Self-excited oscillation of the director field in cholesteric liquid crystalline droplets under a temperature gradient

Abstract

In this study, we demonstrate a self-excited oscillation induced in cholesteric liquid crystalline droplets under a temperature gradient. At equilibrium, a winding Maltese cross pattern with a point defect was observed via polarised microscopy in the droplets dispersed in an isotropic solvent. When the temperature gradient was applied, the pattern was deformed owing to the Marangoni convection induced by the gradient. Here, when both the droplet size and temperature gradient were sufficiently large, the periodic movement of the defect together with the pattern deformation was observed, which demonstrated the self-excited oscillation of the director field. To describe this phenomenon, we theoretically analysed the flow and director fields by using Onsager's variational principle. This principle enabled the simplified description of the phenomenon; consequently, the time evolution of the director field could be expressed by the phenomenological equations for the two parameters characterising the field. These equations represented the van der Pol equation, which well expressed the mechanism of the self-excited oscillation.

Differential rotation in cholesteric pillars under a temperature gradient

“…In addition, the assumed director field could have a slight incompatibility with the real structure. Particularly, in the present study, the interface between LC and the solvent has a weak anchoring property 16,18,26,27 , which can deform the helical structure around the edge region of the pillar. For these reasons, the rotational torque and behaviour in Region-III may become different from the theoretical consideration.…”

“…However, Ḟ is actually negligibly small in the present case because the dynamic (timedependent) director deformation is just scarcely observed under POM and hence not so significant. As for the dissipation function, the coupling terms between the flow and director fields can be described as [26][27][28][29][30] (…”

Morphogenesis of a chiral liquid crystalline droplet with topological reconnection and Lehmann rotation

“…1(b)-(e). This indicates that the director field has a radial alignment and a point defect exists in the droplet [18,23,37]. During the cooling process, a point defect first appeared at the droplet centre (Fig.…”

“…Subsequently, keeping T constant and increasing T0, we obtained the I+Ch phases for Type-A and Type-B, respectively. In these situations, we observed the droplets under constant T0 and [18,23,37,38]. In this situation, director rotation cannot be driven unless the director field is deformed.…”

Propagation of periodic director and flow patterns in a cholesteric liquid crystal under electroconvection

“…Deformation is induced by the rotational viscous force due to the existence of circulating flows (Fig. 6(a) and (b)) [2,24,43]. In this case, large distortions are periodically localised in the director field, as shown in Fig.…”