Liquid Crystal Bridges

Perry Ellis, Susannah Doss, Jaya Vallamkondu, Edward Danemiller, Mark Vernon and Alberto Fernandez-Nieves

### Introduction

Nematic liquid crystals (NLC) are birefringent rod-like molecules that prefer to align with their long axis roughly parallel. We use the director n to describe the local average orientation of a group of molecules, as seen schematically in Figure 1A. Under confinement, the liquid crystal can have defects; these are places where the director is undefined. This can be seen in Figure 1B for two possible nematic configurations in 3D, the radial hedgehog and the hyperbolic hedgehog.

Fig. 1: (A), schematic demonstrating the director as a local average of the orientation of the NLC molecules. (B), two possible director configurations for a 3D hedgehog defect. (C), schematic of a waist structure. Note how the angle $$\theta$$ is less than 90 degrees and the two radii of curvature fall on opposite sides of the surface. (D), schematic of a barrel structure. Note how the angle $$\theta$$ is greater than 90 degrees and the two radii of curvature fall on same side of the surface.

In this work, we examine the role of curvature on the director configuration by looking at NLC confined to either a waist or a barrel. These shapes are seen schematically in Figure 1C,D. Note how the two radii of curvature for a barrel both originate inside the barrel while $$R_2$$ for the waist lies outside the waist. This means that the product of the two principal curvatures, the Gaussian curvature $$K = \frac{1}{R_1}\frac{1}{R_2}$$, is negative for a waist but positive for a barrel. When we confine the NLC to a bridge, we force the director to be perpendicular to the boundary; this is referred to as homeotopic boundary conditions. This means that regardless of the curvature of the bridge, there will be a defect in the bulk. Since our setup allows us to move between waists and barrels with different shape, we can explore the role of the sign and magnitude of the Gaussian curvature on the type of defect(radial, hyperbolic, etc.) found in the bulk.

### The Experiment

We create the NLC bridges by sandwiching a NLC droplet between two microscope slides. One of the slides is fixed and the other is connected to a micromanipulartor; this allows us to adjust the distance between the slides, H, to change the shape of the bridge. Depending on the setup, we can either observe the bridge from the side or from the top. These setups can be seen schematically in Figure 2A,B.

Fig. 2: (A), schemtic of the experimental setup used to observe a NLC bridge from the side. (B), schemtic of the experimental setup used to observe a NLC bridge from the top. (C), bright-field image of a liquid bridge with a waist structure viewed from the side with the bridge dimensions illustrated schematically. (D), bright-field images of a liquid bridge with a waist structure viewed from the top. The images show the two different defect structures we observe in NLC bridges. (E), bright-field image of a liquid bridge with a barrel structure viewed from the side with the bridge dimensions illustrated schematically. (F), bright-field images of a liquid bridge with a barrel structure viewed from the top. The images show the two different defect structures we observe in NLC bridges.

### Brief Results

We use the side view to characterize the shape of the bridge, as seen in the bright-field images of a waist and barrel in Figure 2C,E respectively. However, we must use the top view to characterize the defect type, as see in the bright field images in Figure 2D,F. Depending on the height, H, and diameter, D, of the bridge, as defined schematically in Figure 2C,E, we observe a transition between a ring defect structure and a point defect structure in both waists and barrels. The defect structures and transition paths are illustrated schematically from the side in Figure 3.

Fig. 3: Schematics of the defect structures and transtion paths for a waist and a barrel. The director schematics are drawn as a cross-section viewwed from the side.

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 30332-0430, USA
Phone: 404-385-3667 Fax: 404-894-9958
alberto.fernandez [at] physics.gatech.edu