Coulomb-like interaction in nematic emulsions induced by external torques exerted on the colloids

Abstract

An external mechanical torque on colloids immersed in a nematic liquid crystal can induce a Coulomb-like 1/r interaction between them [Lev and Tomchuk, Phys. Rev. E 59, 591 (1999); Lev, ibid. 65, 021709 (2002)]. In this paper we show that the director-mediated Coulomb-like interaction of two colloids is determined by the vectors Gamma perpendicular (1) and Gamma perpendicular (2) of the transverse external torques exerted upon these colloids. We derive the 1/r potential in which the scalar product -(Gamma perpendicular (1) x Gamma perpendicular (2)) of the two torques plays the role of the product of two electrostatic charges. The 1/r interaction is attractive for (Gamma perpendicular (1) x Gamma perpendicular (2))>0 and repulsive for (Gamma perpendicular (1) x Gamma perpendicular (2))<0 ("parallel torques" attract whereas "antiparallel torques" repel each other). The vector of transverse torque determines the two-component "elastic charge" (dyad), which is illustrated by the 1/r2 and 1/r3 terms in the elastic energy (the elastic analogs of the monopole-dipole and dipole-dipole interactions). The general status of the pairwise approach to nematic emulsions is considered in terms of the elastic charge density.