Topological Changes in Bipolar Nematic Droplets under Flow
Original Entry: Aaron Goldfain, AP 225, Fall 2012
Authors: A. Fernández-Nieves, D. R. Link, M. Márquez, and D. A. Weitz
Publication: A. Fernández-Nieves, D. R. Link, M. Márquez, and D. A. Weitz. Topological Changes in Bipolar Nematic Droplets under Flow. Phys. Rev. Lett. (2007) vol. 98 article 087801.
The Poincaré theorem asserts that drops of nematic liquid crystal must always have a topological surface charge of +2, but a variety of defect and director configurations satisfy this. This Letter describes a method to change the configuration of such drops. In short, the defects in nematic droplets that flow through a microfluidic device are shown to oscillate between two equilibrium configurations.
The director field within nematic liquid crystal drops is characterized by the boundary conditions on the surface of the drop. Typically, the molecules of the liquid crystal have normal or planar anchoring to the surface. Normal anchoring means the director field is perpendicular to the surface, and planar means it is parallel to the surface. The nematic drops considered in this Letter are subject to planar anchoring at the boundary, for which there are three main defect configurations, shown in Figure 1. The bipolar configuration has two splay, point disclinations on the droplet's surface, the concentric has a line disclination though the droplet, and the escaped concentric has two bend, point disclinations on the surface.
The liquid crystal used by the authors is 5CB, which has a bend elastic constant that is greater than the splay elastic constant. Therefore, splay disclinations are cost less energy than bend disclinations, and the bipolar configuration is more favorable than the escaped concentric configuration. Also, the line disclination in the concentric configuration is unstable, and tends to break into the third dimension forming two bend disclinations. Accordingly, concentric configurations are not typically observed because they quickly become escaped concentric.
Microfluidics are used to create nematic droplets surrounded by water with polyvinyl alcohol (PVA) added to the water to induce parallel boundary conditions on the droplets. The droplets then flow down a 10 by 100 μm channel where they are imaged between crossed polarizers. Flow around the drop induces two circular flows within the drop. Figure 2 shows a sequence of images of a nematic drop as it flows down the channel. The defects are splay when moving around the edge of the drop (2d, 2i), and bend when moving along the top and bottom of the drop (2f, 2g). Thus, the drop periodically changes being escaped concentric and bipolar. The authors also image the droplets with a birefringent plate, which enables them to quantitatively show when the defects are splay and bend.
If the flow is stopped, the droplets stay with the same defect type, and the defects relax to equilibrium at opposite sides of the drop. So, if the drop is escaped concentric when flow is stopped, it will not morph into the lower energy bipolar configuration, which is the state of all drops before flow is induced. This implies there is a significant energy barrier between the two states, and that the flow induced within the drop is enough to overcome the barrier.
The authors dismiss the claim that the PVA in the water could have become aligned by the flow, and this keeps the defects from rearranging in the escaped concentric configuration when flow is stopped. To test this, they heat the sample until the droplet is isotropic, then cool it and find that they always assume a bipolar configuration. Because of this, they claim an energy barrier associated with the director field, and not the PVA makes the escaped concentric phase stable. Additionally, they argue that since the drop is squished in a rectangular channel, it costs even more to rearrange the director field. The authors conclude by claiming that this is the only known method to create escaped concentric drops from with a liquid crystal that normally form bipolar drops.
This Letter describes a very interesting phenomenon, a novel application of microfluidics, and a different way to manipulate the director field of liquid crystals in a controlled manner. The beginning of the article also provides a good qualitative introduction to nematic liquid crystals and their defect structures.
However, as a whole I find the Letter somewhat lacking for a PRL publication. For example, there are no quantitative discussions (experimental or theoretical) of the energy associated with the different director configurations. Also, the quantitative strength of the energy barrier between configurations is not discussed or compared with the system's thermal energy. The velocity and associated energy with the flow induced within the droplets is not discussed either. Additionally, when testing if the stability of the escaped concentric drops could be due to PVA alignment, the authors do not consider the effects that an increased temperature or phase transition in the droplet would have on the PVA molecules surrounding the droplet. Finally, it would be interesting to see what happens to escaped concentric droplets that are in channel that doesn't squish them. Does moving the droplets into a bigger channel allow them to relax to the bipolar configuration?
 A. Fernández-Nieves, D. R. Link, M. Márquez, and D. A. Weitz. Topological Changes in Bipolar Nematic Droplets under Flow. Phys. Rev. Lett. (2007) vol. 98 article 087801.