General elastic interaction in nematic liquid crystals colloids

TL;DR

This paper introduces a comprehensive free energy functional for elastic interactions in nematic liquid crystal colloids, accounting for arbitrary orientations and surface anchoring, revealing new multipole interaction terms absent in electrostatics.

Contribution

It presents a generalized elastic interaction model for colloids in nematic liquid crystals, including new multipole terms due to broken axial symmetry.

Findings

Derived a new free energy functional for colloid-LC interactions.

Identified non-zero spur of quadrupole tensor in symmetry-breaking cases.

Established analogies and differences with electrostatics.

Abstract

The new free energy functional that describes general elastic interaction between colloidal particles and nematic liquid crystal has been proposed. It generalizes results of the paper \cite{lupe} on the case of arbitrary orientation of colloidal particles and is valid for arbitrary surface anchoring strength. Formal analogies and differences between electric particles and colloidal particles in LC are found. It is first time shown that spur of the quadrupole moment tensor is different from zero $Sp\hat{Q}_{\mu}\neq 0$ in the case of axial symmetry breaking of the director field around colloidal particle in contrast to electrostatics. New general presentation for the elastic interaction between arbitrary colloids is obtained which contains new multipole terms connected with $Sp\hat{Q}_{\mu}\neq 0$ that are absent in the standard electrostatics.