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Dipolar colloids in the nematostatics: tensorial structure, symmetry, different types, and pictures
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
email: victorpergam@yahoo.com

In spite of the analogy to the electrostatics, the 3d colloidal nematostatics is substantially different both in its mathematical structure and physical implications. The general tensorial structure of elastic multipoles derived in Refs.[V. M. Pergamenshchik and V. O. Uzunova, Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] allows for a classification of different types of colloids in the nematostatics. The elastic multipoles consist of two tensors (dyads). Based on this structure, I identify possible types of elastic dipoles. An elastic dipole is characterized by amplitudes of three 2 x 2 tensors and a two-component vector. The three coefficients describe dipole's isotropic strength, anisotropy, and chirality; while the vector repersents dipole's longitudinal component. Besides the four pure types there are eight mixed types of elastic dipoles. Possible symmetry groups of the director field related to the four dipolar types and their mixtures are found and described. The different symmetries are illustrated by sketches of correspondent dipolar colloids. It is stressed that the azimuthal anchoring plays a nontrivial role for the elastic multipoles. For instance, a helicoidal component of the surface anchoring easy axes of a colloid with the quadrupolar shape symmetry can make it a chiral elastic dipole. Important particular cases of the dipole-dipole pair interaction potentials are derived and discussed.
PACS: 61.30.Dk - Continuum models and theories, liquid crystal structure
PACS: 61.30.Jf - Defects in liquid crystals
PACS: 82.70Dd - Colloids
PACS: 01.55.+b - General physics

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