Interactions of distinct quadrupolar nematic colloids

Abstract

The effective interaction between spherical colloids in nematic liquid crystals is investigated in the framework of the Landau-de Gennes theory. The colloids differ in their surface interaction with the nematic liquid crystal. The particles induce quadrupolar far-field distortions in the nematic matrix, favouring homeotropic and the other degenerate planar anchoring of the nematic director. In the strong anchoring regime the colloids with homeotropic anchoring are accompanied by an equatorial disclination line defect, known as “Saturn-ring”, while the colloids with degenerate planar anchoring nucleate a pair of antipodal surface defects, called “boojums”. In the linear (large-distance) regime, the colloidal interactions are of the quadrupolar type, with quadrupoles of opposite signs. These are attractive when the colloids are aligned either parallel or perpendicular to the far-field director. At short distances, non-linear effects including “direct” interactions between defects give rise to a repulsion between the particles, which prevents them from touching each other. This finding supports the stability of nematic colloidal square crystallites the assembly of which has been reported recently.