Coexistence of Two Colloidal Crystals at the Nematic-Liquid-Crystal–Air Interface

Glycerol droplets at a nematic-liquid-crystal–air interface form two different lattices—hexagonal and dense quasihexagonal—which are separated by the energy barrier and can coexist. Director distortions around each droplet form an elastic dipole. The first order transition between the two lattices is driven by a reduction of the dipole-dipole repulsion through reorientation of these dipoles. The elastic-capillary attraction is essential for the both lattices. The effect has a many-body origin.

Figure 1

HL-to-DL transition: (a) experimental setup; (b) crossed-polarizer texture of coexisting HL and DL, inset: magnified texture of DL; (c) magnified texture (no analyzer) of DL and its scheme (d); elastic dipoles in HL (e) and DL (f). The dashed in-plane projection of the director line illustrates that tilt of $\mathbf{b}$ induces some tilt of this line on the upper NLC surface (at the meniscus).

Figure 2

DL-to-HL transition induced by the vertical electric field $E\sim {10}^4\mathrm{V}/\mathrm{m}$. Insets: polarizing microscopy textures of droplets in DL (a) and HL (b).

Figure 3

Time dependence of the center-to-center distance between two $3\mu \mathrm{m}$ droplets. The horizontal electric field, $E=8\times {10}^4\mathrm{V}/\mathrm{m}$, is turned on at $t=0$ to bring the droplets together and turned off at $t=37\mathrm{s}$, causing repulsion. Scale bar on first image is $3\mu \mathrm{m}$.

Figure 4

Equilibrium free energy (FE) of the lattice structure per single rhomb $BA{B}^{\prime }{A}^{\prime }$ vs distance $r$ for different ${\theta }_m$. $K=7\mathrm{pN}$, $h=30\mu \mathrm{m}$, $R=3\mu \mathrm{m}$, $W={10}^{-5}\mathrm{J}{\mathrm{m}}^{-2}$. Rightward the pick at $r_B=3.9$, $\theta =0$; minimum at $r\simeq 5$ corresponds to HL. Leftward the pick at $r_B=3.9$, $\theta ={\theta }_m$, the minima correspond to DL: 1. ${\theta }_m=0$ (the dot extension to $r<r_B$ shows the FE for $\theta =0$); 2. ${\theta }_m=0.55$ (appearance of the second minimum); 3. ${\theta }_m=0.75$ ($r_{\mathrm{DL}}=2.7$); 4. ${\theta }_m=0.83$ ($r_{\mathrm{DL}}=2.24$); 5. ${\theta }_m=0.855$ ($r_{\mathrm{DL}}=2.0$ for the first time); 6. ${\theta }_m=0.9$ ($r_{\mathrm{DL}}=2$). Inset: FE minimum $F\mathbf{(}{r}_{\mathrm{DL}}({\theta }_m),{\theta }_m,\xi \mathbf{)}$ vs anisotropy $\xi$ for the curves 3–6.