Experimental probes of bond orientational order models of blue phase III of chiral liquid crystals.

Abstract

Recently, a cubic bond orientational order model was proposed for blue phase (BP) III [Phys. Rev. Lett. 71, 2757 (1993)]. It was suggested that in blue phase III, although there is no periodic translational symmetry, a cubic orientational order persists. A spatially independent fourth-rank tensor ${\mathit{B}}_{\mathrm{\ensuremath{\alpha}}\mathrm{\ensuremath{\beta}}\mathrm{\ensuremath{\mu}}\ensuremath{\nu}}^{4}$ was used to describe the cubic bond orientational order. In this paper, we show that since BP III is chiral, the bond orientational order parameter is expected to vary in space. Depending on the relative magnitudes of the elastic constants in the free energy, the cubic bond orientational order will twist along either a fourfold ([001]) or a threefold ([111]) symmetry direction. Due to the twist, the cubic symmetry of the bond orientational order is replaced by a lower point symmetry group, ${\mathit{D}}_{4}$(422) or ${\mathit{D}}_{3}$(32). Using Landau theory and dimensional analysis, we find that if there is a chiral cubic bond orientational order in BP III, there should be a measurable birefringence even in the absence of an external field. This is inconsistent with the knowledge that BP III is optically isotropic without a field. We also point out that a phase with cubic bond orientational order can be distinguished from an isotropic phase using field induced birefringence experiments.