Formation of grid patterns in an ac-driven electroconvection system.

Abstract

We report the formation mechanism of a unique pattern observed in ac-driven electroconvection of nematic liquid crystals (NLCs), in which many well-organized grid cells are very regularly aggregated in a two-dimensional plane, globally forming a nearly perfect grid pattern (GP). Intuitively, the formation of such a pattern is unpredictable; usually, the perfectly regular normal roll (NR) showing a preferred roll direction is observed in this system by imposing a fixed initial direction of an NLC. The GP was investigated by varying the ac voltage and frequency. To characterize the GP, the density ρ_{GP}, the width a and length b of the grids, and the oscillation period T_{GP} of an inner optical pattern of the grids were measured; moreover, the lengths L[over ¯]_{x} and L[over ¯]_{y} characterizing phase-jump lines (PJLs) in the GP were examined. By taking into account the process of evolution from a fluctuating NR with defects to the GP, the velocity and director fields of the GP are estimated. Furthermore, in comparison with the bimodal mechanism proposed in the earlier study, a possible mechanism for the GP formed by the PJLs is discussed; various routes to GPs depending on the ac frequency are proposed.