Flexoelectric blue phases

We describe the occurence and properties of liquid crystal phases showing two dimensional splay and bend distortions which are stabilised by flexoelectric interactions. These phases are characterised by regions of locally double splayed order separated by topological defects and are thus highly analogous to the blue phases of cholesteric liquid crystals. We present a mean field analysis based upon the Landau--de Gennes Q-tensor theory and construct a phase diagram for flexoelectric structures using analytic and numerical results. We stress the similarities and discrepancies between the cholesteric and flexoelectric cases.Comment: 4 pages, accepted for publication in Phys. Rev. Let

Stabilising the Blue Phases

We present an investigation of the phase diagram of cholesteric liquid crystals within the framework of Landau - de Gennes theory. The free energy is modified to incorporate all three Frank elastic constants and to allow for a temperature dependent pitch in the cholesteric phase. It is found that the region of stability of the cubic blue phases depends significantly on the value of the elastic constants, being reduced when the bend elastic constant is larger than splay and when twist is smaller than the other two. Most dramatically we find a large increase in the region of stability of blue phase I, and a qualitative change in the phase diagram, in a system where the cholesteric phase displays helix inversion.Comment: 15 pages, 6 figure

Rheology of cholesteric blue phases

Blue phases of cholesteric liquid crystals offer a spectacular example of naturally occurring disclination line networks. Here we numerically solve the hydrodynamic equations of motion to investigate the response of three types of blue phases to an imposed Poiseuille flow. We show that shear forces bend and twist and can unzip the disclination lines. Under gentle forcing the network opposes the flow and the apparent viscosity is significantly higher than that of an isotropic liquid. With increased forcing we find strong shear thinning corresponding to the disruption of the defect network. As the viscosity starts to drop, the imposed flow sets the network into motion. Disclinations break-up and re-form with their neighbours in the flow direction. This gives rise to oscillations in the time-dependent measurement of the average stress.Comment: 4 pages, 4 figure

Switching dynamics in cholesteric blue phases

Blue phases are networks of disclination lines, which occur in cholesteric liquid crystals near the transition to the isotropic phase. They have recently been used for the new generation of fast switching liquid crystal displays. Here we study numerically the steady states and switching hydrodynamics of blue phase I (BPI) and blue phase II (BPII) cells subjected to an electric field. When the field is on, there are three regimes: for very weak fields (and strong anchoring at the boundaries) the blue phases are almost unaffected, for intermediate fields the disclinations twist (for BPI) and unzip (for BPII), whereas for very large voltages the network dissolves in the bulk of the cell. Interestingly, we find that a BPII cell can recover its original structure when the field is switched off, whereas a BPI cell is found to be trapped more easily into metastable configurations. The kinetic pathways followed during switching on and off entails dramatic reorganisation of the disclination networks. We also discuss the effect of changing the director field anchoring at the boundary planes and of varying the direction of the applied field.Comment: 17 pages, 11 figure

The liquid-crystalline smectic blue phases

Smectic blue phases (BPSm) are new mesophases of thermotropic liquid crystals, which exhibit a double geometrical frustration: the extension of chirality in three spatial dimensions like the classical blue phases, and helical twist competing with smectic order, as in the TGB phases. The existence of a quasi-long range smectic order in BPSm phases breaks the cubic symmetry of classical blue phases. The symmetries of these new phases have been determined by X-ray scattering and optical polarizing microscopy experiments.Comment: 5pages, 13 figure

Thermodynamics of Blue Phases In Electric Fields

We present extensive numerical studies to determine the phase diagrams of cubic and hexagonal blue phases in an electric field. We confirm the earlier prediction that hexagonal phases, both 2 and 3 dimensional, are stabilized by a field, but we significantly refine the phase boundaries, which were previously estimated by means of a semi-analytical approximation. In particular, our simulations show that the blue phase I -- blue phase II transition at fixed chirality is largely unaffected by electric field, as observed experimentally.Comment: submitted to Physical Review E, 7 pages (excluding figures), 12 figure

Phase Diagrams For The Blue Phases Of Highly Chiral Liquid Crystals

Polarizing microscopy and optical-activity measurements are used to determine the phase diagram for the blue phases of chiral-racemic mixtures of terephthaloyloxy-bis-4-(2\u27-methylbutyl) benzoate. Contrary to an earlier report, it is the second blue phase (BP II) rather than the first blue phase (BP 1) that is not stable relative to the other blue phases at high chirality. With this development, all phase diagrams for the blue phases reported to date have the same topology. Using similar data for two other highly chiral systems, it is found that a simple scaling of the temperature and chiral-fraction axes produces phase diagrams in quantitative agreement with the present results. Thus, in spite of differences in molecular structure, the number of chiral centers, and phase-transition temperatures, these three systems possess remarkably similar phase diagrams and lend evidence for a universal phase diagram for the blue phases