Feedback-controlled solute transport through chemo-responsive polymer membranes

TL;DR

This paper presents a theoretical model of chemo-responsive polymer membranes that exhibit nonlinear, feedback-driven solute transport, including bistability and hysteresis, with potential for self-regulating membrane applications.

Contribution

It introduces a nonlinear-feedback solution-diffusion model capturing how membrane responsiveness affects solute flux and permeability, revealing tunable nonlinear transport behaviors.

Findings

Membrane feedback can significantly alter solute flux, increasing or decreasing it by orders of magnitude.

The model predicts steady-state bistability and hysteresis in force--flux relations due to membrane responsiveness.

Tuning solute-membrane interactions enables control over nonlinear transport features.

Abstract

Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we study theoretically the consequences of membrane responsiveness and feedback on the steady-state force--flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, $c_0$, the driving force, $f$, and the polymer volume fraction, $\phi$. In our model, solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force--flux relations, $j(f)$, which we quantify in terms of the system's differential permeability, $\mathcal{P}_\text{sys}^{\Delta}\propto {\mathrm{d}j}/{\mathrm{d}f}$. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force, and largely tunable by attractive versus repulsive solute--membrane interactions. Moreover, controlling the input, $c_0$ and $f$, can lead to steady-state bistability of $\phi$ and hysteresis in the force--flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.