Combined Edge and Anisotropy Effects on Fickian Mass Diffusion in Polymer Composites

The common methods used to determine the diffusion coefficients of polymer composites are based on the solution of Fickian diffusion equation in one-dimensional (1D) rectangular domain. However, these diffusivities usually involve errors primarily due to finite sample dimensions and anisotropy introduced by fiber reinforcements. In this study, the solution of transient, three-dimensional (3D) anisotropic Fickian diffusion equation is nondimensionalized using six parameters. The solution is then used to analyze the combined contribution of finite sample dimensions and anisotropy to the errors involved in diffusion constants calculated by 1D methods. The small time solution of the Fickian diffusion equation in 3D domain is used to analyze the slope used in diffusivity calculations. It is shown that the diffusion coefficient calculated by the 1D approach is exact only if the correct slope of percent mass gain versus root square time curve at $t=0$ is used. However, it has also been shown that depending on the part geometry and degree of anisotropy, there might be considerable differences between the measured slope from the experimental data and the actual slope at $t=0.$ The mismatch between the slopes results in as much as 50% errors in estimates of diffusion coefficients. Using the 3D solution in nondimensional form, the magnitudes of these errors are studied. A least-square curve-fit method, which yields accurate anisotropic diffusion coefficients, is proposed. The method is demonstrated on artificially generated experimental data for a polymer composite containing 50% unidirectional reinforcement. The anisotropic diffusion coefficients used to generate the data are recovered with less than 1% error.