Colloidal interactions in two dimensional nematics

TL;DR

This paper investigates the interactions between disks in a 2D nematic liquid crystal, revealing complex behaviors such as defect rearrangements and anisotropic attraction at short distances through analytical and numerical methods.

Contribution

It combines analytical tensor formalism and finite element simulations to elucidate defect-mediated interactions in 2D nematics, highlighting novel short-range attraction phenomena.

Findings

Defects form quadrupoles causing repulsive interactions at large distances.

Short-range interactions can become attractive due to defect rearrangements.

Preferred disk orientations change from oblique to perpendicular as they approach.

Abstract

The interaction between two disks immersed in a 2D nematic is investigated (i) analitically using the tensor order parameter formalism for the nematic configuration around isolated disks and (ii) numerically using finite element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short range attraction in all directions is still anisotropic. As the distance between the disks decreases their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular.