Numerical Simulations of Gas Sorption Experiments in Polymers: Influence of Aspect Ratio and Pressure Increase Rate on the Determination of Diffusion Coefficient

Abstract

Diffusion and sorption phenomena of gases in polymers are of relevance for a number of technological applications, e.g., polymer foaming and membrane technology. The diffusion coefficient and the solubility, which depend on temperature and applied gas pressure, can be determined using the buoyancy method. In this work, the influence of two important parameters are investigated, i.e., the dimensions of the polymer sample and the pressure increase rate, on the accuracy of the determination of the diffusion coefficient D using gas sorption measurements. Numerical simulations on effectively two-dimensional diffusion phenomena in polymers are performed in order to obtain “ideal” experimental data. This set of “ideal” experimental data for polymer samples with specified geometrical dimensions is used for determination of the diffusion coefficient based on the analytical solution of Fickian diffusion in one spatial dimension. Different fitting procedures for determination of the diffusion coefficient are compared. Because of the finite time, which is necessary for pressure increase in a sorption experiment, the influence of pressure increase rate is also studied. This analysis reveals that an aspect ratio larger than 32 and a time for pressure increase smaller than approximately 3 × 10−9 m2D−1 is necessary for a reliable determination of diffusion coefficient D.