The normalization of the micropore-size distribution function in the polanyi-dubinin type of adsorption isotherm equations

The problem of the normalization of the micropore-size distribution (MSD) based on the gamma-type function is presented. Three cases of the integration range (widely known in the literature) of MSD, characterizing the geometric heterogeneity of a solid, are considered (val(=B, E-0, and/or x)) i.e., from zero to infinity, from val(min) to infinity, and the finite range from val(min), up to val(max)-due to the boundary setting of an adsorbate-adsorbent system. The physical meaning of the parameters of the gamma-type function (rho and nu) is investigated for the mentioned intervals. The behavior and properties of this MSD function are analyzed and compared with the fractal MSD proposed by Pfeifer and Avnir. The general conclusion is that if adsorption proceeds by a micropore filling mechanism and the structural heterogeneity is described in the finite region (val(min), val(max)), for all cases of the possible values of the parameters of the MSD functions, the generated isotherms belong to the first class of the IUPAC classification (i.e., Langmuir-type behavior is observed). For the other cases (val epsilon < 0, infinity) and val epsilon < Val(min), infinity)) some erroneous and ambiguous results are obtained. (C) 2000 Academic Press.