Flexoelectric fluid membranes in electric field. Shape equations and exact solutions

TL;DR

This paper derives shape equations for axisymmetric fluid membranes under a uniform electric field, incorporating flexoelectric effects and curvature-induced polarization, and provides exact solutions linking model parameters to physical properties.

Contribution

It introduces a comprehensive shape equation including flexoelectric and polarization effects and presents exact solutions with parameter connections.

Findings

Derived shape equations for membranes in electric fields.

Included flexoelectric and polarization effects in the model.

Provided exact solutions with parameter mappings.

Abstract

The shape equation for an axisymmetric fluid membrane is derived, assuming action of an uniform external electric field. The flexoelectric contribution to the free energy of the membrane, stemming from the latter is accounted within the theory by Steigmann and Agrawal. Additionally, we have introduced, in the aforementioned functional, another term associated with a curvature induced membrane polarization, as the latter was first hypothesized by A. Petrov. Some exact Naito-type solutions of the studied equation are given, with the free parameters linked to the model ones.