Membrane matrix fraction free volume

In contrast to the LCP results just presented, in glassy polymers used as gas separation membranes, free volume influences diffusion coefficients much more than solubility coefficients. Figure 6 provides an example of this effect. In this figure, the solubility, diffusivity, and permeability of methane in a series of glassy, aromatic, amorphous poly(isophthalamides) [PIPAs] are presented as a function of the fractional free volume in the polymer matrix. (More complete descriptions of the transport properties of this family of materials are available elsewhere (59, 40)). The fractional free volume is manipulated systematically in this family of glassy polymers by synthesizing polymers with different substituent and backbone elements as shown in... 

PV performance of a polymeric membrane is deeply related to the swelling of the membrane. When a membrane is swollen or plasticized by transporting species, the interactions between the polymer chains tend to be diminished, and the membrane matrix will therefore experience an increase in the free volume. The fractional free volume (FFV) (Equation 9.9) of polymers is defined as follows ... 

Free volume present in nanocomposite systems plays a major role in determining the overall performance of the membranes. Positron annihilation lifetime spectroscopy (PALS) is an efficient technique used for the analysis of free volume. The diffusion of permeant through polymeric membranes can be described by two theories, namely, molecular and free-volume theories. According to the free-volume theory, the diffusion is not a thermally activated process as in the molecular model, but it is assumed to be the result of random redistributions of free-volume voids within a polymer matrix. Cohen and Turnbull developed the free-volume models that describe the diffusion process when a molecule moves into a void larger than a critical size, Vc- Voids are formed during the statistical redistribution of free volume within the polymer. It is found that the relative fractional free volume of unfilled polymer decreases on the addition of layered silicates. The decrease is attributed to the interaction between layered silicate and polymer because of the platelet structure and high aspect ratio of layered silicates. The decrease is explained to the restricted mobility of the chain segments in the presence of layered silicates. This results in reduced free-volume concentration or relative fractional free volume [49]. 

Another possible approach to indirectly characterize the membrane morphology is based on the investigation of the free volume within the matrix. Density measurements [119,120] and positron annihilation lifetime spectroscopy evaluation [47] are common methods. Typically, the comparison between the theoretical density or free volume (calculated by simple additivity rules) and the experimental one can reveal the presence of a good interfacial morphology or the presence of interface voids or clustering formation. Fig. 7.13 shows the influence of filler content on the morphology of poly(trimethylsilyl propyne) (PTMSP)/Ti02 NCMs in terms of the volumetric fraction of interface voids as calculated from a comparison of the expected and measured membrane density [119],... 

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