Sorption-diffusion mechanism theory

The theory of transport in microporous solids is complex and involves many aspects and steps. Although many aspects has been treated separately (e.g., sorption, diffusion, simulation studies, mechanisms, etc.) there are no coherent descriptions of permeation and separation in microporous membrcmes covering all the important aspects. In this chapter an attempt is made to introduce such a description. It is useful to give a qualitative picture first (Section 9.4.2.1). 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

J.H. Petropoulos, Mechanisms and Theories for Sorption and Diffusion of Gases in Polymers, in Polymeric Gas Separation Membranes, D.R. Paul and Y.P. Yampol skii (eds), CRC Press, Boca Raton, FL, pp. 17-82 (1994). 

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