Modeling flows of confined nematic liquid crystals.

The flow of nematic liquid crystals in tightly confined systems was simulated using a molecular theory and an unsymmetric radial basis function collocation approach. When a nematic liquid crystal is subjected to a cavity flow, we find that moderate flows facilitate the relaxation of the system to the stable defect configuration observed in the absence of flow. Under more extreme flow conditions, e.g., an Ericksen number Er=20, flows can alter the steady-state defect structure observed in the cavity. The proposed numerical method was also used to examine defect annihilation in a thin liquid crystal film. The flows that arise from shear stresses within the system result in a higher velocity for s = +1∕2 defect than for the defect of opposing charge. This higher velocity can be attributed to reactive stresses within the deformed liquid crystal, which result in a net flow that favors the motion of one defect. These two examples serve to illustrate the usefulness of radial basis functions methods in the context of liquid crystal dynamics both at and beyond equilibrium.

Using localized surface plasmon resonances to probe the nanoscopic origins of adsorbate-driven ordering transitions of liquid crystals in contact with chemically functionalized gold nanodots.

We report that localized surface plasmon resonances (LSPRs) of gold nanodots immersed under liquid crystals (LCs) can be used to characterize adsorbate-induced ordering transitions of the LCs on the surfaces of the nanodots. The nanoscopic changes in ordering of the LCs, as measured by LSPR, were shown to give rise to macroscopic ordering transitions of the LCs that were observed by polarized light microscopy. The results reported herein suggest that (i) LCs may be useful for enhancing the sensitivity of LSPR-based detection of binding events and (ii) that LSPR measurements of gold nanodots provide a means to characterize the nanoscopic origins of macroscopic, adsorbate-induced LC ordering transitions.

Nanoparticles in nematic liquid crystals: interactions with nanochannels.

A mesoscale theory for the tensor order parameter Q is used to investigate the structures that arise when spherical nanoparticles are suspended in confined nematic liquid crystals (NLCs). The NLC is "sandwiched" between a wall and a small channel. The potential of mean force is determined between particles and the bottom of the channels or between several particles. Our results suggest that strong NLC-mediated interactions between the particles and the sidewalls of the channels, on the order of hundreds of k(B)T, arise when the colloids are inside the channels. The magnitude of the channel-particle interactions is dictated by a combination of two factors, namely, the type of defect structures that develop when a nanoparticle is inside a channel, and the degree of ordering of the nematic in the region between the colloid and the nanochannel. The channel-particle interactions become stronger as the nanoparticle diameter becomes commensurate with the nanochannel width. Nanochannel geometry also affects the channel-particle interactions. Among the different geometries considered, a cylindrical channel seems to provide the strongest interactions. Our calculations suggest that small variations in geometry, such as removing the sharp edges of the channels, can lead to important reductions in channel-particle interactions. Our calculations for systems of several nanoparticles indicate that linear arrays of colloids with Saturn ring defects, which for some physical conditions are not stable in a bulk system, can be stabilized inside the nanochannels. These results suggest that nanochannels and NLCs could be used to direct the assembly of nanoparticles into ordered arrays with unusual morphologies.

Anisotropic nanoparticles immersed in a nematic liquid crystal: defect structures and potentials of mean force.

We report results for the potential of mean force (PMF) and the defect structures that arise when spherocylindrical nanoparticles are immersed in a nematic liquid crystal. Using a dynamic field theory for the tensor order parameter Q of the liquid crystal, we analyzed configurations, including one, two, and three elongated particles, with strong homeotropic anchoring at their surfaces. For systems with one nanoparticle, the most stable configuration is achieved when the spherocylinder is placed with its long axis perpendicular to the far-field director, for which the defect structure consists of an elongated Saturn ring. For systems with two or three nanoparticles with their long axes placed perpendicular to the far-field director, at small separations the defect structures consist of incomplete Saturn rings fused with new disclination rings orthogonal to the original ones, in analogy to results previously observed for spherical nanoparticles. The shape of these orthogonal rings depends on the nanoparticles' configuration, i.e., triangular, linear, or parallel with respect to their long axis. A comparison of the PMFs indicates that the latter configuration is the most stable. The stability of the different arrays depends on whether orthogonal disclination rings form or not, their size, and the curvature effects in the interparticle regions. Our results suggest that the one-elastic-constant approximation is valid for the considered systems; similar results were obtained when a three-constant expression is used to represent the elastic free energy. The attractive interactions between the elongated particles were compared to those observed for spheres of similar diameters. Similar interparticle energies were observed for linear arrays; in contrast, parallel and triangular arrays of spherocylinders yielded interactions that were up to 3.4 times stronger than those observed for spherical particles.