Ordered Equilibrium Structures of Patchy Particle Systems

Soft matter systems, typically consisting of mesoscopic particles in a microscopic solvent, can form a surprisingly rich variety of solid, ordered structures at low temperature. A reliable prediction which solid phases will appear for given particle interactions under certain thermodynamic conditions has been considered a major problem in (soft) condensed matter physics for several decades. In this thesis, we present a prediction method based on heuristic global optimization schemes such as evolutionary algorithms. In order to find the most stable configuration of a system at a given thermodynamic state point, the particle arrangement corresponding to the global minimum of the appropriate thermodynamic potential, such as the (free) energy or enthalpy, is identified. We apply these optimization methods to model systems for so-called patchy colloidal particles. Patches are defined as finite regions on the colloidal surface, which differ in their physical or chemical properties from the rest of the surface. Such particles are characterized, in addition to the isotropic excluded volume interactions of the colloids, by attractive as well as repulsive directional interactions induced by the patches. Novel synthesization techniques yield particles with desired properties. Thus, patchy particles are often seen as building blocks that are able to self-assemble into well-defined ordered macroscopic structures under certain external conditions. The systems we investigate range from finite clusters to bulk crystals in two as well as three dimensions.