Localized adsorption model entropy

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Many systems give linear plots of pjn against p over a limited ranges of pressure, but such linearity does not by itself imply conformity with the Langmuir model. As already indicated, a second condition is that the energy of adsorption should be independent of surface coverage. Thirdly, the differential entropy of adsorption should vary in accordance with the ideal localized model (Everett, 1950). That no real system has been found to satisfy all these requirements is not surprising in view of the complexities noted here and in subsequent chapters. 

The periodic adsorption potential of surfaces and the potential barriers between adjacent sites lower than the desorption energy must result such that the state of adsorbates is intermediate between the ideal mobile and localized models. The lateral migration across the surface must make a positive contribution to the entropy of the adsorbate. 

As it can be seen from Fig. 5.22, when moving from the localized adsorption towards the mobile model, we can expect smooth decrease in the entropy of desorption. The entropy of the adsorbate which experiences lateral diffusion was discussed, in particular, by Patrikiejew, et al. [95]. They approached the problem by assuming that a fraction of the molecules is in completely mobile state, while the others are completely localized. Then they suggested that the canonical partition function (9ml... 

Up to this point the essential equations have been presented. Now, it is possible to analyze the work carried out in connection with the classical thermodynamic approach. The first systematic study of a thermodynamic adsorption quantity was perhaps the work done by de Boer and coworkers [10] on the determination, interpretation and significance of the enthalpy and entropy of adsorption. Their papers analyzed almost all aspects of the experimental determination of the entropy and how to interpret the values obtained in terms of two extreme models, i.e., those of mobile and locahzed adsorption, which today have lost much of their usefulness. To catalog the behavior of the adsorbed film as localized or mobile is a very simplistic solution and it has been demonstrated [9] that in most cases the adsorbed film is neither completely localized nor completely mobile. This approach also is somehow outdated because numerical simulations provide a better microscopic interpretation of the system s behavior. 

Cassel [29,30] showed, using Gibbs adsorption isotherm, that the surface tension of the adsorbed film atP = Pq is negative, arising from the total disregard of the interaction forces. Since the BET model assumes the existence of localized adsoq>tion at all levels, the molecules being located on top of one another, and since the adsorption can take place in the nth layer before the (n-/>th layer is filled, the adsorbed phase is built up not as a series of continuous layers, but as a random system of vertic molecular columns. Halsey [31] pointed out that the combinational entropy term associated with these random molecular piles is responsible for the stability of the BET adsorbed layers at... 

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