We have investigated the self-assembly scenario of patchy colloidal particles in a two-dimensional system. The energetically most favourable ordered particle arrangements have been identified via an optimization tool that is based on genetic algorithms. Assuming different simple models for patchy colloidal particles, which include binary mixtures as well as attraction and repulsion between the patches, we could identify a broad variety of highly non-trivial ordered structures. The strategies of the systems to self-assemble become evident from a systematic variation of the pressure: (i) saturation of patch bonds at low pressure and close packing at high pressure and (ii) for intermediate pressure values, the strategy is governed by a trade-off between these two energetic aspects. The present study is yet another demonstration of the efficiency and the high reliability of genetic algorithms as versatile optimization tools.

The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is extremely difficult to predict the large variety of ordered equilibrium structures that these particles are able to undergo under the variation of external parameters, such as temperature or pressure. Here we show that, by a novel combination of two theoretical tools, it is indeed possible to predict the self-assembly scenario of patchy colloidal particles: on one hand, a reliable and efficient optimization tool based on ideas of evolutionary algorithms helps to identify the ordered equilibrium structures to be expected at T = 0; on the other hand, suitable simulation techniques allow to estimate via free energy calculations the phase diagram at finite temperature. With these powerful approaches we are able to identify the broad variety of emerging self-assembly scenarios for spherical colloids decorated by four patches and we investigate and discuss the stability of the crystal structures on modifying in a controlled way the tetrahedral arrangement of the patches.Experimental and theoretical investigations have provided unambiguous evidence that colloids with chemically or physically patterned surfaces (commonly known as "patchy particles") are very promising mesoscopic entities that can be used in hierarchical self-assembly processes to build up colloidal super-structures 1,2 . The anisotropy in the interactions of such particles in combination with the limited functionality and selectivity of the bonds offer unlimited possibilities for selfassembly scenarios. Thus, patchy particles are celebrated "to become the elementary brick of tomorrow's self-assembled materials" 3 , with promising applications in photonic crystals, drug-delivery, electronics 4 , biomaterials, or catalysis 5 .The possibility to tailor the interactions of patchy particles almost deliberately represents the basis for "bottom-up" strategies which allow to build up materials with desired properties, starting from adequately designed units. Suitable experimental techniques 6-9 allow to position patches on the colloidal surface and to define their spatial extent with high precision. A very impressive example for such an approach is a recent work on triblock Janus particles 5 : after decorating colloids with two hydrophobic caps of tunable area, particles selforganize in the two-dimensional Kagome lattice target structure. Complementary computer simulations 3,10 have provided a complete phase diagram of the system, including also the disordered, fluid phase.For the case of triblock Janus particles the self-assembly scenarios were easy to "guess". However, for more complex decorations and three dimensional systems, it is considerably more difficult to identify all ordered structures into which the particles might self-assemble. Semi-empirical approaches, applied over many years in hard matter physics, rely on a p...

We consider several patchy particle models that have been proposed in literature and we investigate their candidate crystal structures in a systematic way. We compare two different algorithms for predicting crystal structures: (i) an approach based on Monte Carlo simulations in the isobaric-isothermal ensemble and (ii) an optimization technique based on ideas of evolutionary algorithms. We show that the two methods are equally successful and provide consistent results on crystalline phases of patchy particle systems.

We numerically study the phase behavior of colloidal particles with two charged patches at the poles and an oppositely charged equatorial belt. Interactions between particles are described using the inverse patchy colloid model, where the term inverse emphasizes the difference with respect to conventional patchy particles: as a consequence of the heterogeneous charge distribution, the patches on the particle surface repel each other, whereas the patches and non-patch regions mutually attract. For the model parameters considered in this work, the system exhibits an unusual equilibrium phase diagram characterized by a broad region where a novel structure composed of parallel colloidal monolayers is stable.