Disclination loops, standing alone and around solid particles, in nematic liquid crystals

A suspended particle with specific director anchoring on its surface introduces a complex distortion field in a nematic liquid crystal matrix. Topological defects—disclination loops, boojums, and hedgehogs, are needed to match the director near the particle surface with that at the far distance, which is determined by boundary conditions on the sample. This paper analyzes the elastic energy and stability of a singular loop of wedge disclination and the first-order transition of the radial hedgehog into a wide singular loop, driven by an external magnetic field. The far field of distortions, created by a ‘‘Saturn ring’’ of disclination around the spherical radial particle, allows one to calculate the potential of interaction between such particles and with the surface of the liquid crystal. Particles are repelled from each other and from the rigidly anchored surface with the potential U∼1/${\mathit{r}}^3$. If the sample surface has soft anchoring, the particle is attracted to it at close distances and is repelled, if beyond the anchoring coherence length ${\xi }_{\mathit{w}}$. Several experiments to test these conclusions are suggested.