Zero temperature phase diagram of the square-shoulder system.

Particles that interact via a square-shoulder potential, consisting of an impenetrable hard core with an adjacent, repulsive, steplike corona, are able to self-organize in a surprisingly rich variety of rather unconventional ordered, three-dimensional structures. Using optimization strategies that are based on ideas of genetic algorithms, we encounter, as we systematically increase the pressure, the following archetypes of aggregates: low-symmetry cluster and columnar phases, followed by lamellar particle arrangements, until at high pressure values compact, high-symmetry lattices emerge. These structures are characterized in the isobaric-isothermal ensemble as configurations of minimum Gibbs free energy. Based on simple considerations, i.e., basically minimizing the number of overlapping coronas while maximizing at the same time the density, the sequence of emerging structures can easily be understood. In contrast to a previous contribution [G. J. Pauschenwein and G. Kahl, Soft Matter 4, 1396 (2008)], we present here a systematic investigation of this phenomenon, considering a short, an intermediate, and a large shoulder width.