Structures of the cholesteric liquid crystal droplets with parallel surface anchoring

Abstract

Model structures of cholesteric liquid crystal droplets embedded in a medium which enforces parallel surface anchoring are treated. Structures with disclination lines of integer and half-integer strength are obtained by minimising the Frank free energy. The constant order parameter approximation appropriate for droplets which are large compared to the cores of defects and the approximate ansatz with the molecular director everywhere tangential to the concentric spherical surfaces are used. Within this approach the structure with a diametrical disclination line is the most stable. Its free energy is compared to that of the non-twisted bipolar structure and to that of the two twisted structures. The well-known structure with a radial disclination line and that with a double radial disclination line not found in the known literature are presented. It is shown that surface free energy terms, usually omitted in the minimization, do not influence substantially the stability of the structures discussed. The phase diagram is constructed and the theoretical predictions are compared with available experimental results. Further an approximate description of a possible director field escape close to the defect lines is discussed.