Application of the Elovich equation to the kinetics of occlusion. Part 3.—Heterogeneous microporosity

Abstract

A model is considered in which occlusion takes place in parallel in an array of micropores with different coefficients of diffusion. The rate equation for occlusion in a pore is approximated by a parabolic or by an exponential equation, and the rate for the overall process is obtained by summing the rates in the pores. The plot of V_t/V_∞ against ln t, where V_t and V_∞ are the amounts sorbed at times t and infinity, respectively, is sigmoid and has an intermediate part with greatest slope. The slope of this intermediate part is related to the heterogeneity of the system. If v_E(E) is constant, where E is the energy of activation for diffusion and v_E the pore volume for an energy between E and E+ dE, the reciprocal of the slope is equal to the difference between the highest and lowest E divided by RT. If E is constant the slope is close to 0.2.