THEORETICAL BASIS FOR THE POTENTIAL-THEORY ADSORPTION-ISOTHERMS - THE DUBININ-RADUSHKEVICH AND DUBININ-ASTAKHOV EQUATIONS

An isotherm equation is derived for adsorption of gases and vapors on microporous and mesoporous solids from statistical mechanical principles. The adsorbed phase is assumed to be a two-dimensional fluid subjected to a force field represented by a mean potential (Phi). It is shown the heretofore empirical Dubinin-Astakhov (D-A) equation and Dubinin-Radushkevich (D-R) equation (i.e., the potential theory) are approximated forms of this isotherm. For adsorption in micropores and mesopores, the fractional adsorption (theta) is much greater than the relative pressure (P/P-0); the general isotherm is thereby reduced to the D-A and D-R equations. From the approximated forms of the general isotherm, it is shown that the exponent; n in the D-A equation is related to the degree of pore filling at the reference state (eta(0)); as a consequence it depends on the adsorbate as well as the pore structure of the adsorbent. Moreover, the characteristic energy of adsorption (E) in the D-A and D-R equations is proportional to the mean potential (Phi). Thus, the dependence off on pore size can be obtained directly from first principles without resorting to empirical correlations. The low-pressure limit of the general isotherm is Henry's law. It is shown that from Henry's constant, i.e., one adsorption data point, it is possible to calculate the heat of adsorption.