Identification and classification of clusters of dipolar colloids in an external field

Colloids can acquire a dipolar interaction in the presence of an external AC electric field. At high field strength, the particles form strings in the field direction. However, at weaker field strength, competition with isotropic interactions is expected. One means to investigate this interplay between dipolar and isotropic interactions is to consider clusters of such particles. Therefore, we have identified, using the GMIN basin-hopping tool, a rich library of lowest energy clusters of a dipolar colloidal system, where the dipole orientation is fixed to lie along the z axis and the dipole strength is varied for m-membered clusters of 7 ≤ m ≤ 13. In the regime where the isotropic and dipolar interactions are comparable, we find elongated polytetrahedral, octahedral, and spiral clusters as well as a set of non-rigid clusters, which emerge close to the transition to strings. We further implement a search algorithm that identifies these minimum energy clusters in bulk systems using the topological cluster classification [J. Chem. Phys. 139 234506 (2013)]. We demonstrate this methodology with computer simulations, which show instances of these clusters as a function of dipole strength.