UC Santa Barbara

Phase separation of a binary mixture, which consists of isotropic fluid, such as a flexible polymer, and nematic liquid crystal, can be induced from temperature quench. The separation process proceeds through the initial nucleation of small particles and subsequent growth and coarsening, and a variety of final morphologies can be obtained. This work is focused on the numerical investigation of nucleation and ordered structure formation of a flexible polymer in a nematic liquid crystal matrix confined between two parallel walls in both a 2D and a 3D channel geometry. The model is of Landau-de Gennes type for a conserved, compositional order parameter and a non-conserved, orientational tensor order parameter and allows a study of the system at the nanoscale.

This is the first time the full model has been utilized to learn the phase separation in confined geometries for a 3D geometry. The resulting system is numerically stiff, with several high order nonlinear coupled terms. In addition, to preserve the total volume of the species and be consistent with the variation of the free energy, a nontrivial boundary condition has to be enforced at the walls. These pose a significant numerical challenge that we overcome with the implementation of a linearly implicit method and an extrapolated boundary condition.

Our numerical investigation focuses on the effects of wall and surface anchoring on the nucleation of ordered, polymer-rich domains as well as in the selection of lamellae. In addition, the role of different energies in the system, and the elastic dipole configuration which critically contributes to the formation of structures are also explored.

In 2D, we find that chains of polymer-rich droplets nucleate, starting at the walls and aligned with them, and continue to form until they fill up much of the channel. Without orientational defects observed in the liquid crystal-rich phase, the droplets eventually coalesce, coarsen, and the linear chain order is destroyed. We have justified this by showing that the dipole defect cannot be sustained by the Landau-de Gennes model and instead it splits into two $-1/2$ point defects in a 2D channel and a $-1/2$ disclination ring in a 3D channel. In 3D, the polymer nucleates into layers of cylindrical structures, instead of droplets, whose principal axis is oriented with the wall anchoring angle. We also find that when the liquid crystal component is initially in isotropic state, stable equilibrium lamellae can be obtained for both homeotropic and planar surface anchoring conditions, in 2D and 3D.