Elastic interaction between colloidal particles in confined nematic liquid crystals

TL;DR

This paper develops a theoretical framework for elastic interactions of colloidal particles in confined nematic liquid crystals, revealing how confinement and boundary conditions influence interaction ranges and zones.

Contribution

It introduces general formulas for self and interaction energies of colloids in confined nematics, highlighting the effects of boundary conditions on interaction screening and decay lengths.

Findings

Interaction is exponentially screened with decay length L/π.

Planar boundary conditions alter attraction and repulsion zones.

Quadrupolar decay length is half of dipolar decay length.

Abstract

The theory of elastic interaction of micron size axially symmetric colloidal particles immersed into confined nematic liquid crystal has been proposed. General formulas are obtained for the self energy of one colloidal particle and interaction energy between two particles in arbitrary confined NLC with strong anchoring condition on the bounding surface. Particular cases of dipole-dipole interaction in the homeotropic and planar nematic cell with thickness $L$ are considered and found to be exponentially screened on far distances with decay length $\lambda_{dd}=\frac{L}{\pi}$. It is predicted that bounding surfaces in the planar cell crucially change the attraction and repulsion zones of usual dipole-dipole interaction. As well it is predicted that \textit{the decay length} in quadrupolar interaction is \textit{two times smaller} than for the dipolar case.