  Linear defects such as dislocations and disclinations in ordered materials
attract foreign particles since they replace strong elastic distortions at the
defect cores. In this work, we explore the behavior of isotropic droplets
nucleating at singular disclinations in a nematic liquid crystal, predesigned
by surface photopatterning. Experiments show that in the biphasic
nematic-isotropic region, although the droplets are attracted to the
disclination cores, their centers of mass shift away from the core centers as
the temperature increases. The shift is not random, being deterministically
defined by the surrounding director field. The effect is explained by the
balance of interfacial anchoring and bulk elasticity. An agreement with the
experiment can be achieved only if the model accounts for the disparity of the
nematic elastic constants; the so-called one-constant approximation, often used
in the theoretical analysis of liquid crystals, produces qualitatively wrong
predictions. In particular, the experimentally observed shift towards the bend
region around a +1/2 disclination core can be explained only when the bend
constant is larger than the splay constant. The described dependence of the
precise location of a foreign inclusion at defect cores on the elastic and
surface anchoring properties can be used in the rational design of microscale
architectures.
