Structure and shape of nematic liquid-crystal microdroplets

We calculate the continuous dependence of structure and shape of tangentially anchored nematic liquid-crystal microdroplets on the parameters of anchoring strength w₀ and radius r, at fixed temperature, using a numerical relaxation method and Landau--de Gennes theory. The structure is characterized by spatially varying order parameter and director fields S and n^, and the shape of a free droplet is assumed to be a prolate ellipsoid. For droplets of fixed spherical shape, we find discontinuous and discontinuous order-disorder and uniform-distorted transitions of S induced by r and by w₀, respectively, and uniform-distorted transitions of n^ induced by both r and w₀. For free droplets, we show that the surface interactions can indeed induce prolateness, which increases toward a limiting value as the volume becomes smaller, and which is nearly proportional to w₀/{σ}, where {σ} is the director-independent part of the surface tension.