Theory and Simulation of Freeze-Fracture in Cholesteric Liquid Crystals

A theory of fracture in spatially varying anisotropic glass is developed to interpret electron micrographs of freeze-fractured surfaces of cholesteric samples. The expression for energy per unit area released by crack formation is $\gamma \propto {\left[\mathbf{n}·\right(1+b{\mathbf{Q}}_1\left)·\mathbf{n}\right]}^{\frac{1}{2}}$, where $Q_1$ is the traceless Landau tensor for unit order parameter and $\mathbf{n}$ is a unit vector normal to the crack surface. The two parameters of the theory are $b$, which is a function of the ratio of length to width of molecule, and a crack-precursor length. Contours closely matching those observed in the laminar cholesteric texture and in blue phase I are generated.