Long-range Casimir interactions between impurities in nematic liquid crystals and the collapse of polymer chains in such solvents

The elastic interactions between objects embedded in a nematic liquid crystal are usually caused by the average distortion - rather than by the fluctuations - of the nematic orientational field. We argue that for sufficiently small particles, the nematic-mediated interaction originates purely from the fluctuations of the nematic director. This Casimir interaction decays as d(-6), d being the distance between the particles, and it dominates van der Waals interactions close to the isotropic-to-nematic transition. Considering the nematic as a polymer solvent, we show that the onset of this Casimir interaction at the isotropic-to-nematic transition can discontinuously induce the collapse of a flexible polymer chain from the swollen state to the globular state, without crossing the Theta-point.