Simple and complex sorption−solution isotherms for membrane polymers: A statistical thermodynamic fluctuation theory

Simple, site-specific adsorption isotherm models, such as GAB and other generalizations of BET, fit strikingly well to experimental isotherms of simple shapes for glassy and rubbery polymers. However, the structures of dense polymers do not necessarily resemble the unrestricted layer-by-layer adsorption mechanism on one type of sorption site assumed by these models. Since polymers contain micropores, sorptive likely (ad)sorbs on the internal surfaces of the free (accessible) volume voids, and dissolves in the polymer phase. While the empirical dual mode sorption model and its variants address this duality, other common models assume chiefly only one of the two mechanisms. Moreover, the simplified models do not fit complex isotherms, such as those for alcohols and poly[(trimethylsilyl)propyne] (PTMSP). The statistical thermodynamic fluctuation theory is adopted here to capture the sorption-solution duality consistently even for the complex isotherms. The statistical thermodynamic ABC isotherm derived from this theory involves the sorbate-sorbent and mono-, di-, and tri-sorbate interactions expressed by sorbate number correlations. This work shows that BET, GAB, dual-mode sorption model, Flory-Huggins, and ENSIC models are special cases of the ABC isotherm. The isotherm multiplicativity principle has been derived from the number fluctuation relationship to model complex isotherms.