Energetic 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. 

If the surface of the adsorbent is energetically heterogeneous rather than homogeneous each step of the isotherm will be replaced by an assortment of steps, corresponding to the completion of a monolayer on the different homogeneous patches of the surface. If the steps are sufficiently numerous... 

In practice the kinetics are usually more complex than might be expected on this basis, siace the activation energy generally varies with surface coverage as a result of energetic heterogeneity and/or sorbate-sorbate iateraction. As a result, the adsorption rate is commonly given by the Elovich equation (15) ... 

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. 

Heterogeneous Ideal Adsorbed S olution TheoTy (HIAST). This IAS theory has been extended to the case of adsorbent surface energetic heterogeneity and is shown to provide improved predictions over lAST (12). 

Jaroniec, M., Gilpin, R. K., Kaneko, K. and Choma, J., Evaluation of energetic heterogeneity and microporosity of activated carbon fibers on the basis of gas adsorption isotherms, Langmuir, 1991, 7(1 1), 2719 2722. 

In addition to purely energetical heterogeneity one should also take into account some basic aspects of possible heterogeneities resulting from geometrical effects. The simplest and yet experimentally quite important geometric effects are due to the finite size of crystallites. Experimental measurements ave clearly demonstrated that the size of typical crystallites may be quite small (of the order of 50-100 A [116,132] and quite large (of the order of 10 A [61]. 

Similarly to the previously considered case of the first-order transitions, the above picture applies to a specific situation in which the sample exhibits just one type of crystallites, all of the same size, and where we neglect the effects of energetical heterogeneity that are bound to be present at the crystallite boundaries. In real samples one expects to find a distribution of the crystallite sizes, and hence more complex behavior. 

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. 

This is the result of an action of assumptions that were set at the derivation of BET (as well as Langmuir) equations eneigetically homogeneous surfaces and the absence of lateral interactions of G/G type (see Figure 9.14). But, the surfaces of real PSs are usually energetically heterogeneous, the... 

In real catalysis the actual situation will even be far more complex. Energetic heterogeneity due to the participation of various structural elements of the surface and interactions between adsorbed species are just a few of the complicating factors coming into play. Nevertheless it is concluded that adequate description of the kinetics may be achieved on the basis of the outlined strategy as long as the analysis is restricted to a limited range of parameters, which condition will frequently be full-filled with practical reaction situations. 

Energetic heterogeneity of the crystal interface even in the case of an ideal MS crystal, more so for non-ideal ones [84]. 

The results of theoretical potential calculations (18, 19) suggest considerable energetic heterogeneity within the zeolite cavities. In such calculations the probe molecule is, however, represented as a point center of force, and for polyatomic molecules the effect of molecular rotation will reduce any such variations in potential through the cavity. For such systems the idealized model, which assumes a uniform potential throughout the free volume, may not be too unrealistic. 

For an energetically heterogeneous surface, where centers of different adsorption intensity are scattered, a superposition of the Langmuir isotherm results in... 

In 1925, Taylor (1, 2) introduced the concept of geometric and energetic heterogeneity of solid catalyst surfaces. Since that time the importance of heterogeneity in chemisorption and catalytic processes is undisputed and the existence of active sites on catalytically active solid surfaces is no longer a matter of controversy. Our knowledge about the chemical nature of these sites, however, is still very poor and there are only few cases in which their concentration (or number per unit surface area) could be determined satisfactorily. 

The mode of action in LSC is adsorption, but the process is quite complicated because molecules of the mobile phase compete with analyte molecules for the active sites on the solid surface and silica is energetically heterogeneous. Any water present in the system will be strongly attracted to the silica surface, and there is evidence that there can be two or three layers of water adsorbed on silica. The most strongly adsorbed water layer cannot be removed with dry solvents, but the other layers can be. To get silica completely dry requires heating to temperatures above 200°C. Because of its importance in LSC, silica has been thoroughly studied further details can be found in a number of published works.5,6... 

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