Mixtures of Blue Phase Liquid Crystal with Simple Liquids: Elastic Emulsions and Cubic Fluid Cylinders

We numerically investigate the behavior of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, $\chi$, setting the balance between interfacial and elastic forces. When $\chi$ and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a cubic array of fluid cylinders. For larger $\chi$, the isotropic phase arranges primarily into liquid emulsion droplets which coarsen very slowly, rewiring the blue phase disclination lines into an amorphous elastic network. Our blue phase-simple fluid composites can be externally manipulated: an electric field can trigger a morphological transition between cubic fluid cylinder phases with different topologies.

Figure 1

Formation of a cubic fluid cylinder phase. (a) BPI disclination network (blue ribbons). (b) In a $90:10$ BP:isotropic mixture with low $\sigma$ ($\chi \equiv \sigma \xi /K\approx 0.019$), the isotropic fluid self-organizes to form tubes following the cubic symmetry of the BPI disclination network. (c) The free energy of the system as a function of time $t$ (simulations performed using parameter set $A$ [22]).

Figure 2

Dynamics of BP mixtures with different values of $\chi$ and LC:isotropic composition. (a)–(e) Dynamics of a low interfacial tension system ($\chi \approx 0.019$), with $85:15$ composition, starting from an initially mixed state. Snapshots correspond to: (a) $t=2\times {10}^5$ (simulation steps); (b) $t=7\times {10}^5$, (c) $t=1\times {10}^6$, (d) $t=2.5\times {10}^6$, (e) $t=9.6\times {10}^6$. (Simulations performed using parameter set $B$ [22].) (f)–(j) Dynamics of an $80:20$ BP mixture with higher interfacial tension ($\chi \approx 1.9$). Snapshots correspond to: (f) $t=1.8\times {10}^6$, (g) $t=2.1\times {10}^6$, (h) $t=2.2\times {10}^6$, (j) $t=6.4\times {10}^6$. (Simulations performed using parameter set $C$ [22]).

Figure 3

Time evolution of the domain length scale $L(t)$ for different values of $\chi$ and emulsion compositions.

Figure 4

Dynamics of a $90:10$ mixture of low $\sigma$ ($\chi \approx 0.019$) in a strong electric field along the $z$ axis (into the page). The strength of the field is quantified by the dimensionless quantity $e=\sqrt{27{\epsilon }_a{E}^2/(32\pi A_0\gamma )}$: in our case, $e\approx 0.24$ (given the mapping in [24], this may be realized with $E\sim 25\mathrm{V}/\mu \mathrm{m}$ for a LC with ${\epsilon }_a\sim 1.8\times {10}^{-10}\mathrm{F}/\mathrm{m}$). (a) Snapshot of the starting configuration at $t=0$ (no field). When the field is on, the isotropic fluid (red) follows the rapidly reorganizing defect network (blue). (b), (c) Snapshots corresponding to $t=5\times {10}^4$ (b), and to $t=2\times {10}^5$ (c). (d) Plot of the domain length scale $L(t)/\lambda$ as a function of time. (Simulations performed using parameter set $D$ [22]).