Liquid crystal boojum-colloids

Abstract

Colloidal particles dispersed in a liquid crystal (LC) lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic behaviour is well understood. The short-distance behaviour depends on the structure and dynamics of the topological defects nucleated near the colloidal particles and a full nonlinear theory is required to describe it. Spherical colloidal particles with strong planar degenerate anchoring nucleate a pair of antipodal surface topological defects, known as boojums. We use the Landau–de Gennes theory to resolve the mesoscopic structure of the boojum cores and to determine the pairwise colloidal interactions. We compare the results in three (3D) and two (2D) spatial dimensions for spherical and disc-like colloidal particles, respectively. The corresponding free energy functionals are minimized numerically using finite elements with adaptive meshes. Boojums are always point-like in 2D, but acquire a rather complex structure in 3D, which depends on the combination of the anchoring potential, the radius of the colloid, the temperature and the LC elastic anisotropy. We identify three types of defect cores in 3D that we call single, double and split-core boojums, and investigate the associated structural transitions. The split-core structure is favoured by low temperatures, strong anchoring and small twist to splay or bend ratios. For sufficiently strong anchoring potentials characterized by a well-defined uniaxial minimum, the split-core boojums are the only stable configuration. In the presence of two colloidal particles, we observe substantial re-arrangements of the inner defects in both 3D and 2D. These re-arrangements lead to qualitative changes in the force-distance profile when compared to the asymptotic quadrupole–quadrupole interaction. In line with the experimental results, the presence of the defects prevents coalescence of the colloidal particles in 2D, but not in 3D systems.