Single particle states of colloidal particles in 2D periodic potentials

Colloidal particles when subjected to a periodic array of potential wells are observed to adopt discrete stable configurations depending on the particle size/array wavelength ratio. Experimentally, the configuration states are determined for singlets, doublets and triplets of identical spheres in a periodic array of traps. The energy landscape of a single spherical particle is obtained by considering the refraction of the incident light as it passes throughout the particle. Then, the energy of a dumbbell is determined as the superposition of two singlets. The energy of a triplet is calculated as the superposition of a dumbbell and a single particle. As it is shown here, this direct method predicts accurately the stable particle configurations as observed in the experiments. The method can be generalized to obtain the potential energy of an n-particle aggregate, using as building blocks the energies of singlets and doublets.