Quadrupolar particles in a nematic liquid crystal: effects of particle size and shape.

We investigate the effects of particle size and shape on the quadrupolar (Saturn-ring-like) defect structures formed by a nematic liquid crystal around nm-sized and mum -sized particles with spherical and spherocylindrical shapes. We also report results for the potentials of mean force in our systems, calculated using a mesoscale theory for the tensor order parameter Q of the nematic. Our results indicate that for pairs of nm-sized particles in close proximity, the nematic forms "entangled hyperbolic" defect structures regardless of the shape of the nanoparticles. In our calculations with nanoparticles we did not observe any other entangled or unentangled defect structures, in contrast to what was reported for pairs of mum -sized spherical particles. Such a finding suggests that the "entangled hyperbolic" defect structures are the most stable for pairs of nanoparticles in close proximity. For pairs of mum -sized particles, our results indicate that the nematic forms entangled "figure-of-eight" defect structures around pairs of spheres and spherocylinders. Our results suggest that the transition between "entangled hyperbolic" and figure-of-eight defect structures takes place when the diameter of the particle is between D=100 nm and 1 microm . We have also calculated the torques that develop when pairs of spherocylindrical nanoparticles in a nematic approach each other. Our calculations suggest that the nematic-mediated interactions between the nm-sized particles are fairly strong, up to 5700 k{B}T for the case of pairs of spherocylindrical nanoparticles arranged with their long axis parallel to each other. Furthermore, these interactions can make the particles to bind together at specific locations, and thus could be used to assemble the particles into ordered structures with different morphologies.