Twist or shout: competition of curvature and alignment in chiral liquid crystal membranes

We study the effect of curvature on chiral membranes with interactions that favor alignment with the local surface normal. Unlike many other previously studied cholesteric surfaces, such membranes have an in-plane pitch axis, as opposed to one normal to the plane. The aligning interaction is mathematically equivalent to a magnetic field locally normal to the surface, and hence we expect a transition from a cholesteric to an aligned phase at a finite interaction strength, as pointed out by Meyer and deGennes. Starting with the directors confined to a fixed cylindrical geometry, we numerically determine the tilt angle of the directors relative to the normal, as a function of the pitch and the interaction strength. We find evidence of the aligning transition, along with additional effects due to the curvature of the surface. We also present a theoretical model that predicts the behavior determined by the numerical analysis, including the structure of the observed pi-walls. Finally, to probe the effect of intrinsic curvature, we study unduloid-shaped membranes that allow a continuous increase of Gaussian curvature from a cylinder to a sphere. Our work systematically elucidates the effect of domain curvature on chiral membranes.