This Letter investigates the defect structures that arise between two colloidal spheres immersed in a nematic liquid crystal. Molecular simulations and a dynamic field theory are employed to arrive at molecular-level and mesoscopic descriptions of the systems of interest. At large separations, each sphere is surrounded by a Saturn ring defect. However, at short separations both theory and simulation predict that a third disclination ring appears in between the spheres, in a plane normal to the Saturn rings. This feature gives rise to an effective binding of the particles. The structures predicted by field theory and molecular simulations are consistent with each other.

Monte Carlo simulations and dynamic field theory ͑DyFT͒ are used to study the interactions between dilute spherical particles, dispersed in nematic and isotropic phases of a liquid crystal. A recently developed simulation method ͑expanded ensemble density of states͒ was used to determine the potential of mean force ͑PMF͒ between the two spheres as a function of their separation and size. The PMF was also calculated by a dynamic field theory that describes the evolution of the local tensor order parameter. Both methods reveal an overall attraction between the colloids in the nematic phase; in the isotropic phase, the overall attraction between the colloids is much weaker, whereas the repulsion at short range is stronger. In addition, both methods predict a new topology of the disclination lines, which arises when the particles approach each other. The theory is found to describe the results of simulations remarkably well, down to length scales comparable to the size of the molecules. At separations corresponding to the width of individual molecular layers on the particles' surface, the two methods yield different defect structures. We attribute this difference to the neglect of density inhomogeneities in the DyFT. We also investigate the effects of the size of spherical colloids on their interactions.

Monte Carlo simulations and dynamic field theory are used to study spherical particles suspended in a nematic liquid crystal. Within these two approaches, we investigate the binding of the defects to the particles, the adsorption of a particle at a solid surface, and two particles interacting with each other. Quantitative comparisons indicate good agreement between the two approaches. A Monte Carlo method based on the combination of canonical expanded ensemble simulations with a density-of-state formalism is used to determine the potential of mean force between one particle and a hard wall. On the other hand, the potential of mean force is evaluated using a dynamic field theory, where the time-dependent evolution of the second rank tensor includes two major aspects of liquid crystalline materials, namely the excluded volume and the long-range order elasticity. The results indicate an effective repulsive force that acts between the particle and the wall. Layer formation at the surface of the hard wall gives rise to local minima in the potential of mean force. The director profile for a particle at contact with a solid surface is characterized by a disclination line distorted and attracted towards the wall. The structure of the nematic for two particles at short distances is also investigated. Our results indicate a structure where the two particles are separated by a circular disclination line. The potential of mean force associated with this configuration indicates an effective attractive interaction between the two particles.

Insertion of spherical particles into a uniform nematic liquid crystal gives rise to the formation of topological defects. In the present work, we investigate how a spherical particle accompanied by its topological defects interacts with neighboring disclination lines. We perform two- and three-dimensional dynamic simulations to analyze the effect of a particle on the annihilation process of two disclination lines. The dynamics of the liquid crystal is described by a time-dependent evolution equation on the symmetric traceless order parameter that includes some of the salient features of liquid crystalline materials: excluded volume effects, or equivalently, short-range order elasticity and long-range order elasticity. At the surface of the particle, the liquid crystal is assumed to exhibit strong homeotropic anchoring. The particle is located between two disclination lines of topological charges +1/2 and -1/2. Two-dimensional simulations indicate that the topological defects bound to the particle mediate an interaction between the two disclination lines which increases the attraction between them. This result is confirmed by three-dimensional simulations that provide a complete description of the director field and of the order parameter around the particle. These simulations indicate that a spherical particle between two disclination lines can be surrounded by a Saturn ring, and suggest that the dynamic behavior of disclination lines could be used to report the structure of a defect around the particle.

We use a self-consistent Ornstein-Zernike approximation to study the Blume-