Non-Fickian mesoscopic modeling of sorption and permeation in polymer nanocomposite membranes

Abstract

To investigate the interactions among nanoscale effects, viscoelasticity, and diffusion in polymer nanocomposite membranes, we have developed a non-Fickian mesoscopic model that describes the dynamics of penetrant concentration and the polymer conformation tensor. The model consists of nonlinear governing equations, supplemented by an expression for internal stresses. Key dimensionless parameters are crucial to the analysis: structure-mixing constant $g_{\mathrm{m}}$, diffusion Deborah number ${\mathrm{De}}_{\mathrm{m}}$, nanofillers content $\mathrm{wt}\%$ and aspect ratio $\mathrm{\alpha }$, and orientation parameter. Numerical simulations demonstrate their effects on mass uptake, concentration, conformation, local and accumulated stresses, and permeation fluxes. Non-Fickian diffusion arises as ${\mathrm{De}}_{\mathrm{m}}$ approaches unity. The maximum stress decreases with $g_{\mathrm{m}}$ and $\alpha$, but increases with ${\mathrm{De}}_{\mathrm{m}}$ or $\mathrm{wt}\%$. The permeation time lag increases with $g_{\mathrm{m}}$, ${\mathrm{De}}_{\mathrm{m}},$ $\alpha$, and $\mathrm{wt}\%$. The model's predictions show good agreement with sorption and permeation data.