Edge Effects on the Determination of Fickian Mass Diffusivity of Polymers

Abstract

Models based on one-dimensional solution of Fickian diffusion equation are commonly used to characterize diffusion coefficients of polymers. These methods are known to have errors due to edge effects, which are believed to be compensated by correction factors. In order to better understand these errors and performance of various correction factors, non-dimensional solution of diffusion equation in a three-dimensional rectangular domain is used to simulate artificial mass diffusion data. The simulated data is then utilized to analyze the errors associated with commonly used methods of diffusivity determination for a variety of geometries with aspect ratios ranging from 1 to 100. The diffusivity values are shown to be highly dependent on the approach used in determining the initial slope of the percent mass gain versus root square time curve. The previously proposed correction factors failed to yield accurate diffusion coefficients and are found to have up to 70% error. A simple, yet accurate method for determination of mass diffusivity of isotropic materials based on the solution of Fickian equation in three-dimensional domain is proposed. The applicability of the method is demonstrated with experimental data and good agreement is observed.