Periodic cylindrical bilayers self-assembled from biblock polymers

Amphiphilic polymers in aqueous solutions can self-assemble to form bilayer membranes, and their elastic properties can be captured using the well-known Helfrich model involving several elastic constants. In this paper, we employ the self-consistent field model to simulate sinusoidal bilayers self-assembled from diblock copolymers where an appropriate constraint term is introduced to stabilize periodic bilayers with prescribed amplitudes. Then, we devise several methods to extract the shape of these bilayers and examine the accuracy of the free energy predicted by the Helfrich model. Numerical results show that when the bilayer curvature is small, the Helfrich model predicts the excess free energy more accurately. However, when the curvature is large, the accuracy heavily depends on the method used to determine the shape of the bilayer. In addition, the dependence of free energy on interaction strength, constraint amplitude, and constraint period are systematically studied. Moreover, we have devised a method for attaining equilibrium states through the adjustment of constraints. Within the self-consistent field model, these equilibrium states manifest as distinct periodic cylindrical bilayers, which are consonant with the theoretical predictions formulated using the shape equations.