Modeling of diffusion through nanocomposite membranes

The diffusion process of a simple fluid through a complex polymer/clay nanocomposite membrane embedding a complex interface is modeled using the generalized bracket/General Equation for Non-Equilibrium Reversible and Irreversible Coupling (GENERIC) formalism. The complex interface is characterized, on a mesoscopic level of description, by a second-order area tensor A. A set of governing equations describing the time evolution of concentration, flux, internal structure (of the complex polymeric membrane) and area tensor is obtained. Four parameters appear in the governing equations. Two parameters characterize the importance of elasticity and mixing and the remaining two parameters account for the effects of the complex interface. An extension of Fick's second law, which includes the convective fluxes due to the change of polymer internal structure and complex interface, is derived for the flux evolution. The model describes the diffusion process quantitatively quite well.