Frustrated nematic order in spherical geometries

Abstract

The prospect of mimicking molecular chemistry with colloidal rather than molecular building blocks could enable unprecedented control over the properties of microstructured materials 1 . The usual absence of directionality to the interaction between colloids has limited the complexity of the structures they can spontaneously form. One way to address this is to coat spherical colloid particles with a thin layer of nematic liquid crystal 2 and functionalize 3 the unavoidable defects or bold spots that arise when nematic order is established on the surface of a sphere 4,5 . The number and arrangement of these defects can vary 2,6-16 , providing flexibility for tuning directional interactions that are more difficult to achieve by other methods [17][18][19][20][21][22][23][24][25][26] . Yet, many theoretically predicted structures have not been observed and control over defect location remains elusive. In this work, we show that varying the thickness of a nematic liquid crystal shell enables us to systematically control the number and orientation of defects formed. For thin shells, these defects can be engineered to emulate the linear, trigonal and tetrahedral geometries of sp, sp 2 and sp 3 carbon bonds, respectively. Such control opens up the possibility to engineer particles with tunable-valence and directional-binding capabilities.To fabricate spherical nematic shells, we generate double emulsions with a microcapillary device 27 ; these consist of a nematic drop that contains a smaller aqueous drop, all inside an aqueous continuous phase. Both the inner and outer water phases contain 1 wt% polyvinyl alcohol, which stabilizes the emulsion against coalescence and enforces tangential anchoring of the rod-like molecules of the nematic liquid crystal, pentylcyanobiphenyl. The resulting double-emulsion drops are characterized by an outer radius, R, of around 50 µm and an inner radius, a, that are varied to produce shells of different average thicknesses,h = R − a, as schematically shown in Fig. 1a. With this microfluidic method the thinnest shells that we can generate haveh ≈ 1 µm. However, it is possible to significantly reduce this value by increasing the volume of the inner drop once the double emulsion is formed. We achieve this by inducing a difference in osmotic pressure between the inner and outer water phases through the addition of a salt, CaCl 2 . As pentylcyanobiphenyl has a finite permeability to water, an incoming flow of water from the outer phase can be established if the inner drop contains a higher salt concentration than the outer phase. By controlling this difference, we can control the kinetics of the process and ultimately the thickness of the shells.The thinnest shells have four defects, each with a topological charge s = 1/2, reflecting the π rotation experienced by the local nematic direction along a path encircling each defect. As a result, the total topological charge on the sphere is equal to 4 × 1/2 = 2; this is consistent with a mathematical theorem due to Poincaré and Hopf, which establish...

One-piece micropumps from liquid crystalline core-shell particles

“…They could thus be manufactured at moderate temperatures in a surrounding aqueous medium [31][32][33][34] . With an isotropization temperature of 80 1C, the reactive monomer mixture used in this study needs to be processed at elevated temperatures and requires a customized heat-resistant microfluidic device 30 .…”

Geometry of thresholdless active flow in nematic microfluidics

“…In this section we will show that, in general, a shell with nonvanishing Gaussian curvature G generates a nonvanishing active force f a . To prove this result, we first assume that, if the shell is very thin, the component ofn perpendicular to the surface is negligible everywhere inside the shell [34][35][36], i.e., planar anchoring conditions. In this case, we can decompose the active force f a (x) at position x along three orthogonal directions: (i) the local surface normalN, (ii) the nematic directorn, and (iii) the tangent vectort perpendicular to bothN andn, shown in Fig.…”

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment

“…In the more recent past, microfluidics was starting to be used as a tool to generate liquid crystal droplets [30][31][32], to study their wonderful properties [33][34][35][36], and to investigate confinement and motion of topological defects [37][38][39][40], and potential applications [41]. However, the possibility to use the available microfluidic techniques for studying the fundamental behaviour of liquid crystal flows within minute confinements was never explored.…”

“…The investigations hitherto cover a wide range of homeotropic confinements: LC cells [178,[184][185][186], capillaries [99,[187][188][189], droplets [36,190], micro-cavities [125,191], and porous networks [192,193]. In spite of the practical relevance of confinements with rectangular cross-sections, especially microchannels, the resulting equilibrium of the nematic director has not been experimentally analyzed yet.…”