On the interaction of dipolar filaments

The interactions of dipolar filaments such as magnetic needles and chains in strong homogeneous magnetic/electric field are investigated theoretically. Revisiting the case of uniformly magnetized/polarized parallel needles of finite size L and separated by a distance R , all the relevant regimes of attraction and/or repulsion are properly addressed and discussed. At short inter-needle separation ( R/L $ \lesssim$ 0.2, the repuive pair potential of two facing needles is governed by R-1 in strong contrast with R-3 at long separations (R/L ≳ 2.5). This softening is attributed to an efficient long-range screening owing to the relatively long needle extension in this regime. This whole understanding of dipolar needles effective interaction is then used to grasp that of dipolar chains made up of spherical dipolar beads. When excluded-volume correlations are weak (i.e., the chains are a few beads apart), chains and needles possess virtually the same effective interaction. However, at short separation there is a remarkable hardening upon approaching two chains in registry in qualitative contrast to the needles case.