Elastic charge density representation of the interaction
via the nematic director field |
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Authors: | V M Pergamenshchik V O Uzunova |
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Institution: | (1) Korea University, Display and Semiconductor Physics, Jochiwon-eup, Yeongi-gun, Chungnam, 339-700, South Korea;(2) Institute of Physics, prospect Nauki, 46, Kiev, 03039, Ukraine |
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Abstract: | The interaction between particle-like sources of the
nematic director distortions (e.g., colloids, point
defects, macromolecules in nematic emulsions) allows for a useful
analogy with the electrostatic multipole interaction between
charged bodies. In this paper we develop this analogy to the level
corresponding to the charge density and consider the general
status of the pairwise approach to the nematic emulsions with
finite-size colloids. It is shown that the elastic analog of the
surface electric charge density is represented by the two
transverse director components on the surface imposing the
director distortions. The elastic multipoles of a particle are
expressed as integrals over the charge density distribution on
this surface. Because of the difference between the scalar
electrostatics and vector nematostatics, the number of elastic
multipoles of each order is doubled compared to that in the
electrostatics: there are two elastic charges, two vectors of
dipole moments, two quadrupolar tensors, and so on. The
two-component elastic charge is expressed via the vector of
external mechanical torque applied on the particle. As a result,
the elastic Coulomb-like coupling between two particles is found
to be proportional to the scalar product of the two external
torques and does not directly depend on the particles' form and
anchoring. The real-space Green function method is used to develop
the pairwise approach to nematic emulsions and determine its form
and restrictions. The pairwise potentials are obtained in the
familiar form, but, in contrast to the electrostatics, they
describe the interaction between pairs (dyads) of the elastic
multipole moments. The multipole moments are shown to be uniquely
determined by the single-particle director field, unperturbed by
other particles. The pairwise approximation is applicable only in
the leading order in the small ratio particle
size-to-interparticle distance as the next order contains
irreducible three-body terms. |
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Keywords: | 61 30 Dk Continuum models and theories of liquid crystal structure 61 30 Jf Defects in liquid crystals 82 70 Dd Colloids 01 55 +b General physics |
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