Quadrupolar forces and aggregation of nematic droplets

The electrostatic quadrupolar interaction between spherical nematic droplets in an isotropic (and nonconducting) liquid is calculated. It is found to have an anisotropic form U _q ∝1/R ⁵, where R is the distance between droplets, with repulsion for droplets having parallel orientation of the quadrupole moments and attraction at oblique angles around the orthogonal orientation. In an external magnetic field aligning the orientations of the quadrupole moments, a competition of the quadrupolar repulsion and van der Waals attraction (U _vdW∝ 1/R ⁶) leads to a specific spatial organization of droplets which is in fact often reported in experimental observations (see the monograph by P. Drzaic, Liquid Crystal Dispersions, World Scientific, Singapore (1995) and references cited therein). Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 747–752 (25 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.