Novel wall defects in Lamellar soft matter

Abstract

Two-dimensional soft materials such as flexible membranes offer an ideal testing ground for fundamental concepts involving order (symmetry), low-energy excitations, topological defects, and fluctuations. This thesis studies the interplay between geometry, topology, and elasticity in two-dimensional soft materials. Gaussian (intrinsic) curvature of membranes acts as a source of topological defects in orientational order [1, 2]. Conversely, topological defects tend to bend flat, deformable ordered membranes to reduce in-plane stresses. Positive and negative disclinations (vortices) prefer locally positive and negative Gaussian curvatures respectively. The interplay between Gaussian curvature and topological defects is strikingly illustrated by the Poincaré-Hopf index theorem. According to this theorem, a sphere with in-plane orientational order must have an isolated disclination or isolated disclinations with total index 2.