Surface Diffusion and Entropy of Adsorbate

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 

It means that the resulting entropy is the sum of two contributions. They derived this and other thermodynamic functions for the whole range of fractional coverage value, as well as the Langmuir isotherm, by using the procedures of statistical thermodynamics. 

Let us look for a simple way to approximate the entropy of the adsorbed state as a function of b- We will assume that d is larger enough than e, to neglect the frequency of desorptions. 

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

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