Foundations of the fluctuation theory of adsorption on microcrystalline particles

Fundamentals of the equilibrium fluctuation theory of adsorption of molecules on microcrystalline particles taking into account the atomic structure of nonuniform surfaces were developed. The importance of taking into account the discrete character of adsorption centers in constructing adsorption isotherm equations was demonstrated. This changes the type of the mathematical apparatus in the search for a maximum distribution function term in a grand canonical ensemble: instead of differential derivatives, symmetrized difference derivatives should be used. The fluctuation theory of adsorption was generalized to ideal multicomponent mixtures of molecules. Adsorption isotherm equations for multicomponent mixtures on uniform and nonuniform surfaces taking into account limited sizes of the surface of various microcrystal faces and fluctuation contributions were obtained. The equations describe the influence of equilibrium fluctuations on adsorption isotherms for adsorbent particles of all sizes, from nanometric to macroscopic. An analysis of the equations showed that the influence of fluctuations was strongest at low coverages for each microcrystal face. The simplest case of taking fluctuations into account in the presence of contributions of lateral interactions in the mean field approximation was discussed.