Numerical results for the blue phases

Abstract

We review recent numerical work investigating the equilibrium phase diagram, and the dynamics, of the cholesteric blue phases. In equilibrium numerical results confirm the predictions of the classic analytical theories, and extend them to incorporate different values of the elastic constants, or the effects of an applied electric field. There is a striking increase in the stability of blue phase I in systems where the cholesteric undergoes helical sense inversion, and the anomalous electrostriction observed in this phase is reproduced. Solving the equations of motion allows us to present results for the phase transition kinetics of blue phase I under dielectric or flexoelectric coupling to an applied electric field. We also present simulations of the blue phases in a flow field, showing how the disclination network acts to oppose the flow. The results are based on the Landau-de Gennes exapnsion of the liquid crystal free energy: that such a simple and elegant theory can predict such complex and subtle physical behaviour is remarkable.

Blue-phase liquid crystal droplets

“…1), it is of interest to highlight the main differences with respect to the behavior of the corresponding bulk material (8,10,12). First, the range of stability of the blue phases is different: for the droplet's size and anchoring strength considered here, BPI is stable over a wider range of temperature.…”

“…1; the dotted line divides the cholesteric and BPI regions and shows that BPI is expected at higher chiralities. An alternative representation of the phase diagram, common in the literature for chiral LCs in the bulk (10,12,15), can be obtained by replacing N by the definition of chirality, namely…”

“…For completeness, simulations are carried out from different initial conditions, including a uniform state, a random configuration, the bulk ansatz for BPI and BPII (10,12), and the DSS and RSS configurations (see Supporting Information for details about these initial configurations). Note that the RSS structure represents the stable state for strong planar anchoring and high chirality (41).…”

“…The symmetry properties of blue phases (BPs) have attracted considerable attention, as have their potential applications in a wide range of technologies (3)(4)(5)(6)(7). Theoretical and computational studies of the bulk structure and dynamics of BPs have helped elucidate their nature (1,8,(9)(10)(11)(12)(13)(14)(15) in considerable detail. In the bulk, however, BPs are only found in a narrow range of temperature, between the cholesteric and the isotropic phases (1-6, 10-18), thereby placing limits on their practical utility.…”

A model for the Pockels effect in distorted liquid crystal blue phases

“…7,9 These effects are conventionally interpreted in terms of dielectric coupling, though they have also been considered as a result of flexoelectric coupling. 5,[10][11][12][13] It is the Kerr effect that has been of particular interest in the context of display devices because it operates on a time scale of 10 À5 -10 À4 s, which is much quicker than the time scale of field-induced phase changes and electrostriction. [14][15][16] Further, the effective Kerr coefficient in the BPs is remarkably large compared to conventional materials: values 10 2 -10 4 times larger than for nitrobenzene have been reported.…”