Maximizing entropy by minimizing area: Towards a new principle of self-organization

We propose a heuristic explanation for the numerous non-close-packed crysta l structures observed in various colloidal systems. By developing an analog y between soap froths and the soft coronas of fuzzy colloids, we provide a geometrical interpretation of the free energy of soft spheres. Within this picture, we show that the close-packing rule associated with hard-core inte ractions and positional entropy of particles is frustrated by a minimum-are a principle associated with the soft tail and internal entropy of the soft coronas. We also discuss these ideas in terms of crystal architecture and p air distribution functions and analyze the phase diagram of a model hard-sp here-square-shoulder system within the cellular theory. We find that the A1 5 lattice, known to be area minimizing, is favored for a reasonable range o f model parameters and so it is among the possible equilibrium states for a . variety of colloidal systems. We also show that in the case of short-rang e convex potentials the A15 and other non-close-packed lattices coexist ove r a broad ranges of densities, which could make their identification diffic ult.