Multiple equilibria analyses of gas-porous solid isotherms

This article confirms the physical significance of a new method for determining adsorption energy distributions in porous materials. The premise of the model is that an adsorption isotherm consists of several equilibrium processes corresponding to adsorption into a distinct pore size regime. A distribution type equilibrium constant, K, involving the gas and adsorbate in a pore of capacity n describes each process. In order to define the n's and K's for all the processes involved, isotherms are collected at several temperatures to minimize the ratio of unknowns to knowns. In this article the model is extended to a series of adsorptives and it is shown that the resulting K's, Delta H's, and n's are not meaningless empirical fit parameters but have the meaning suggested by the model. The Delta G's vary linearly with Delta H for each pore size regime and both correlate linearly with the square root of the van der Waals a parameter, a(1/2). In addition to providing strong support for the physical significance of the parameters, these correlations enable prediction of the K values for adsorption of a new adsorptive by a characterized adsorbent given the a parameter of the adsorptive. The correlations show that the strongest binding corresponds to the adsorptive selecting pores from the distribution available that match its molecular dimensions. The n's for the different adsorptives provide insight into the pore distribution in the solid and about the pores utilized in the adsorption of different adsorptives. Prediction of the K's from a and estimating n's from molecular diameters is suggested as a way to attain the long-range goal of predicting the total isotherm for a new adsorptive from molecular properties. The practical application of this information for use in separations is illustrated. The concept of effective pressure, P-eff, is introduced for catalysis to allow comparison of the concentrating effect of different microporous solids.