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

An isotherm equation is derived for adsorption of gases and vapors on microporous and mesoporous solids from statistical mechanical principl es. The adsorbed phase is assumed to be a two-dimensional fluid subjec ted to a force field represented by a mean potential (Phi). It is show n the heretofore empirical Dubinin-Astakhov (D-A) equation and Dubinin -Radushkevich (D-R) equation (i.e., the potential theory) are approxim ated forms of this isotherm. For adsorption in micropores and mesopore s, 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 t he degree of pore filling at the reference state (eta(0)); as a conseq uence it depends on the adsorbate as well as the pore structure of the adsorbent. Moreover, the characteristic energy of adsorption (E) in t he 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 fi rst principles without resorting to empirical correlations. The low-pr essure 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.