Mobile 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. 

The entropy of a mobile adsorption process can be determined from the model given in [4], It is based on the assumption that during the adsorption process a species in the gas phase, where it has three degrees of freedom (translation), is transferred into the adsorbed state with two translational degrees of freedom parallel to the surface and one vibration degree of freedom vertical to the surface. From statistical thermodynamics the following equation for the calculation of the adsorption entropy is derived ... 

The adsorption behavior of atoms and compounds for most of the experiments used in the described correlations were evaluated using differently defined standard adsorption entropies [28,52-57], Adsorption data from more recent experimental results were evaluated applying the model of mobile adsorption [4], In addition, data from previous experiments were reevaluated using this model. 

The above equations, especially Eq. 5.54 (and so the mobile adsorption model) obtained wide use in radiochemistry of TAEs. The adsorption entropy was calculated from Eq. 5.33 accepting A/V = 1. Several authors proposed approximate... 

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... 

Experimental observations of these empirical correlations clearly prove the postulated proportionality. These correlations suggest a similarity between the bond (with lower coordination) of the adsorbed particles to the modified surface and the bond to the surface of the pure macroscopic phase of the compound, which is relevant for the desublimation process. The adsorption behavior of atoms and compounds for most of the experiments used in the described correlations were evaluated using differently dehned standard adsorption entropies [65-70]. Adsorption data from more recent experimental results were evaluated applying the model of mobile adsorption [4]. Hence, data from previous experiments were re-evaluated using the latter model. These correlations based on estimated standard sublimation enthalpies allow predictions of adsorption enthalpies for selected compounds for the case of zero surface coverage. These results are only valid for experimental conditions using the same reactive gases, and thus, similarly modified stationary surfaces. 

An example illustrates the usefulness of Table II. Suppose a certain adsorption reaction is 0.5 order, and it is concluded that dissociation accompanies adsorption that is. Step 2 applies. Suppose also that L has been found by a nonkinetic method to be 10 sites cm, and that according to TST L is calculated to be 10 sites cm . To decrease the calculated value of L by a factor of 100 means that AS (a negative quantity) as calculated from the model is 18.4 e.u. (that is, 2 x 9.2 e.u.) too low. Thus, in this example the gas did not lose as much entropy upon adsorption as had been supposed. Such a result could indicate that the dissociated fragments are mobile, not limited to fixed sites. 

The values of — AH for benzene are in the range 10-12 kcal/mole,15,19-20 being intermediate between values attributed to pure dispersion forces for saturated hydrocarbons and those in which more specific forces are involved. Furthermore, Ron and coworkers calculated the entropies of adsorption for benzene and concluded that the mobile gas model of adsorption was applicable, and Whalen18 found no simple relationship between the hydroxy site content and benzene adsorption. These results confirm the conclusions reached from the infrared data that benzene adsorption is essentially due to dispersion forces which should be greater than with saturated compounds, and that no hydrogen bonding is involved. 

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. 

The formula 5.32 for the standard entropy of the adsorbate in the mobile adsorption model can be rewritten as ... 

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. 

When a reactant molecule adsorbs on a particular site, entropy is lost compared with the reactant state in solvent or gas phase. This was described earlier in the chapter on zeolites. Within the rigid lock and key model, this entropy loss would be maximum, thus reducing the free energy gained upon adsorption. This is an additional reason why an optimum fit between reactant and enzyme cavity is not preferred. When the fit between the reactant and the cavity is not optimum, the reactant will maintain some mobility in the adsorbed state, hence the entropy loss is less. The basic mechanistic principles for enzyme catalysis discussed so far include the induced fit of the enzyme cavity as a response to substrate shape and size, pretransition-state stabilization of activated molecules and the principle of optimum motion. A reaction that proceeds through intermediates via transient covalent bonds is preferred. 

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