Hysteresis and Isotherm Equations in Gas−Solid Adsorption from Maximum Entropy Production

Abstract

Hysteresis and isotherm equations in gas−solid adsorption have been investigated by using a variational condition derived from the constraint of maximum irreversible entropy production. Functional formulation for the adsorption entropy has been stated through a useful formulation for the isotherm equations. The ideal adsorption law was rewritten in the integral form involving the sum between a continuous function and a Dirac distribution located at the concentration value where fluid condensation is expected. The real adsorption law was related to the broadening of the impulsive term that is driven by the entropy production. To generalize the entropy definition to a functional dependence in the adsorbate concentration, the sum among the ideal continuous law, a delta convergent sequence and a perturbation which is sensitive to the broadening degree, was considered in the integral equation for the real adsorption isotherm. Application of the Euler−Lagrange theorem pointed out two different behaviors that can be identified with ascending (adsorption) and descending (desorption) curves of a cycle at a constant temperature. They can be approximated to formally equivalent expressions which involve the sum between the ideal law in the gaslike regime and two liquidlike contributions respectively related to the Kelvin equation and a modified Freundlich adsorption. Accordingly, the difference between real and ideal isotherms has been introduced as a quantity independent of the adsorption law in the low concentration regime. A phenomenological description of some hysteresis loops and experimental data is presented. The theoretical procedure pointed out here is quite general and implicitly suggests a possible relationship with other hysteresis mechanisms (i.e., magnetic).