Orientation distribution and transitions in polymer-dispersed liquid crystalline droplets

Dispersions of liquid crystalline droplets in a polymeric matrix are of interest in a variety of applications, including display technology and the fabrication of self-reinforced composite materials. The material properties, which are affected by the liquid crystalline orientation distribution in the droplet, appear to depend sensitively on the nature of the interface between the liquid crystalline dispersed phase and the isotropic matrix material. The orientation distribution satisfies a minimum free energy condition in a quiescent droplet.;Orientation distributions in droplets of liquid crystals with homeotropic anchoring are computed with a simulated annealing algorithm that minimizes the free energy of the Oseen-Frank continuum theory. A first-order transition between axial and radial conformations at a critical value of a parameter that represents the effect of droplet size and surface and bulk potentials is observed in spherical droplets. A similar transition occurs in a deformed droplet at a critical extension.;The droplets exhibit multiple orientational steady states that are separated by finite energy barriers over the entire range of the dimensionless ratio of surface to elastic forces, with maximum transition energy densities of the order of 2,000 Pa for a typical liquid crystalline droplet with a spherical radius of 1 micron. The transition energy densities decrease with elongation to spheroidal droplets with aspect ratios of four or more, indicating that droplet elongation is favored to drive surface-induced transitions.;We also compute the surface-induced droplet morphology and the free energy pathway as a cylindrical liquid crystalline filament with preferred homeotropic interface orientation passes through a sequence of sinusoidal perturbations and breaks up into droplets. A first-order morphological transition with a finite energy barrier of the order of 2,400 J/m3 (Pa) for an equivalent droplet with a radius of 1mum is required when the perturbation amplitude exceeds a critical value. This result is consistent with a kinetic trapping explanation proposed by Inn and Denn [J. Rheology, 49, 887-895 (2005)] for a delayed transition from a gel to a dispersed droplet morphology in blends of 4'-octyl-4-biphenylcarbonitrile (8CB) and poly(dimethyl siloxane).