Abstract
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 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 nontrivial topology of the director field and also multiply connected tactoid-in-tactoid 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 π. 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 a function of I–N interfacial tension anisotropy in the approximation of 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.
Highlights
In thermotropic systems with a relatively weak surface anisotropy, the Rapini–Papoular surface potential or even a simpler quadratic dependence σ (α) ∝ (α −α )2 is often sufficient to describe the anchoring phenomena. This might not be true in the case of a lyotropic liquid crystal (LC) with a large w; observation of the first-order anchoring transition of lyotropic chromonic liquid crystals (LCLCs) in contact with solid substrates suggests that the surface potential should be different from the Rapini–Papoular form [58]
To measure w in a more reliable manner, we would need to determine the surface tension more accurately than presently possible and expand the range of numerical simulations to the range of parameters characterizing the tactoids in LCLCs; this work is in progress
We illustrate how the balance of anisotropic surface energy and internal elasticity shapes complex morphogenetic developments of tactoidal forms and topological defects emerging in dynamic phase transitions between the isotropic and nematic phases
Summary
The pioneering observations by Bernal and Fankuchen [51] of the I–N phase transition in lyotropic N formed by tobacco mosaic virus dispersed in water revealed that the N droplets with tangential director orientation are of a peculiar elongated shape with two-cusped ends [51] These shapes were called tactoids [51, 52]; for more studies, see [35,36,37,38,39, 53,54,55]. It is expected that the structure of nuclei in the I–N phase transitions would be highly nontrivial, in terms of both their shape and the interior director structure, as the representative energies σ0R2, σ0wR2 and KR might vary in a much wider range than in thermotropic LCs. in thermotropic systems with a relatively weak surface anisotropy, the Rapini–Papoular surface potential or even a simpler quadratic dependence σ (α) ∝ (α −α ) is often. This might not be true in the case of a lyotropic LC with a large w; observation of the first-order anchoring transition of LCLCs in contact with solid substrates suggests that the surface potential should be different from the Rapini–Papoular form [58]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
