Techniques Used to Study the Permeability of Polymers and Nanocomposites

Techniques Used to Study the Permeability of Polymers and Nanocomposites 

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]. 

PALS is a nondestmctive technique that provides an effective approach for the study of the free volume in the solid state. It is based on the localization of the positronium (Ps) in the free volume holes because of their repulsion by the surrounding atoms. Generally, the annihilation spectra in polymers consist of three exponentially decaying components that correspond to the three main processes of their annihilation [50]. Each of these processes is characterized by the mean lifetime and the probability of annihilation (intensity). The longest lifetime corresponds to the annihilation process of o-Ps in the free volume holes. This is the process that is used to estimate the free volume in the amorphous polymers. The size of the free volume holes, R, in the polymer can be determined from the measured lifetime, so Ps, using the semiempirical equation 

The relative intensity gives the probability for the formation of o-Ps, which is proportional to the number of holes, that is, the overall free volume [51,52]. Plotting the measured lifetime of the o-Ps and the intensity as a function of clay particles loading, one can estimate any variation in the polymer free volume that may be caused by the presence of the nanoclay particles [51]. 

further, use is made of reactive additives, then the working time of the composite film becomes 

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