Chiral smectic A membranes: Unified theory of free edge structure and twist walls

Monodisperse suspensions of rodlike chiral $fd$ viruses are condensed into a rod-length thick colloidal monolayers of aligned rods by depletion forces. Twist deformations of the molecules are expelled to the monolayer edge as in a chiral smectic $A$ liquid crystal, and a cholesteric band forms at the edge. Coalescence of two such isolated membranes results in a twist wall sandwiched between two regions of aligned rods, dubbed $\pi$-walls. By modeling the membrane as a binary fluid of coexisting cholesteric and chiral smectic $A$ liquid-crystalline regions, we develop a unified theory of the $\pi$-walls and the monolayer edge. The mean-field analysis of our model yields the molecular tilt profiles, the local thickness change, and the crossover from smectic to cholesteric behavior at the monolayer edge and across the $\pi$-wall. Furthermore, we calculate the line tension associated with the formation of these interfaces. Our model offers insights regarding the stability and the detailed structure of the $\pi$-wall and the monolayer edge.