Tilt Modulus of Bilayer Membranes Self-Assembled from Rod–Coil Diblock Copolymers

Abstract

Quantitatively understanding membrane fission and fusion requires a mathematical model taking their underlying elastic degrees of freedom, such as the molecule’s tilt, into account. Hamm–Kozlov’s model is such a framework that includes a tilt modulus along with the bending modulus and Gaussian modulus. This paper investigates the tilt modulus of liquid-crystalline bilayer membranes by applying self-consistent field theory. Unlike the widely used method in molecular dynamics simulation which extracts the tilt modulus by simulating bilayer buckles with various single modes, we introduce a tilt constrain term in the free energy to stabilize bilayers with various tilt angles. Fitting the energy curve as a function of the tilt angle to Hamm–Kozlov’s elastic energy allows us to extract the tilt modulus directly. Based on this novel scheme and focused on the bilayers self-assembled from rod–coil diblock copolymers, we carry out a systematic study of the dependence of the tensionless A-phase bilayer’s tilt modulus on the microscopic parameters.