Hedgehog defect structure in a mixture of a nematic liquid crystal and an isotropic substance

EZEQUIEL R. SOULÉ; ALEJANDRO D. REY

Boston

Conferencia; MRS 2011 fall meeting; 2011

Materials Research Society

The aim of this work is to study the defect structure and solute distribution in a hedgehog droplet configuration, for the case of a mixture of a nematic liquid crystal and an “impurity” (isotropic substance). The structure of a hedgehog defect and its dependence on temperature is well known for a pure liquid crystal, but it has not been widely studied for a mixture.  Two approaches are used to analyze this problem. This two complementary techniques have been used for pure liquid crystals as well. The first one is based in a simplified theory that considers the core of the defect as an isotropic phase. The free energy of the system is written as the sum of the bulk free energies of each phase, the interfacial free energy and the energy of the distortions in the nematic phase. All the terms, in principle, are functions of the composition of each phase. The equilibrium values of the radius and the concentration in the defect are calculated by minimizing the free energy.  The second approach is based in minimizing the full Landau-de Gennes free energy functional, which is written in terms of the homogeneous (or bulk), and gradients contributions to free energy, the last one accounting both for interfaces and distortions.  It is observed that the radius of the defect increases as the temperature and concentration of the nematic phase approach the phase transition conditions. Far from saturation, the defect radius depends principally on the difference between the concentration of the nematic phase and the concentration of a saturated nematic phase. Close to saturation conditions there is a strong temperature dependence. As the concentration in the nematic approaches the saturation concentration, the concentration in the isotropic core approaches the concentration of the equilibrium isotropic phase. For a small supersaturation, a nematic phase with a defect may still exist, but the temperature range for the existence of this metastable phase is reduced with respect to the bulk, undistorted, defect-free nematic phase. This effect is analogous to the metastability of the hedgehog configuration in pure liquid crystals for small superheating.