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) b ased on the gamma-type function is presented. Three cases of the integratio n range (widely known in the literature) of MSD, characterizing the geometr ic 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-adsor bent system. The physical meaning of the parameters of the gamma-type funct ion (rho and nu) is investigated for the mentioned intervals. The behavior and properties of this MSD function are analyzed and compared with the frac tal MSD proposed by Pfeifer and Avnir. The general conclusion is that if ad sorption proceeds by a micropore filling mechanism and the structural heter ogeneity is described in the finite region (val(min), val(max)), for all ca ses of the possible values of the parameters of the MSD functions, the gene rated 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 ambig uous results are obtained. (C) 2000 Academic Press.