Designing a bernal spiral from patchy colloids

A model potential for colloidal building blocks is defined with two different types of attractive surface sites, described as complementary patches and antipatches. A Bernal spiral is identified as the global minimum for clusters with appropriate arrangements of three patch-antipatch pairs. We further derive a minimalist design rule with only one patch and antipatch, which also produces a Bernal spiral. Monte Carlo simulations of these patchy colloidal building blocks in the bulk are generally found to corroborate the global optimization results.