Dual mode model discussion

Based on the recent study of the permeabilities of Kapton polyi-mlde to CO2/CH mixtures (2]L, ), it is expected that for systems which can be described by the generalized dual mode model (17), the permeability ratio of CO2 over CH in a mixture can be approximated to within about 20% by using the respective pure component permeabilities. Consequently, for the present general discussion, pure-component values will be used in Equation 7 in the following sections for discussing this Important system. 

Useful informetion regarding the characteristics of a particular separator aimngement often can be obtained through parametric studies. Separator specifications used in the following calculation are shown in Table 20.6-1 unless stated otherwise. Experimental permeability parameters, according to the dual-mode model, obtained from dense film-pure ges measurements34 36 are summerized in Table 20.6-2. For simplicity, only the results for a binaiy-component feed will he discussed. 

At the lowest temperature (-900C) and at the lowest pressure (3 atm), the xenon spectrum for the sorbed line is rather broad, possibly asymmetric or bimodal. This would indicate an asymmetric or bimodal distribution of sorption environments on a fairly short length scale. More complicated descriptions of amorphous environments might consider the effects of the presence of an amorphous/crystalline interfacial region or of two sorption environments as proposed in the dual mode model. The low pressure, low temperature spectra being discussed have the poorest signal to noise and better spectra are needed to characterize this situation properly. 

At the empirical level, alternative ways of representing the data (which may or may not utilize the dual mode concept) are possible 33,34). Accordingly, interest in the model embodied in Eqs. (5), (8) and (9) centers primarily around the question of its physical meaningfulness and significance, as well as its predictive potential. The results of recent research will be discussed below mainly from this point of view. 

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. 

The concept of dual mode sorption was first dearly demonstrated and quantified by Michaels, Vieth and Barrie in 1963 The same authors also discussed its effect on the diffusion process itself. Vieth and his co-workers aibsequently extended these findings to a number of polymer-gas systems and elaborated the theoretical aspects of the problem In particular, a model for diffusion in glassy polymers, which has come to be known as the totd inunobilization model, was developed by Vieth and Sladek ... 

In the case of cellulose acetate, however, it does appear dutt breakdown of the assumption of constant values of and Dp occurs. Presumably, this hypeisen vity of cellulose acetate may derive from its apparent special affinity for CO2 discussed in the context of Table 20.3-1. Stem and Saxena have described a generati form of the dual-mode tianspoit model that peimits handling situations in which nonconstancy of Dp and Df, manifest thonselves. It is reasontdrfe to assume that the next generation of gas separation membrane p ymets will be even mote resistant to plastidzatkm ffian polysulfone and cellulose acetate, so dial the assumption of constancy of these tranqioit parameieis should be well justified. 

As is clear solid oxide electrolytes are not useful for applications as oxygen separation membrane, unless operated with external circuitry (oxygen pump) or as a constituent phase of a dual-phase membrane. Both modes of operation, classified in this paper as electrochemical oxygen separation, are briefly discussed in Section 10.4.3. But we first start with a discussion of the models that have been developed to describe the oxygen semi-permeability of solid oxide... 

Photoinduced electron transfer is a subject characterised, particularly at the present time, by papers with a strongly theoretical content. Solvent relaxation and electron back transfer following photoinduced electron transfer in an ensemble of randomly distributed donors and acceptors, germinate recombination and spatial diffusion a comparison of theoretical models for forward and back electron transfer, rate of translational modes on dynamic solvent effects, forward and reverse transfer in nonadiabatic systems, and a theory of photoinduced twisting dynamics in polar solvents has been applied to the archetypal dimethylaminobenzonitrile in propanol at low temperatures have all been subjects of very detailed study. The last system cited provides an extended model for dual fluorescence in which the effect of the time dependence of the solvent response is taken into account. The mechanism photochemical initiation of reactions involving electron transfer, with particular reference to biological systems, has been discussed by Cusanovich. ... 

---