Curvature Instability of Membranes near Rigid Inclusions

TL;DR

This paper develops a general elasticity theory for membranes with curvature instability near rigid inclusions, revealing new shape solutions and stabilization mechanisms involving quartic curvature terms, and proposes experimental methods to measure membrane properties.

Contribution

It introduces a quartic curvature expansion in membrane elasticity theory and analytically studies membrane shapes near inclusions, uncovering new stable configurations and shape exponents.

Findings

New shape solutions for curvature unstable membranes.

Stabilization of membranes by quartic curvature terms.

Method to measure quartic curvature modulus experimentally.

Abstract

In multicomponent membranes, internal scalar fields may couple to membrane curvature, thus renormalizing the membrane elastic constants and destabilizing the flat membranes. Here, a general elasticity theory of membranes is considered that employs a quartic curvature expansion. The shape of the membrane and its deformation energy near a long rod-like inclusion are studied analytically. In the limit where one can neglect the end-effects, the nonlinear response of the membrane to such inclusions is found in exact form. Notably, new shape solutions are found when the membrane is curvature unstable, manifested by a negative rigidity. Near the instability point (i.e. at vanishing rigidity), the membrane is stabilized by the quartic term, giving rise to a new length scale and new scale exponents for the shape and its energy profile. The contact angle induced by an applied force at the inclusion provides a method to experimentally determine the quartic curvature modulus.