Coarsening dynamics of biaxial nematic liquid crystals

We study the coarsening dynamics of two- and three-dimensional biaxial nematic liquid crystals, using Langevin dynamics. Unlike previous work, we use a model with no a priori relationship among the three elastic constants associated with director deformations. Biaxial nematics possess four topologically distinct classes of defects, three of which have half-integer charge, while the fourth, which plays a minor role in coarsening, is of integer charge. We find a rich variety of coarsening behavior, including the presence of one, two, or three of the half-integer classes at late times, depending on the relative values of the elastic constants and the resulting energetics of the decay channels of the defects. The morphology of the defect tangle in three dimensions when all three classes are present is particularly interesting. Rather than forming independent defect loops (as occurs when only one or two of the classes are present), the defect lines meet at junction points which are distributed uniformly throughout the system. As the system coarsens some pairs of neighboring junction points approach each other and annihilate, allowing the formation of nonintersecting loops each formed from a single defect class. These loops then shrink independently during the very final stages of the coarsening sequence.