Transport in polymer membranes beyond linear response: Controlling permselectivity by the driving force

TL;DR

This study investigates how external driving forces influence membrane permeability beyond linear response, revealing nonlinear permselectivity and providing a theoretical framework validated by simulations for controlling transport in polymer membranes.

Contribution

It introduces a novel definition of force-dependent permeability and demonstrates how permeability and permselectivity can be tuned by external forces beyond linear response.

Findings

Permeability becomes highly nonlinear at low permeability regimes.

External forces can significantly enhance permselectivity.

Continuum theory agrees qualitatively with detailed simulations.

Abstract

In the popular solution-diffusion picture, the membrane permeability is defined as the product of the partition ratio and the diffusivity of penetrating solutes inside the membrane in the linear response regime, i.e., in equilibrium. However, of practical importance is the penetrants' flux across the membrane driven by external forces. Here, we study nonequilibrium membrane permeation orchestrated by a uniform external driving field using molecular computer simulations and continuum (Smoluchowski) theory in the stationary state. In the simulations, we explicitly resolve the penetrants' transport across a finite monomer-resolved polymer network, addressing one-component penetrant systems and mixtures. We introduce and discuss possible definitions of nonequilibrium, force-dependent permeability, representing `system' and `membrane' permeability. In particular, we present for the first time a definition of the differential permeability response to the force. We demonstrate that the latter turns out to be significantly nonlinear for low-permeable systems, leading to a high amount of selectiveness in permeability, called `permselectivity', and is tunable by the driving force. Our continuum-level analytical solutions exhibit remarkable qualitative agreement with the penetrant- and polymer-resolved simulations, thereby allowing us to characterize the underlying mechanism of permeabilities and steady-state transport beyond the linear response level.