Defect Induced Shape Instabilities in Hexagonally Textured Free-Standing Membranes

PEZZUTTI A; VILLAR MA; VEGA DA

Princeton, NJ, USA

Workshop; Through the Looking-glass: a Glimpse into the Geometry and Topology of Materials; 2012

Princeton Center for Theoretical Science

We study the coupling between geometry and defects in flexible membranes suffering a symmetry breaking phase transition. The system is described through a simple model that includes a Brazovskii contribution for the crystalline phase and a Helfrich-Canham free energy penalization for the membrane shape. At the early stage of the phase separation process there is a poor coupling between the membrane shape and the order parameter describing liquid-to- crystal transition. Then, the membrane geometry is determined by the bending stiffness and surface tension. During the nucleation and growth process, defects appear naturally. The overall dynamics is governed by the interplay between the geometry of the host membrane and the defects of the hexagonal texture.