Electrically induced structure transition in nematic liquid crystal droplets with conical boundary conditions

Polymer-dispersed liquid crystal composites have been a focus of study for a long time for their unique electro-optical properties and manufacturing by “bottom-up” techniques at large scales. In this paper, nematic liquid crystal oblate droplets with conical boundary conditions (CBCs) under the action of electric field were studied by computer simulations and polarized optical microscopy. Droplets with CBCs were shown to prefer an axial-bipolar structure, which combines a pair of boojums and circular disclinations on a surface. In contrast to droplets with degenerate planar boundary conditions (PBCs), hybridization of the two structure types in droplets with CBCs leads to a two-minima energy profile, resulting in an abrupt structure transition and bistable behavior of the system. The nature of the low-energy barrier in droplets with CBCs makes it highly sensitive to external stimuli, such as electric or magnetic fields, temperature, and light. In particular, the value of the electric field of the structure reorientation in droplets with CBCs was found to be a few times smaller than the one for droplets with PBCs, and the droplet state remained stable after switching off the voltage.

Figure 1

Director configurations in an equatorial cross section of nematic oblate droplets: (a) bipolar, (b) radial, (c) axial, and (d) axial-bipolar. The $XY$-coordinate plane coincides with the PDLC film plane here and below.

Figure 2

Droplet structures for ${\theta }_0={90}^{\circ }$ at (a) $e=0$, (b) $e=3.9$, (c) $e=5.9$, and (d) $e=7.8$. Hereafter, the director vectors are colored in correspondence with the direction (red along the $x$ axis, green along the $y$ axis, and blue along the $z$ axis). (e) Dependencies of the free energy $F_{\text{total}}$, the order parameter $Q_{zz}$, and the bipolar axis tilt angle $\alpha$ on the dimensionless electric field $e$. The continuous structural transformation at $e^{*}\approx 5.7$ is marked with a red dashed line.

Figure 3

Droplet structures for ${\theta }_0={40}^{\circ }$ at (a) $e=0$, (b) $e=1.7$, (c) $e=1.8$, and (d) $e=3.9$. Disclination is shown with a thick red line. (e) Dependencies of the free energy $F_{\text{total}}$, the order parameter $Q_{zz}$, and the bipolar axis tilt angle $\alpha$ on the dimensionless electric field $e$. The discontinuous structural transformation at $e_c\approx 1.75$ is marked with a red dashed line.

Figure 4

Polarized optical microscopy images of LC droplet: without the analyzer, made when the polarizer is perpendicular (first row) and parallel (second row) to the bipolar axis; in the crossed polarizers, when the polarizer is parallel (third row) and at a ${45}^{\circ }$ angle (fourth row) to the bipolar axis. (a) Initial state $E=0$; (b) at $E=72\text{mV}/\mu \text{m}$; (c) at $E=80\text{mV}/\mu \text{m}$; (d) in 5 h after switching off. The droplet size in the film plane is $13\mu \text{m}$. The polarizer directions are indicated by the double arrows. The schemes of the director lines and topological defects in the cross section parallel to the film plane are presented for the voltage (e) below and (f) above the threshold value.

Figure 5

Dependency of the dimensionless total free energy ($F_{\text{total}}$) of the droplet with ${\theta }_0={40}^{\circ }$ on the bipolar axis tilt angle $\alpha$ at no electric field ($e=0$) and above the structural transformation ($e=1.95$). Dashed lines show the value of $F_{\text{total}}$ at $\alpha =0$.