Dispersions of ellipsoidal particles in a nematic liquid crystal

Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitative experiments, reveal novel LC configurations with peculiar topological properties around the ellipsoids, depending on their aspect ratio and the boundary conditions imposed on the nematic order parameter. The latter also determine the preferred orientation of ellipsoids in the nematic field, because of elastic torques, as well as the morphology of particles aggregates.Comment: 31 pages, 11 figure

Nonlinear nonequilibrium dynamics in a nematic liquid crystal.

Liquid crystals are elongated molecules with a rich and surprising phase behavior. Nonequilibrium conditions open a myriad possibilities of manipulating matter, and reach collective states not accessible under equilibrium conditions. We perform nonequilibrium molecular dynamics simulations of a nematic liquid crystal flowing around a colloidal particle. Because of a mismatch between the nematic far field alignment and the local orientation of the liquid-crystal molecules at the surface of the colloid, defect topologies arise if the host is in thermodynamic equilibrium. We study the flow-induced modications of these topological defects. We find that Saturn ring defects are convected downstream along the flow direction, which is in agreement with experimental observations [1]. As Poiseuille flow is initiated, the Saturn ring is deformed. The degree of deformation is analyzed quantitatively in terms of characteristic geometric parameters fitted to suitable projections of the Saturn ring. Our results suggest that smaller Saturn rings are shifted downstream while approximately maintaining their circular shape, whereas larger ones exhibit an elastic deformation in addition. Additionally, we show that flow distorts Boojum defects into an asymmetrically larger downstream lobe. For a Janus colloid, exhibiting a Boojum defect and a Saturn ring defect, we find that the Boojum defect facing the upstream direction is destroyed and the Saturn ring is convected downstream. Furthermore, we study a similar system of a nematic liquid crystal flowing around a cylindrical pillar. We report flow-induced cavitation in an anisotropic fluid. Cavitation domains nucleate due to a sudden drop in pressure upon flow past the cylindrical obstacle. The inception and growth of cavitation domains ensue in the laminar flow regime. We study the physical principles governing the cavitation phenomena in nematic liquid crystals, and identify a critical value of the Reynolds number for cavitation inception that scales inversely with the characteristic order parameter of the nematic liquid crystal. Strikingly, the critical Reynolds number can be as low as about 50% of the cavitation threshold in the isotropic liquid crystal. These findings suggest that long range ordering, and its tunability, can be potentially applied as a novel control parameter to modulate cavitation inception in anisotropic fluids. Additionally, we find very good agreement with earlier micro fluidic experiments [2] at smaller flow speeds before cavitation initiates. Our simulations are able to reproduce the structural changes within the micro fluidic channel at different flow speeds

Computer Simulations of Faceted Nanoparticles and Carbon Nanotubes in Liquid Crystals

The purpose of this research is to investigate the use of liquid crystals (LCs) to manipulate and organize faceted nanoparticles and carbon nanotubes (CNTs). Computer simulations at different levels of detail are used to study these systems. Results from this project will be relevant for potential applications of these systems in displays, nanoscale electronics, electro-optical switches, and in the development of composites with unique mechanical, thermal and/or electronic properties. In this research, two independent but directly related projects were carried out. In the first part of the research, we investigated the torque that develops when faceted nanoparticles, namely cubes and triangular prisms, are immersed in a nematic LC. We used a mesoscale theory in terms of the tensor order parameter Q(r) to model the nematic. Homeotropic anchoring condition of the NLC is imposed on the surfaces of faceted nanoparticles. Our results indicate that, when the particle is oriented at an out-of-plane orientation (i.e. unstable configuration), it moves away immediately from that state and then slowly orients itself back to the stable configuration (i.e. in-plane orientation). The magnitude of the out-of-plane torques is similar to that of in-plane torques. In case of an isolated nanoprism system, the torque reaches maximum when the particle orients with one of its rectangular sides parallel to the far field director n(r). In contrast, the torque of an isolated nanocube system reaches maximum when the particle orients with its four lateral faces parallel to the far field director n(r). In the second part of our research, we investigated the effect of varying the molecular structure and the phase of the LC on the CNTs interactions by performing MD simulations. Our results suggest that increasing the chain length of the hydrophobic tail of the nCB LC molecule decreases the tendency of aggregation for CNTs in nCB LCs. Additionally, varying the phase of the nCB LC is insufficient to decrease the tendency of aggregation for CNTs

Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom

We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of the model and the associated closed set of equations of state involving four order parameters, proving the integrability and exact solvability of the model. The equations of state are specified via a suitable representation of the orientational order parameters, which imply two-order parameter reductions in the absence of external fields. A detailed exact analysis of the equations of state reveal a rich phase diagram where isotropic versus uniaxial versus biaxial phase transitions are explicitly described, including the existence of triple and tricritical points. Results on the discrete models are qualitatively consistent with their continuum analog. This observation suggests that, in more general settings, discrete models may be used to capture and describe phenomena that also occur in the continuum for which exact equations of state in closed form are not available.Comment: 27 pages, 5 figure

Computer simulations of liquid crystals

Molecular simulations performed on modern computers provide a powerful tool for the investigation of both static and dynamic properties of liquid crystals. In this thesis several properties of liquid crystal mesogens have been investigated using state-of-the-art Monte Carlo (MC) and molecular dynamics (MD) simulation techniques. The helical twisting power, βm, determines the pitch of the chiral nematic phase produced when a nematic liquid crystal is doped with a low concentration of chiral solute molecules. A new simulation technique that allows the prediction of both the sign and the magnitude of βm is described. The method employs fully atomistic MC simulations of a chiral dopant molecule in the presence of a twisted nematic solvent composed of Gay-Berne particles. Eighteen different chiral dopant molecules were examined and in all cases the results were in good agreement with existing experimental data. The Kirkwood correlation factor, g(_1), has been evaluated for the molecules PCH5, PCH5-C1, me5NF and GGP5C1 using MD simulations in the pre-transitional region of the isotropic phase. The calculations employed an all-atom force field, which was developed specifically for liquid crystal molecules. PCH5 and meSNF were seen to favour anti-parallel dipole alignment whereas, PCH5-C1 and GGP5C1 preferred a parallel arrangement of the molecular dipoles. With the exception of GGP5C1, the simulations gave g(_1) values that were in accordance with existing experimental dielectric measurements. Detailed analysis of the MD trajectories showed that certain molecular pair configurations were preferred in the bulk and indicated which molecular groups were responsible for the stabilization of these configurations. Equilibrium molecular dynamics simulations were carried out in order to evaluate the rotational viscosity coefficient, γ(_1), for a Gay-Berne mesogen using two independent analysis techniques. The methods gave consistent results, which were comparable to experimental data for real mesogens of similar shape and size

Role of surface-like elastic constants in the phenomenology of confined nematics

Confined nematics are a natural setting to study aspects relating to phenomenology of symmetry breaking, evolution and dynamics of topological defects. In this study we highlight the interplay of the surface-like elastic constants with the phenomenology mentioned above. We exploit nematics confined to cylinders to study a spontaneous reflection symmetry breaking phase transition. The role of saddle-splay elasticity in driving this transition is described in detail. We also confine nematics to rectangular geometries which reveal novel director and defect configurations. We uncover surprising aspects regarding the scaling of surface-like elastic constants by studying morphological transitions of spherical nematic droplets. We exploit a monodomain- like configuration and the director arrangement in tactoids to shed light on the physics governing the nematic- biphasic transition of lyotropic chromonic liquid crystals. We also confine nematics to toroidal geometries with radial anchoring to delineate the coupling of geometry with the director configuration. Finally, the role of differential polarizability is demonstrated in the accurate determination of order parameters of liquid crystals.Ph.D