Predicting particle transport through an aging polymer using vacancy diffusion

Understanding the process of particle transport is important for various applications such as separation, storage and blockage of selected particles within a polymer. The diffusivity of particles has been related to the fractional free volume f within a sample by the expression D(f) = A exp(−B/f) for certain constants A and B. Polymers are known to undergo physical aging such that the free volume distribution changes over time towards an equilibrium. This phenomenon has been well explained by the vacancy diffusion model established by Curro et al. [J.G. Curro, R.R. Lagasse, R. Simha, Macromolecules 15 (1982) 1621]. Using both the diffusion expression and the vacancy diffusion model, this paper models particle transport in aging, unaged and aged polymer samples.