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

Abstract

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