Elovich equation variation

In general, therefore, despite the usefulness of the Elovich equation as a method of representing data on rates of adsorption, not only the variation of the two important parameters a, and b with pressure and temperature, but also the presence of discontinuities, require that any acceptable theoretical model should, at least qualitatively, explain these results. Therefore, we first discuss the various theoretical interpretations of this equation. 

For an immobile adsorbate, the Elovich equation is obeyed for any variation of —AH with coverage when heterogeneity comprises both site and induced effects. For a mobile adsorbate, the Elovich equation is applicable when —AH decreases linearly with increase of patch number and also with increase of coverage on each patch, i.e., [cf. Eq. (47)]. 

The assumption that, for a nonuniform surface, E increases linearly with increase of coverage is unrealistic from a physical viewpoint it is however, a convenient postulate from a mathematical viewpoint, particularly when it is realized that a surface comprising a small number of homogeneous patches, each patch having different E values on which there may or may not be induced effects, gives rise to an adsorption rate which subscribes well to an Elovich equation this model is an acceptable physical description for adsorbents in the form of powders or evaporated films. Similarly, models comprising uniform surfaces, but with site creation or exclusion, may be analyzed and extended to give conclusions of the same natures as those derived from a variation of E over a nonuniform surface mathematically, however, the extension to, e.g., interaction effects between two different adsorbates is more cumbersome. 

Barriol and Rivail 80) also derived an equation of the Elovich form using a model in which it was assumed that all sites in a particular region must be simultaneously unoccupied before adsorption could occur, and obtained appropriate expressions for the probable existence of such regions. Meller 81) also obtained an exponential variation of the number of adsorption sites by another different approach. 

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