Curvature Instability of Membranes near Rigid Inclusions

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.