Theory of elastic interaction between colloidal particles in the nematic cell in the presence of the external electric or magnetic field

TL;DR

This paper develops a Green function method to analyze elastic interactions between colloidal particles in nematic cells under external electric or magnetic fields, predicting new effects like deconfinement and particle stabilization.

Contribution

It provides general formulas for various elastic interactions in nematic cells with external fields and predicts novel phenomena such as deconfinement and field-induced particle stabilization.

Findings

Deconfinement effect near Frederiks transition for dipole particles.

Field-induced attraction and stabilization of particles along the electric field.

Significant changes in attraction and repulsion zones under external fields.

Abstract

The Green function method developed in Ref.[S. B. Chernyshuk and B. I. Lev, Phys. Rev. E \textbf{81}, 041707 (2010)] is used to describe elastic interactions between axially symmetric colloidal particles in the nematic cell in the presence of the external electric or magnetic field. General formulas for dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions in the homeotropic and planar nematic cells with parallel and perpendicular field orientations are obtained. A set of new results has been predicted: 1) \textit{Deconfinement effect} for dipole particles in the homeotropic nematic cell with negative dielectric anisotropy $\Delta\epsilon<0$ and perpendicular to the cell electric field, when electric field is approaching it's Frederiks threshold value $E\Rightarrow E_{c}$. This means cancellation of the confinement effect found in Ref. [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801, (2008)] for dipole particles near the Frederiks transition while it remains for quadrupole particles. 2) New effect of \textit{attraction and stabilization} of the particles along the electric field parallel to the cell planes in the homeotropic nematic cell with $\Delta\epsilon<0$ . The minimun distance between two particles depends on the strength of the field and can be ordinary for . 3) Attraction and repulsion zones for all elastic interactions are changed dramatically under the action of the external field.