Colloidal membranes of hard rods: unified theory of free edge structure and twist walls
Monodisperse suspensions of rod like 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 π-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 π-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 π-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 π-wall and the monolayer edge.