions the kinetics of establishment of equilibrium will also not differ from those on a uniform surface. Thus, the initial velocity is proportional to the pressure and approaches equilibrium exponentially. 

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). 

How is one to reconcile the shape of the adsorption isotherm deduced for a uniform surface with the fact that, as we have seen here, the surface is heterogeneous ... 

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 ... 

Fig. 6. A Frumkin-Fowler s adsorption isotherm for uniform surfaces. B, C Adsorption isotherm for heterogeneous surfaces with condensation [after Ref. 89]...

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