Predicting Universal Pattern Formation on Spheres with Application to Self-Assembly of Patchy Colloids

Patchy colloids, colloidal particles with attractive or repulsive patches, serve as a central example of building blocks for self-assembly [1]. The patches can be created using e.g. glancing angle deposition, but recently interest has turned towards using self-assembly for creating the patterns themselves [2]. We present theory for predicting pattern formation of isotropically interacting particles on spheres, based on a relaxation of a Potts-like model who's interactions can be diagonalized (a generalization of the approach in [3]). We give a simplified model of immiscible surfactants on gold nanoparticles [4,5] which we use to demonstrate the theory. We use the theory to design patchy particles for self-assembly of specific geometric structures.\\[4pt] [1] E. Bianchi, R. Blaak, and C. N. Likos, Phys. Chem. Chem. Phys. 13 (2011)\\[0pt] [2] A. M. Jackson, J. W. Myerson, and F. Stellacci, Nat. Mater. 3 (2004)\\[0pt] [3] E. Edlund and M. Nilsson Jacobi, Phys. Rev. Lett. 105 (2010)\\[0pt] [4] C. Singh et al., Phys. Rev. Lett. 99 (2007)\\[0pt] [5] I. C. Pons-Siepermann and S. C. Glotzer, Soft Matter 8(23) (2012)