  Amphiphilic polymers in aqueous solutions can self-assemble to form bilayer
membranes, and their elastic properties can be captured by 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 a proper 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
obtain certain periodic cylindrical bilayers that are equilibrium states of the
self-consistent field model, which agree with the theoretical predictions made
by the shape equations.
