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 dif ferential 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.

Atomistic simulations of pristine and nanoparticle reinforced hydrogels: A review

“…Since PNIPAM exhibits a volume transition temperature similar to that of human body temperature, so it is widely used as a responsive polymer 260 . In order to develop the drug delivery applications, it becomes essential to study the molecular transport in thermoresponsive polymer membranes 261–263 . In 2018, Kanduc et al 259 elucidated the diffusion behavior of polar and nonpolar penetrants in PNIPAM hydrogels using MD based simulations.…”

“…260 In order to develop the drug delivery applications, it becomes essential to study the molecular transport in thermoresponsive polymer membranes. [261][262][263] In 2018, Kanduc et al 259 elucidated the diffusion behavior of polar and nonpolar penetrants in PNIPAM hydrogels using MD based simulations. The PNIPAM was modeled using an OPLS-based force field.…”

Phenol release from pNIPAM hydrogels: scaling molecular dynamics simulations with dynamical density functional theory

“…Without this term, which is small at low cargo concentrations, the DDFT is equivalent to the Smoluchowski approach. 70 Performing the functional differentiation, the corresponding chemical potential reads as 32,33,44 bm c ðr; tÞ ¼ ln r c ðr;…”

“…Without this term, which is small at low cargo concentrations, the DDFT is equivalent to the Smoluchowski approach. 70…”

A two-phase model that unifies and extends the classical models of membrane transport

“…Decades ago, a spirited debate emerged over which approach is appropriate for swollen membranes (7)(8)(9)(10)(11)(12), which persists to this day. Variants of both models continue to be discussed and criticized, for example, in treating reverse osmosis membranes (13,14), with ongoing reframing of the classical models (15,16). For example, recent neutron scattering studies of water transport in polyamide reverse osmosis (PARO) membranes suggested SD to be invalid and motivated a proposed change in the strategic design of future PARO membranes, toward reducing tortuosity rather than enhancing selective solubility and diffusivity (17).…”