Feedback-controlled solute transport through chemo-responsive polymer membranes

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, $\varphi$. 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 $\varphi$ 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.

11 pages, 7 figures

References in corpus (10)

• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Catalyzed bimolecular reactions in responsive nanoreactors
• Power functional theory for many-body dynamics
• Hamiltonian and Brownian systems with long-range interactions: V. Stochastic kinetic equations and theory of fluctuations
• Tuning the Selective Permeability of Polydisperse Polymer Networks
• Cosolute partitioning in polymer networks: Effects of flexibility and volume transitions
• Modeling of stimuli-responsive nanoreactors: rational rate control towards the design of colloidal enzymes
• Cross-linker effect on solute adsorption in swollen thermoresponsive polymer networks
• Transport in polymer membranes beyond linear response: Controlling permselectivity by the driving force
• Equilibrium Stochastic Delay Processes

Cited by in corpus (1)

• Nonequilibrium friction and free energy estimates for kinetic coarse-graining -- Driven particles in responsive media