Adsorption site heterogeneity

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. 

At low adsorbate loadings, the differential heat of adsorption decreases with increasing adsorbate loadings. This is direct evidence that the adsorbent surface is energetically heterogeneous, ie, some adsorption sites interact more strongly with the adsorbate molecules. These sites are filled first so that adsorption of additional molecules involves progressively lower heats of adsorption. 

We can think of a heterogeneous catalyst as a collection of active sites (denoted by ) located at a surface. The total number of sites is constant and equal to N (if there is any chance of confusion with N atoms, we will use the symbol N ). The adsorption of the reactant is formally a reaction with an empty site to give an intermediate I (or more conveniently R if we explicitly want to express that it is the reactant R sitting on an adsorption site). All sites are equivalent and each can be occupied by a single species only. We will use the symbol 6r to indicate the fraction of occupied sites occupied by species R, making N6r the number of occupied sites. Hence, the fraction of unoccupied sites available for reaction will be 1 - 0r The following equations represent the catalytic cycle of Fig. 2.7 ... 

Inhibitors are species that bind to enzymes, modifying their activity. Competitive inhibitors bind at the same site as the substrate binds this is analogous to competitive adsorption in heterogeneous catalysis. The reaction scheme becomes ... 

Its capability to titrate sites on heterogeneous surfaces makes photoemission of adsorbed xenon in principle a particularly attractive technique for investigating the surfaces of catalysts. Unfortunately, the technique has its limitations, because the Xe 5p /2 peak has a finite linewidth of about 0.4 eV. If a surface possesses more than three to four different adsorption sites, the spectra may become too... 

The heterogeneous reaction is assumed to depend on the surface area and fraction of the surface covered. Allowing for the competition between Ni(CO)4 and CO for adsorption sites... 

General Observations About x. its Relationship to the Overall Partitioning Coefficient and to the Concept of Surface-Site Heterogeneity. One approach to metal/particle surface interactions which has been developed, historically, in a variety of forms, is a conceptual model that assumes only two conditions for surface sites occupied by an adsorbate or unoccupied. In applying this approach to the solid/aqueous solution interface, the adsorption... 

In their description of metal ion adsorption, Benjamin and Leckie used an apparent adsorption reaction which included a generic relationship between the removal of a metal ion from solution and the release of protons. The macroscopic proton coefficient was given a constant value, suggesting that x was uniform for all site types and all intensities of metal ion/oxide surface site interaction. Because the numerical value of x is a fundamental part of the determination of K, discussions of surface site heterogeneity, which are formulated in terms similar to Equation 4, cannot be decoupled from observations of the response of x to pH and adsorption density. As will be discussed later, It is not the general concept of surface-site heterogeneity which is affected by what is known of x> instead, it is the specific details of the relationship between K, pH and T which is altered. 

The observation that the macroscopic proton coefficient is a function of adsorption density and pH has several implications for macroscopic modeling of cation and anion adsorption. The dependency of x on pH and T affects 1) the relationship of the macroscopic partitioning coefficient to pH and adsorption density, 2) the notion of metal ion preferences for a particular surface in systems with multiple solid phases, 3) the accuracy of predictive models when used over a range of adsorption density and pH values, and 4) conclusions about site heterogeneity based upon partitioning expressions which use constant proton coefficients. 

The competition for adsorption sites is very important for the kinetics of a heterogeneous catalytic reaction. For this reason sites,, are included as a reactant in the kinetic model. As a site must be either free or occupied by one of the surface intermediates, there is a conservation law for the coverages... 

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