Liquid Crystals in Electric Field

Phase transitions occur in various systems in electric field. To treat such problems we need to construct a Ginzburg-Landau free energy including electrostatic interactions and electric field effects under each given boundary condition.1) The gross variables include the order parameter ψ, the polarization p, and the charge density ρ. (Note ψ = p in ferroelectric systems.) In this letter we present such a theory for liquid crystals in nematic states,2) since there seems to be no systematic theory of electric field effects for anisotropic fluids. We also examine the deformation of the director around a charged particle, since the nematic order around a neutral colloid particle or emulsion droplet has been extensively studied.3,4) We shall see that the charge-induced orientation is intensified with decreasing the particle radius R and/or increasing the charge number Z, while the surface anchoring of a neutral particle can be achieved for large radius because the penalty of the Frank free energy needs to be small.