Elastic properties of liquid-crystalline bilayers self-assembled from semiflexible-flexible diblock copolymers

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

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.

Analytical Calculation of the Elastic Moduli of Self-Assembled Liquid-Crystalline Bilayer Membranes

Liquid-crystalline orders are ubiquitous in membranes and could significantly affect the elastic properties of the self-assembled bilayers. Calculating the free energy of bilayer membranes with different geometries and fitting them to their theoretical expressions allow us to extract the elastic moduli, such as the bending modulus and Gaussian modulus. However, this procedure is time-consuming for liquid-crystalline bilayers. In paper reports a novel method to calculate the elastic moduli of the self-assembled liquid-crystalline bilayers within the self-consistent field theory framework. Based on the asymptotic expansion method, we derive the analytical expression of the elastic moduli, which reduces the computational cost significantly. Numerical simulations illustrate the validity and efficiency of the proposed method.

Elastic properties of self-assembled bilayer membranes: Analytic expressions via asymptotic expansion

Bilayer membranes self-assembled from amphiphilic molecules are ubiquitous in biological and soft matter systems. The elastic properties of bilayer membranes are essential in determining the shape and structure of bilayers. A novel method to calculate the elastic moduli of the self-assembled bilayers within the framework of the self-consistent field theory is developed based on an asymptotic expansion of the order parameters in terms of the bilayer curvature. In particular, the asymptotic expansion method is used to derive analytic expressions of the elastic moduli, which allows us to design more efficient numerical schemes. The efficiency of the proposed method is illustrated by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents.