Condensed Matter Physics, 2010, vol. 13, No. 3, p. 33602:129
DOI:10.5488/CMP.13.33602
Title:
Colloidal nematostatics
Author(s):

V.M. Pergamenshchik
(Korea University, Display&Semiconductor Physics, Jochiwoneup, Yeongigun, Chungnam 339700, 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 Coulomblike,
dipoledipole, and quadrupolequadrupole 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 chargewall and dipolewall interaction.
Key words:
nematic colloid, electrostatic analogy, elastic charge and multipoles
PACS:
61.30.Dk, 61.30.Jf, 82.70Dd, 01.55.+b
