Mesoscopic modeling of mass transport in viscoelastic phase-separated polymeric membranes embedding complex deformable interfaces

Abstract

Phase-separated polymeric membranes turn out to offer an alternative and promising solution for enhancing the limited performance exhibited by homopolymer membranes in separation techniques. Here, in order to properly describe mass transport in immiscible membranes embedding a dividing deformable complex interface, we rigorously derive, by using non-equilibrium thermodynamics and continuum mechanics approaches, a genuinely non-linear mesoscopic formulation that extends Fick’s laws and explicitly incorporates the coupling arising between diffusion and structure changes. Thereby, in addition to the penetrants’ mass fraction c, three additional independent structural state variables are adopted, namely the macromolecular chain conformation tensor m; and a scalar Q and a second-rank tensor q respectively for the size and shape anisotropy of the interface area. Our model consists of coupled PDEs and ODEs time evolution equations respectively for the bulk and the boundary dynamics, and provides an expression for the distribution of internal stresses. Our findings show among others that the mechanical changes occurring in the membrane internal structure may have an important effect on mass transport which may consequently exhibit a non-Fickian character. Moreover, the model is also capable of providing the mesoscopic details of the structure changes induced by diffusion. Scaling analysis leads to the emergence of several groups of physical parameters whose influence on mass transport is illustrated; and quantitative as well as qualitative agreements with sorption data (taken from literature) of Toluene in a PP/NBR membrane at different PP contents are shown. Unsteady mass fluxes are also calculated for permeation of PP/NBR to toluene, xylene and benzene and respective time lags are predicted.