Electrostatic Maxwell stress model of the shapes of condensed phase domains in monolayers at the air-water interface

Abstract

The formation mechanism of the shapes of condensed phase domains in monolayers at the air-water interface was investigated taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization generated in normal and in-plane direction. By deriving the shape equation of monolayer domains as the mechanical balance at the domain boundary, we found that the electrostatic energy contributes to the shape equation as electrostatic Maxwell stress. Development of a cusp from condensed phase domains of fatty acid monolayers, which has been experimentally observed, was analyzed by the shape equation. It was found that the development of a cusp originated from the strong Maxwell stress, which was induced by the non-uniform orientational distribution in the fatty acid domain, and that cusped shapes gave a minimum of the free energy of the domain. It demonstrates that the shape equation with Maxwell stress, which is derived in the present study, is useful to study the formation mechanism of the shapes of condensed phase domains in monolayers.