Field-triggered vertical positional transition of a microparticle suspended in a nematic liquid crystal cell

In this paper, based on the numerical calculation of total energy utilizing the Green's function method, we investigate how a field-triggered vertical positional transition of a microparticle suspended in a nematic liquid crystal cell is influenced by the direction of the applied field, surface anchoring feature, and nematic's dielectric properties. The new equilibrium position of the translational movement is decided via a competition between the buoyant force and the effective force built on the microparticle by the elastic energy gradient along the vertical direction. The threshold value of external field depends on thickness L and Frank elastic constant K and slightly on the microparticle size and density, in a Fréedericksz-like manner, but by a factor. For a nematic liquid crystal cell with planar surface alignment, a bistable equilibrium structure for the transition is found when the direction of the applied electric field is (a) perpendicular to the two plates of the cell with positive molecular dielectric anisotropy or (b) parallel to the two plates and the anchoring direction of the cell with negative molecular dielectric anisotropy. When the electric field applied is parallel to both plates and perpendicular to the anchoring direction, the microparticle suspended in the nematic liquid crystal tends to be trapped in the midplane, regardless of the sign of the molecular dielectric anisotropy. Such a phenomenon also occurs for negative molecular dielectric anisotropy if the external field is applied perpendicular to the two plates. Explicit formulas proposed for the critical electric field agree extremely well with the numerical calculation.