Unified Theory of Adsorption Chromatography with Heterogenous Surfaces: Gas, Liquid and Supercritical Fluid Mobile Phases

Abstract

In an earlier study, equations describing solute retention in liquid-solid chromatography (LSC) with a homogeneous adsorbent and a binary liquid mobile phase were derived through application of statistical thermodynamics and a mean-field lattice model. That investigation is extended here to obtain and interpret new equations for energetically and/or structurally heterogeneous adsorbents modelled in terms of a discrete distribution of internally homogeneous surface “patches”. Then, exploiting the isomorphism between binary-liquid and single-fluid critical behavior, the unified theory of the title, applicable to single-component mobile phases, is derived and discussed in some detail. The primary results, equations 23–29, confirm that the natural mobile-phase state variables are its reduced temperature and reduced density. These equations should find their widest use in supercritical fluid chromatography. As a quantitative example of its utility and efficacy, the theory is applied here to gas-solid chromatography (GSC) with a highly adsorbable mobile phase, where, at higher modifier pressures, the stationary phase becomes more like that encountered in LSC than in GSC. The compression of carrier liquid in contact with the adsorbent surface in LSC is also briefly considered.