Theoretical predictions of disclination loop growth for nematic liquid crystals under capillary confinement

The combination of low elasticity modulus, anisotropy, and responsiveness to external fields drives the rich variety of experimentally observed pattern formation in nematic liquid crystals under capillary confinement. External fields of interest in technology and fundamental physics are flow fields, electromagnetic fields, and surface fields due to confinement. In this paper we present theoretical and simulation studies of the pattern formation of nematic liquid crystal disclination loops under capillary confinement including branching processes from a m=+1 disclination line to two m=+1/2 disclination curves that describe the postnucleation and growth regime of the textural transformation from radial to planar polar textures. The early postnucleation and growth of emerging disclination loops in cylindrical capillaries are characterized using analytical and computational methods based on the nematic elastica that takes into account line tension and line bending stiffness. Using subdiffusive growth and constant loop anisotropy, we found that the solution to the nematic elastica is a cusped elliptical geometry characterized by exponential curvature variations. The scaling laws that govern the loop growth reflect the tension to bending elasticity balance and reveal that the loop dilation rate depends on the curvature and normal velocity of the disclination. The line energy growth is accommodated by the decrease in branch-point curvature. These findings contribute to the evolving understanding of textural transformations in nematic liquid crystals under confinement using the nematic elastic methodology.