Structural forces in liquid crystalline blue phases

We show numerically that the interaction potential or force mediated by a liquid crystalline blue phase (BP) between two parallel plates exhibits oscillatory behavior with variation of the interplate distance, when the parallel plates impose strong normal anchoring. Its periodicity is approximately half of the unit-cell dimension of the bulk BP. The interaction arises from the deformation of the confined BP structure around the midplane of the system. The oscillatory interaction can be regarded as a clear manifestation of the BP ordering, because the cholesteric helical alignment adopted by a chiral liquid crystal cannot yield an oscillatory interaction.

Figure 1

(a)–(d) Profiles of disclination lines for $l/p=1.671$, 2.149, $2.626$ and $3.104$, respectively. (e) Disclination lines of a double-helix form for $l/p=1.194$. (f) Undulating disclinations for $l/p=1.273$. (g) Uniform-lying helix of orientational order for $l/p=1.194$. Disclination lines are represented by isosurfaces of $Q_{ij}{Q}_{ij}=0.6$. In (g), local orientational order is described by cylinders, and a helical twist along the horizontal axis can be seen.

Figure 2

(a) The free energy per unit area $\mathcal{F}$ as a function of the rescaled system thickness $l/p$. The legends (a)–(g) are those given in Fig. 1. (b) Plot of the elastic modulus $b^{-1}$ vs the optimum system thickness $l_0$ for the structures in Figs. 1a, 1b, 1c, 1d.