Electrostatic interaction of neutral semipermeable membranes

TL;DR

This paper investigates how neutral semipermeable membranes can generate electrostatic repulsion due to counter-ion permeation, leading to a distance-dependent membrane potential and a disjoining pressure that differs from classical osmotic pressure.

Contribution

It provides a detailed theoretical analysis of electrostatic interactions in neutral membranes, deriving explicit formulas and validating them with simulations, highlighting the role of counter-ion clouds.

Findings

Membranes exhibit a repulsive electrostatic disjoining pressure.

Derived explicit formula deviates from van't Hoff osmotic pressure.

Simulation confirms the validity of the theoretical predictions.

Abstract

We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semipermeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the non-linear Poisson-Boltzmann equation we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van't Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson-Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semipermeable membranes.