Curvature expansion method for polymer self-assembled membranes.

Abstract

Polymer vesicles consist of a thin bilayer membrane, the shape of which can be precisely controlled by adjusting the composition of block copolymers. These self-assembled structures provide a powerful method for mimicking biological cell membranes. A key characteristic of these membranes is their elastic moduli, which play a crucial role in determining their mechanical properties. Traditionally, these moduli are derived by fitting the free energy of different membrane shapes to Helfrich's model. In this paper, we present a curvature expansion method that yields an analytical expression for the moduli within the framework of self-consistent field theory. A significant advantage of our approach is its ability to easily extract higher-order moduli, a task that presents substantial challenges for existing methods.