Disclination interaction in an applied field: Stabilization of the Lehmann cluster

We study the interaction of disclinations in the presence of an applied magnetic or extensional flow field, which tends to align the director. Disclinations and inversion walls in the director field of nematic thermotropic liquid-crystal polymers are imaged at high resolution using the lamellar decoration technique of Wood and Thomas [Nature 324, 655 (1986)]. At intermediate field strengths, where the disclination separation is comparable to the characteristic length for director-field distortions, pairwise interaction no longer dominates, but clusters of disclinations having zero net topological dipole moment are observed to form. The applied field tends to minimize the long-range distortional energy, which is proportional to the square of the dipole moment. As a result, quadrupolar (Lehmann) clusters of disclinations are commonly observed in either magnetically or extensionally flow-aligned samples. These clusters are stabilized at intermediate field strengths, but at high fields, a second-order symmetry-breaking transition occurs that is analogous to the ferromagnetic transition of an Ising magnet. The transition is of the same class as Fr\'eedericksz transition, but it has dimensionality of two instead of one.