Nematic-isotropic phase transition in a liquid-crystal droplet

Abstract

Possible phases in a nematic liquid crystal confined to a spherical submicrometer droplet embedded in a solid polymer are analyzed in terms of a Landau--de Gennes theory. For a droplet with a radial structure we show that the strength of the nematic-polymer interfacial interaction affects the nematic-paranematic (partially ordered isotropic phase) phase transition and may in addition induce a boundary-layer nematic phase. This boundary layer phase exists only in a narrow (\ensuremath{\sim}0.1 K) temperature interval above the nematic phase for a restricted range of interfacial interactions. Also in the radial structure the degree of ordering is suppressed close to the center of the droplet where a defect is located. As the size of the droplet decreases, the relative size of this region of suppressed ordering increases. Below a critical radius ${\mathit{R}}_{\mathit{c}}$ (0.22 \ensuremath{\mu}m for 4-n-pentyl-4'-cyanobiphenyl), if the surface interaction is above a critical value (${\mathit{q}}_{\mathrm{max}}$=1.85\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$), the transition between the nematic phase and the paranematic phase no longer occurs. A three-dimensional phase diagram is presented to demonstrate the effect of the surface interaction strength, droplet radius, and sample temperature on the stability of phases within a droplet.