Phase-field model of topological charge interaction force in nematic liquid crystals

Nematic liquid crystals (LCs) normally contain both integer and half-integer topological charges. In this work, we investigate topological charge evolution dynamics in nematic LCs by the phase-field model. We observe the annihilation of the topological charge, and the total number of charges decreases to two cores with time evolution in a disk. A significant decrease in charges is observed during the initial evolution. The positive topological charge and negative topological charge annihilate depending on the distance between two charges, which can be treated as the interaction force. The form of interaction force is similar to Coulomb’s law, but the force is inversely the distance of defects instead of the square of the distance in Coulomb’s law. Therefore, the present study contributes to the understanding of topological charge evolution dynamics and provides guidance for experiments to design in nematic LCs.