ELECTROSTRICTION OF THE CUBIC BLUE PHASES IN THE PRESENCE OF BOND-ORIENTATIONAL ORDER

The cubic blue phase I displays anomalous electrostriction, i.e., if t he electric held vector is rotated from one crystallographic direction to another, the deformation along the held 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 str ong nonlinear dielectric susceptibility chi(4), as shown by experiment s of Pieranski, 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 desc ription of the blue phases. Indeed, it has been proposed that the blue phase III is a structure of pure bond orientational order. Incorporat ing the bond orientational tensor into the free energy expansion, we h ave calculated the distortion of the O-8(I4(1)32) and O-2(P4(2)32) blu e phase lattices by a weak electric field within the model of rigid he lices. The resulting fourth-order electrostriction tensor is expressed in terms of the order parameters characterizing the O-8 and the O-2 g round states of the undistorted system. The relations generalize studi es of Stark and Trebin [Phys. Rev. A 44, 2752 (1991)]. It is found tha t there exists a range for the coupling strength between Q(r) and chi( 4) where anomalous electrostriction is predicted for blue phase I, in accordance with experiment. Thus bond orientational order seems to pro vide a link between two unsolved problems: that of the anomalous elect rostriction of the blue phase I and that of the structure of the blue phase III.