Domain shapes in lipid monolayers studied as polar cholesteric liquid crystals

¹ Department of Physical Electronics, Tokyo Institute of Technology - 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan
² Center for Advanced Study, Tsinghua University - Beijing 100084, China
³ Institute of Theoretical Physics, The Chinese Academy of Sciences - P.O. Box 2735, Beijing 100080, China

^a iwamoto@pe.titech.ac.jp

Received: 25 March 2010
Accepted: 28 June 2010

Abstract

Both bulk and boundary orientations, and boundary shape equations for tilted lipid domain are derived in analogy with a polar cholesteric liquid crystal. It shows that in a two-dimensional (2D) system the 3D spontaneous splay and chiral elastic energies, the s₀ and q₀ terms of Frank energy, can be regarded as an orientation-dependent line tension, and the domain formation is the equilibrium between the line tension, the surface pressure, the orientational stress, and the dipole-dipole interaction. An obvious and analytic shape solution for pinned boundary orientation for maximum boundary tension has been found and the diverse domain shapes observed in lipid monolayers in the past two decades, such as star, boojum, cardioid, ellipse, bola, and clover-leaf shapes, are dramatically well described by the solution.