We calculate the continuous dependence of structure and shape of tangentially anchored nematic liquid-crystal microdroplets on the parameters of anchoring strength ${\mathit{w}}_0$ 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 ${\mathit{w}}_0$, respectively, and uniform-distorted transitions of n^ induced by both r and ${\mathit{w}}_0$. 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 ${\mathit{w}}_0$/σ, where σ is the director-independent part of the surface tension.

• Received 13 July 1993

DOI:https://doi.org/10.1103/PhysRevE.49.570