The topological soliton decay in a linear defect of the domain structure of twisted nematic

Abstract

In this paper, the topological soliton decay in an oscillating linear defect of electroconvective structure (Williams domains) arising in π/2 twisted nematic liquid crystal are studied. In contrast to planarly oriented nematics, hydrodynamic flows in the domains of a twisted nematic have a helical character. Since, in addition to the tangential velocity component, there is also axial component, the direction of which is opposite in neighboring domains. This feature leads to the formation of stable localized extended objects — linear defects oriented normal to Williams domains. With increasing applied voltage, “zig-zag” oscillations occurs in linear defects. The boundaries between the “zig” and “zag“ states are classical dislocations. It has been found, that the dislocation, moving along the core of the defect, breaks up into an antidislocation and two dislocations. Unlike case of planarly oriented nematics, dislocations are not isolated from each other by unperturbed rolls but remain “bound” by hydrodynamic flows within the core of a linear defect. It is assumed that the splitting of the dislocation occurs as a result of the local instability of the orientational twist mode of the director n due to its strong coupling with the hydrodynamic velocity. In the framework of the sine–Gordon equation, in the presence of a dissipative term and spatial perturbations, the mechanism of a topological soliton (kink) decay into antisoliton and two solitons is considered.