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.     

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.