Wetting of a spherical particle by a nematic liquid crystal

We discuss how the curvature of a substrate influences wetting by a nematic liquid crystal concentrating on the surface of a spherical particle. Our investigation is based on Landau–de Gennes free energy formulated in terms of second-rank nematic order parameter $Q_{\mathrm{ij}}.$ We review the method to treat wetting transitions in curved geometries and calculate the wetting phase diagram in terms of the temperature and a surface coupling parameter. We find that the length of the prewetting line which corresponds to the boundary-layer transitions introduced by Sheng [Phys. Rev. A 26, 1610 (1982)] gradually decreases with a decrease in particle radius until it vanishes completely below a critical radius of about 100 nm. The prewetting line ends at a critical point which we study in detail. By interpreting the effect of curvature as an effective shift in temperature in Landau–de Gennes theory, we are able to formulate a good estimate for the critical temperature as a function of the inverse particle radius. It demonstrates that splay deformations around the particle significantly influence nematic wetting of curved surfaces.