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 (Φ). 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 (θ) is much greater than the relative pressure (P/P₀); 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 (η₀); 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 (Φ). Thus, the dependence of E 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.