Title: Colloidal nematostatics
Author(s):

	V.M. Pergamenshchik (Korea University, Display&Semiconductor Physics, Jochiwon-eup, Yeongi-gun, Chungnam 339-700, South Korea; Institute of Physics, prospect Nauki, 46, Kiev 03039, Ukraine) ,
	V.A. Uzunova (Institute of Physics, prospect Nauki, 46, Kiev 03039, Ukraine)

We give a review of the theory of large distance colloidal interaction via the nematic director field. The new area of nematic colloidal systems (or nematic emulsions) has been guided by the analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V.M. Pergamenshchik, V.O. Uzunova, Eur. Phys. J. E, 2007, 23, 161; Phys. Rev. E, 2007, 76, 011707] develops this analogy at the level of charge density and Coulomb interaction. The analogy is shown to lie in common mathematics based on the solutions of Laplace equation. However, the 3d colloidal nematostatics substantially differs from electrostatics both in its mathematical structure and physical implications. The elastic charge is a vector fully determined by the torque exerted upon colloid, the role of Gauss' theorem is played by conservation of the torque components. Elastic multipoles consist of two tensors (dyads). Formulas for the elastic multipoles, the Coulomb-like, dipole-dipole, and quadrupole-quadrupole pair interaction potentials are derived and illustrated by particular examples. Based on the tensorial structure, we list possible types of elastic dipoles and quadrupoles. An elastic dipole is characterized by its isotropic strength, anisotropy, chirality, and its longitudinal component. An elastic quadrupole can be uniaxial and biaxial. Relation between the multipole type and its symmetry is discussed, sketches of some types of multipoles are given. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in nematostatics for arbitrary director tilt at the wall. The method is applied to the charge-wall and dipole-wall interaction.

Key words: nematic colloid, electrostatic analogy, elastic charge and multipoles
PACS: 61.30.Dk, 61.30.Jf, 82.70Dd, 01.55.+b

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