Equivalency of the Dubinin-Polanyi equations and the QM based sorption isotherm equation. A. Mathematical derivation

It is demonstrated that the most widely used sets of the Dubinin-Polanyi (DP) isotherm equations may be derived from an isotherm equation that has its basis in simple quantum mechanical (QM) assumptions. These derivable isotherms include the Dubinin-Radushkevich (DR), the Dubinin-Astakhov (DA) and the Dubinin-Radushkevich-Kaganer (DRK) equations. The initial derivation in part A assumes no energy distributions other than that obtained in the QM treatment. Using this homogeneous assumption the DR, DA and DIRK equations were found to be valid within 2% over a pressure range that covered at least a factor of 100 for typical ceramic adsorbents. In the course of the derivation, the philosophical problem of dual use of the DR equation for both porosity and open surfaces (DRK equation) is resolved. The methodology for heterogeneous surfaces and comparisons to DP and other isotherms using the heterogeneous assumption are described in part B. (C) 2000 Elsevier Science B.V. All rights reserved.