Electrostriction of the cubic blue phases in the presence of bond orientational order.

Abstract

The cubic blue phase I displays anomalous electrostriction, i.e., if the electric field vector is rotated from one crystallographic direction to another, the deformation along the field changes from dilatation to compression or vice versa. Standard theories of blue phases based on an expansion of the free energy in powers of the alignment tensor Q(r) are not able to explain this anomaly. Cubic blue phases possess a strong nonlinear dielectric susceptibility ${\mathit{\ensuremath{\chi}}}^{4}$, as shown by experiments of Piera\ifmmode \acute{n}\else \'{n}\fi{}ski, Cladis, Garel, and Barbet-Massin [J. Phys. (Paris) 47, 139 (1986)]. Hence the corresponding order parameter, which we denote ``bond orientational tensor,'' must be included in a theoretical description of the blue phases. Indeed, it has been proposed that the blue phase III is a structure of pure bond orientational order. Incorporating the bond orientational tensor into the free energy expansion, we have calculated the distortion of the ${\mathit{O}}^{8}$(I${4}_{1}$32) and ${\mathit{O}}^{2}$(P${4}_{2}$32) blue phase lattices by a weak electric field within the model of rigid helices. The resulting fourth-order electrostriction tensor is expressed in terms of the order parameters characterizing the ${\mathit{O}}^{8}$ and the ${\mathit{O}}^{2}$ ground states of the undistorted system. The relations generalize studies of Stark and Trebin [Phys. Rev. A 44, 2752 (1991)]. It is found that there exists a range for the coupling strength between Q(r) and ${\mathit{\ensuremath{\chi}}}^{4}$ where anomalous electrostriction is predicted for blue phase I, in accordance with experiment. Thus bond orientational order seems to provide a link between two unsolved problems: that of the anomalous electrostriction of the blue phase I and that of the structure of the blue phase III. \textcopyright{} 1996 The American Physical Society.