Anchoring transition and influence of director fluctuations in liquid crystal droplets

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.

Keywords:

• polymer dispersed liquid crystal droplet
• Monte Carlo simulations
• elastic potential

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).