Flexoelectricity and the Entropic Force between Fluctuating Fluid Membranes

TL;DR

This paper investigates how flexoelectricity influences the entropic force between fluctuating biological membranes, revealing a correction that alters the force from attraction to repulsion depending on membrane separation.

Contribution

It introduces an analytical variational perturbation approach to quantify flexoelectric effects on membrane interactions, a novel aspect in membrane biophysics.

Findings

Flexoelectricity modifies the entropic force between membranes.

At close separations, flexoelectricity enhances attraction.

At larger distances, it increases repulsion.

Abstract

Biological membranes undergo noticeable thermal fluctuations at physiological temperatures. When two membranes approach each other, they hinder the out of plane fluctuations of the other. This hindrance leads to an entropic repulsive force between membranes which, in an interplay with attractive and repulsive forces due to other sources, impacts a range of biological functions: cell adhesion, membrane fusion, self-assembly, binding-unbinding transition among others. In this work, we take cognizance of the fact that biological membranes are not purely mechanical entities and, due to the phenomenon of flexoelectricity, exhibit a coupling between deformation and electric polarization. The ensuing coupled mechanics-electrostatics-statistical mechanics problem is analytically intractable. We use a variational perturbation method to analyze, in closed-form, the contribution of flexoelectricity to the entropic force between two fluctuating membranes and discuss its possible physical implications. We find that flexoelectricity leads to a correction that switches from an enhanced attraction at close membrane separations and an enhanced repulsion when the membranes are further apart.