Permeability of Polymer Membranes beyond Linear Response

Abstract

The permeability of a membrane to solute penetrants is well defined on the linear response level simply as the ratio of penetrants’ flux and concentration gradient at the membrane boundary layers. However, nonlinearities emerge in the flux–force relation j(f) for large driving forces f, in which the definition of permeability becomes ambiguous. Here, we study nonequilibrium membrane permeation orchestrated by a generic driving force using penetrant- and monomer-resolved computer simulations of transport in a polymer network, supported by exact solutions of the Smoluchowski (drift–diffusion) equation in the stationary state. In the simulations, we consider the transport across a finite polymer membrane immersed in a reservoir of penetrants, addressing one- and two-component penetrant systems. We calculate the f-dependent inhomogeneous steady-state density profiles, boundary layer concentrations, and fluxes of the penetrants. The Smoluchowski approach, using solely coarse-grained equilibrium partitioning and diffusion profiles as input, exhibits remarkable qualitative agreement with our nonequilibrium simulations, which serves for rationalization of the observations. We discuss possible definitions of nonequilibrium, f-dependent permeability, distinguishing between “system” and “membrane” permeabilities. In particular, we introduce the concept of differential permeability as a response to f. The latter turns out to be a highly nonmonotonic function of f for low-permeable systems, demonstrating how a differential permselectivity is substantially tunable by the driving force beyond linear response.