Dual sorption mode

Partially immobilising sorption ( dual-mode model)... 

Coefficient 5(C) depends on gas condensability as well as polymer-penetrant interactions. Equation (24.2) can be expressed differently using various sorption modes in polymers. These modes, shown in Figure 24.1, are Henry s law sorption, Langmuir-mode sorption, Flory-Huggins mode sorption, dual-mode sorption, and Brunauer-Emmett-Teller (BET) mode sorption. 

Xing B. and J.J. PignateUo (1997). Dual-mode sorption of low-polarity compounds in glassy poly(vinyl chloride) and soil organic matter. Environmental Science and Technology 31 792-799. 

Dual-Mode Gas Sorption and Diffusion in Glassy Polymer Membranes. 97... 

Dual-Mode Ionic Sorption and Diffusion in Charged Polymer Membranes.. 109... 

Membrane-penetrant systems, whose sorption and diffusion properties can be described by Eqs. (5)-(7) with N = 2 ( dual mode sorption and diffusion models ) have attracted much interest. The most important examples of such systems are considered in the next two sections. 

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

Application of the dual mode sorption and diffusion models to homogeneous polymer blend-gas systems 26,65) and filled polymers 66) has also been reported. 

The sorption and diffusion behaviour of gas mixtures is of particular interest from the point of view of membrane gas separation, which is steadily gaining in importance by virtue of its low energy requirements. On the basis of the dual mode sorption model, one may reasonably expect that sorption of a binary gas mixture A, B in the polymer matrix will exhibit little gas-gas interaction and hence will tend to occur essentially additively. In the Langmuir-like mode of sorption, on the other hand, there will be competition between A and B for the limited number of available sites. These considerations led 67) to the following reformulation of Eqs. (8) and (9)... 

It is particularly interesting and instructive to note that application of Henry + Langmuir dual-mode sorption and diffusion models is not confined to glassy polymer-gas systems. Sorption and transport of high affinity ionic species, exemplified by anionic dyes, in charged polymers, exemplified by polyamides at low pH, has been treated in the same way. These systems are of considerable importance both from the bio-mimetic and from the textile processing point of view, but have received limited atten-... 

Application of dual mode sorption models to low affinity ionic species has been reported. Pertinent examples are mentioned here to illustrate the variety of models... 

NR and — CO groups, measured after prior washing of the resin with water 85), was well represented by a Langmuir + Nernst dual mode sorption model at salt concentrations not exceeding 0.2 mol dm 3. A detailed physical interpretation of the relevant parameters was not given, however, neither was the dual mode concept utilized in a corresponding diffusion study 86). 

The sorption of a weak electrolyte by a charged polymer membrane is another case where Nernst + Langmuir-like dual mode sorption, involving the undissociated and dissociated species respectively, may be expected. The concentration of each species in solution follows, of course, from the dissociation constant of the electrolyte. The sorption isotherms of acetic acid and its fluoroderivatives have been analysed in this manner, and the concentration dependence of the diffusion coefficient of acetic acid interpreted resonably successfully, using Nylon 6 as the polymer substrate 87). In this case the major contribution to the overall diffusion coefficient is that of the Nernst species consequently DT2 could not be determined with any precision. By contrast, in the case of HC1, which was also investigated 87 no Nernst sorption or diffusion component could be discerned down to pH = 2 and the overall diffusion coefficient obeyed the relation D = DT2/( 1 — >1D), which is the limiting form of Eq. (25) when p — 00. 

Implications of the Dual-Mode Sorption and Transport Models for Mixed Gas Permeation... 

Figure 3. Schematic representation of the dual mode sorption concept.

The discussion directly following Eq (6) provides a simple, physically reasonable explanation for the preceding observations of marked concentration dependence of Deff(C) at relatively low concentrations. Clearly, at some point, the assumption of concentration independence of Dp and in Eq (6) will fail however, for our work with "conditioned" polymers at CO2 pressures below 300 psi, such effects appear to be negligible. Due to the concave shape of the sorption isotherm, even at a CO2 pressure of 10 atm, there will still be less than one CO2 molecule per twenty PET repeat units at 35°C. Stern (26) has described a generalized form of the dual mode transport model that permits handling situations in which non-constancy of Dp and Dh manifest themselves. It is reasonable to assume that the next generation of gas separation membrane polymers will be even more resistant to plasticization than polysulfone, and cellulose acetate, so the assumption of constancy of these transport parameters will be even more firmly justified. 

One can easily show that the appropriate equation derived from the dual mode sorption and transport models for the steady state permeability of a pure component in a glassy polymer is given by Eq (7) (18) when the downstream receiving pressure is effectively zero and the upstream driving pressure is p ... 

Whereas the dual sorption and transport model described above unifies independent dilatometric, sorption and transport experiments characterizing the glassy state, an alternate model offered recently by Raucher and Sefcik provides an empirical and fundamentally contradictory fit of sorption, diffusion and single component permeation data in terms of parameters with ambiguous physical meanings (28), The detailed exposition of the dual mode model and the demonstration of the physical significance and consistency of the various equilibrium and transport parameters in the model in the present paper provide a back drop for several brief comments presented in the Appendix regarding the model of Raucher and Sefcik,... 

In one of their comparisons between the matrix model and the dual mode model, a somewhat misleading presentation of data is unintentionally offered in Figure 4 of the Raucher and Sefcik paper "Matrix Model of Gas Sorption and Diffusion in Glassy... 

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