Tyler F. Roberts

Nanoparticle self-assembly at the interface of liquid crystal droplets

Significance Controlled assembly of nanoparticles at liquid crystal interfaces could lead to easily manufacturable building blocks for assembly of materials with tunable mechanical, optical, and electronic properties. Past work has examined nanoparticle assembly at planar liquid crystal interfaces. In this work, we show that nanoparticle assembly on curved interfaces is drastically different and arises for conditions under which assembly is too weak to occur on planar interfaces. We also demonstrate that liquid crystal-mediated nanoparticle interactions are strong, are remarkably sensitive to surface anchoring, and lead to hexagonal arrangements that do not arise in bulk systems. All of these elements form the basis for a highly tunable, predictable, and versatile platform for hierarchical materials assembly. Nanoparticles adsorbed at the interface of nematic liquid crystals are known to form ordered structures whose morphology depends on the orientation of the underlying nematic field. The origin of such structures is believed to result from an interplay between the liquid crystal orientation at the particles’ surface, the orientation at the liquid crystal’s air interface, and the bulk elasticity of the underlying liquid crystal. In this work, we consider nanoparticle assembly at the interface of nematic droplets. We present a systematic study of the free energy of nanoparticle-laden droplets in terms of experiments and a Landau–de Gennes formalism. The results of that study indicate that, even for conditions under which particles interact only weakly at flat interfaces, particles aggregate at the poles of bipolar droplets and assemble into robust, quantized arrangements that can be mapped onto hexagonal lattices. The contributions of elasticity and interfacial energy corresponding to different arrangements are used to explain the resulting morphologies, and the predictions of the model are shown to be consistent with experimental observations. The findings presented here suggest that particle-laden liquid crystal droplets could provide a unique and versatile route toward building blocks for hierarchical materials assembly.

Liquid Crystal Mediated Interactions Between Nanoparticles in a Nematic Phase

A continuum theory is used to study the interactions between nanoparticles suspended in nematic liquid crystals. The free energy functional that describes the system is minimized using an Euler-Lagrange approach and an unsymmetric radial basis function method. It is shown that nanoparticle liquid-crystal mediated interactions can be controlled over a large range of magnitudes through changes of the anchoring energy and the particle diameter. The results presented in this work serve to reconcile past discrepancies between theoretical predictions and experimental observations, and suggest intriguing possibilities for directed nanoparticle self-assembly in liquid crystalline media.

Structural Transitions in Cholesteric Liquid Crystal Droplets

Confinement of cholesteric liquid crystals (ChLC) into droplets leads to a delicate interplay between elasticity, chirality, and surface energy. In this work, we rely on a combination of theory and experiments to understand the rich morphological behavior that arises from that balance. More specifically, a systematic study of micrometer-sized ChLC droplets is presented as a function of chirality and surface energy (or anchoring). With increasing chirality, a continuous transition is observed from a twisted bipolar structure to a radial spherical structure, all within a narrow range of chirality. During such a transition, a bent structure is predicted by simulations and confirmed by experimental observations. Simulations are also able to capture the dynamics of the quenching process observed in experiments. Consistent with published work, it is found that nanoparticles are attracted to defect regions on the surface of the droplets. For weak anchoring conditions at the nanoparticle surface, ChLC droplets adopt a morphology similar to that of the equilibrium helical phase observed for ChLCs in the bulk. As the anchoring strength increases, a planar bipolar structure arises, followed by a morphological transition to a bent structure. The influence of chirality and surface interactions are discussed in the context of the potential use of ChLC droplets as stimuli-responsive materials for reporting molecular adsorbates.

Lattice Boltzmann simulation of asymmetric flow in nematic liquid crystals with finite anchoring

Liquid crystals (LCs) display many of the flow characteristics of liquids but exhibit long range orientational order. In the nematic phase, the coupling of structure and flow leads to complex hydrodynamic effects that remain to be fully elucidated. Here, we consider the hydrodynamics of a nematic LC in a hybrid cell, where opposite walls have conflicting anchoring boundary conditions, and we employ a 3D lattice Boltzmann method to simulate the time-dependent flow patterns that can arise. Due to the symmetry breaking of the director field within the hybrid cell, we observe that at low to moderate shear rates, the volumetric flow rate under Couette and Poiseuille flows is different for opposite flow directions. At high shear rates, the director field may undergo a topological transition which leads to symmetric flows. By applying an oscillatory pressure gradient to the channel, a net volumetric flow rate is found to depend on the magnitude and frequency of the oscillation, as well as the anchoring strength. Taken together, our findings suggest several intriguing new applications for LCs in microfluidic devices.

Isotropic-nematic phase transition in the Lebwohl-Lasher model from density of states simulations.

Density of states Monte Carlo simulations have been performed to study the isotropic-nematic (IN) transition of the Lebwohl-Lasher model for liquid crystals. The IN transition temperature was calculated as a function of system size using expanded ensemble density of states simulations with histogram reweighting. The IN temperature for infinite system size was obtained by extrapolation of three independent measures. A subsequent analysis of the kinetics in the model showed that the transition occurs via spinodal decomposition through aggregation of clusters of liquid crystal molecules.

Liquid-crystal mediated nanoparticle interactions and gel formation

Colloidal particles embedded within nematic liquid crystals exhibit strong anisotropic interactions arising from preferential orientation of nematogens near the particle surface. Such interactions are conducive to forming branched, gel-like aggregates. Anchoring effects also induce interactions between colloids dispersed in the isotropic liquid phase, through the interactions of the pre-nematic wetting layers. Here we utilize computer simulation using coarse-grained mesogens to perform a molecular-level calculation of the potential of mean force between two embedded nanoparticles as a function of anchoring for a set of solvent conditions straddling the isotropic-nematic transition. We observe that strong, nontrivial interactions can be induced between particles dispersed in mesogenic solvent, and explore how such interactions might be utilized to induce a gel state in the isotropic and nematic phases.

Erratum: “Liquid-crystal mediated nanoparticle interactions and gel formation” [J. Chem. Phys. 138, 194903 (2013)]

Our manuscript contained several typographical errors within equations, and two within the Discussion section. This document serves to correct these issues so that our simulation conditions may be identically replicated by all readers.