Eur. Phys. J. E (2008) 27: 81-86
https://doi.org/10.1140/epje/i2008-10354-y

Shapes of lipid monolayer domains: Solutions using elliptic functions

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, Singular University, Beijing, 100084, China
³ Institute of Theoretical Physics, The Chinese Academy of Sciences, P.O. Box 2735, Beijing, 100080, China

^* e-mail: iwamoto@pe.titech.ac.jp

Received: 4 December 2007
Revised: 4 June 2008
Published online: 29 July 2008

Abstract

Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative line tension and a positive curvature energy at the boundary, and a corresponding shape equation was derived by the variation of the approximated domain energy (Phys. Rev. Lett. 93, 206101 (2004)). Here we further incorporate surface pressure into the shape equation and show that the equation can be analytically solved: the curvature of the domain boundary is exactly obtained as an elliptic function of arc-length. We find that a circular domain can grow into bean-and peach-like domains with pressure, i.e., dipping and cuspidal transitions of circle by compression. The comparison with the experimental observation shows nice agreement.