Abstract
Micro-droplets of nematic liquid crystals have been investigated under radial boundary conditions, based on a lattice model which incorporates explicitly the elastic properties of the medium as variable parameters in the Hamiltonian. Equilibrium director configurations have been simulated, employing the Monte Carlo technique, as a function of anchoring strength ϵ S at the spherical boundary surface. A very sharp transition from a uniaxial nematic structure to a radially ordered state results in ϵ S being increased beyond a threshold. The flexibility offered by this Hamiltonian is utilised to investigate this structural transition as a function of the splay elastic coefficient K 1. The results indicate several features: (1) the transition is as expected influenced by K 1; (2) the transition seems to be mediated by a process of complete wetting by the outer spherical surface, except for the small uniaxial core region sustained by the elastic energy penalty otherwise incurred; (3) the degree of splay contribution has multiple effects on the transition including changes in the critical anchoring strength at the transition, and the nature of the transition itself; (4) profiles of the director fluctuations across the (concentric) spherical layers indicate evidence of frustration caused by the competing interactions generated in the system due to the boundary conditions imposed.
Acknowledgements
We thank the Center for Modeling Simulation and Design (CMSD), University of Hyderabad for providing its facilities, and GSP would like to thank DST-HPCF for the award of a research fellowship in the project (UH/CMSD/HPCF/2006-07).