Sorption theory

G. D. Halsey, Advances in Catalysisy 4 (1952), presents an excellent critique of the various theories of adsorption in the light of surface heterogeneity. T. L. Hill in the preceding chapter outlines the statistical mechanical and thermodynamics of the different sorption theories. 

This review does not aim for an encyclopedic coverage of the rapidly expanding field of membrane science. The topics treated do, however, present a reasonable sampling of the current literature on membrane science. The subfects treated reflect directly the interests of the authors and many of the topics are fundamentally related to the fact that the membrane is a high polymer. Indeed, the transport and sorption theories presented provide parameters whose physical interpretation often is a useful complement to other methods of physical analysis of the polymeric state. The study of gas sorption and transport in rubbery polymers is petbaps the simplest example of such a case and will be treated first. 

The basic assumptions of the dual mode sorption theory as it applies to the transport model of Vieth and Sladek, have been stated by Vieth et al. in their excellent review of the subject The sorption isotherm was described by the combination of a Henry s law dissolved component, Cp, and a Langmuir hole filling term, Ch, i.e.. 

Most subsequent sorption theories, including those discussed here, have followed this general approach and postulate two forms of sorbed water. These theories may be classified into at least two general types based on the sorption mechanism assumed. One type assumes sorption on internal surfaces and is represented by the Dent theory (52), which is a modification of the classic Brunauer, Emmett, and Teller (BET) theory (53). The second type assumes that the wood-water system forms a solution, exemplified by the Hailwood-Horrobin theory. There have been other theories, not discussed here, that have also been applied to explain water sorption by hygroscopic materials (JO, 54, 55). 

Dent s Surface Sorption Theory. The Dent sorption theory or model (52), in the simple form, is a modification of the BET model, which is itself an extension of the earlier Langmuir model (56). The Langmuir model assumes that a gas (water vapor in the case of wood) is sorbed onto sorption sites on the substrate or sorbent in a mono-layer only. The fraction of sorption sites occupied by the vapor or sorbate is a function of the vapor pressure of the sorbate and approaches unity as the vapor pressure increases. 

Figure 27. Sorption isotherms predicted by BET sorption theory for various values of n (broken lines), compared with the experimental isotherm (solid line). Also shown is the monolayer moisture content Mj (10). (Reproduced with permission from Ref 10. Copyright 1972, Syracuse University Fress.)...

Hailwood-Horrobin Solution Sorption Theory. The Hailwood-Horrobin (57) model treats moisture sorption as hydration of the polymer, taken here to be dry wood, by some of the sorbed water called water of hydration, m. The hydrate forms a partial solution with the remaining sorbed water, called water of solution, m,. An equilibrium is assumed to exist between the dry wood and water and the hydrated wood with an equilibrium constant K. Equilibrium is also assumed to exist between the hydrated wood and water vapor at relative vapor pressure h, with equilibrium constant K2. A third constant is defined as the moisture content corresponding to com-... 

The merits of isotherm analyses by the BET method and other theories are probably best outlined by Adamson (9). We have analyzed our results in terms of several sorption theories (9) and have concluded that those based on the sorption potential are most informative. Polanyi first proposed that the sorption process is dictated by the sorption potential e, where... 

Simpson W (1980) Sorption theories for wood. Wood Fiber, 12(3) 183-95 Sinclair RM and Vincent TA (1964) Yellowing of radiata pine timber. New Zealand Journal of Science, 7(2) 196-206... 

In some cases deviations from Fickian behavior in glassy epoxy polymers (19-25) have been adequately described using dual mode sorption theory (22-24). This theory is based upon the premise that the sorbed penetrant exists in two thermodynamically distinct populations. These populations consist of molecules adsorbed in "holes", and species simply dissolved in the polymer matrix. 

Figure 20 Schematic representation of the dependence of concentration on partial pressure illustrating predications of Henry s law and dual mode sorption theory.

It appears that moisture transport in conditions of less than 100% relative humidity is largely dominated by diffusion. The diffusion phenomenon is best described using dual mode sorption theory. 

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