Morphogenesis of defects and tactoids during isotropic-nematic phase
  transition in self-assembled lyotropic chromonic liquid crystals
  We explore the structure of nuclei and topological defects in the first-order
phase transition between the nematic (N) and isotropic (I) phases in lyotropic
chromonic liquid crystals (LCLCs). The LCLCs are formed by self-assembled
molecular aggregates of various lengths and show a broad biphasic region. The
defects emerge as a result of two mechanisms. 1) Surface anisotropy mechanism
that endows each N nucleus (tactoid) with topological defects thanks to
preferential (tangential) orientation of the director at the closed I-N
interface, and 2) Kibble mechanism with defects forming when differently
oriented N tactoids merge with each other. Different scenarios of phase
transition involve positive (N-in-I) and negative (I-in-N) tactoids with
non-trivial topology of the director field and also multiply connected
tactoids-in-tactoids configurations. The closed I-N interface limiting a
tactoid shows a certain number of cusps; the lips of the interface on the
opposite sides of the cusp make an angle different from pi. The N side of each
cusp contains a point defect-boojum. The number of cusps shows how many times
the director becomes perpendicular to the I-N interface when one
circumnavigates the closed boundary of the tactoid. We derive conservation laws
that connect the number of cusps c to the topological strength m of defects in
the N part of the simply-connected and multiply-connected tactoids. We
demonstrate how the elastic anisotropy of the N phase results in non-circular
shape of the disclination cores. A generalized Wulff construction is used to
derive the shape of I and N tactoids as the function of I-N interfacial tension
anisotropy in the frozen director field of various topological charges m. The
complex shapes and structures of tactoids and topological defects demonstrate
an important role of surface anisotropy in morphogenesis of phase transitions
in liquid crystals.
