Stabilization of a blue phase by a guest component: An approach based on a Landau–de Gennes theory

We discuss, with the aid of numerical calculations based on a Landau–de Gennes theory, the stabilization of a blue phase in chiral liquid crystals by introducing a guest component. Our argument is based on a common speculation that cores of disclination lines with higher free-energy density are replaced by the guest component. We assume that the guest component forms sharp interfaces with the liquid crystal (strong segregation). We show that, by a suitable choice of materials with small interfacial tension, a guest component of volume fraction less than 10% drastically increases the temperature range of thermodynamic stability of a blue phase, in agreement with experiments [Kikuchi et al., Nature Mater. 1, 64 (2002)].

Figure 1

(Color online) (a) Disclination profile of BP I in a cubic unit cell. Here we show the results of our numerical calculation with the temperature $\tau =-5$. The regions with the rescaled free-energy density $f/f_0$ larger than $-10.50$ are depicted. The largest and smallest values of $f/f_0$ in the system are $-6.51$ and $-11.94$, respectively. See text for the definitions of variables $\tau$ and $f/f_0$. (b) Schematic illustration of a double-twist cylinder. The director shows twist in all directions perpendicular to the vertical cylinder axis, in contrast to the $N^{\ast }$ phase whose twist is only along one direction (single twist).

Figure 2

(Color online) Phase diagram of the BP with a guest component of volume fraction $\varphi$. For reference, the boundary between BP I and Iso $\left(\tau \simeq 0.233\right)$ is also shown as a dotted line. Note that $\tau \simeq 1\times \left(T-T^{\ast }\right)$, where the temperatures $T$ and $T^{\ast }$ (at which isotropic phase loses its stability) are in kelvin.