Self-assembly scenarios of patchy colloidal particles

Abstract

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...

Competing ordered structures formed by particles with a regular tetrahedral patch decoration

“…During past years, considerable effort has been dedicated to solve this intricate and challenging problem via different numerical and methodological routes [3,4,5,6,7]. In another contribution [8] we have demonstrated that a suitable combination of two complementary numerical approaches is able to provide a highly satisfactory answer to this yet open issue. To be more specific, we have combined the following two methods: (i) on one hand, an optimization technique, which employs ideas of evolutionary algorithms [9] that is able to predict efficiently and with high reliability ordered equilibrium structures at vanishing temperature; (ii) on the other hand, suitably developed Monte Carlo simulations [10,11] which allow to evaluate accurately, via thermodynamic integration, the thermodynamic properties of a particular ordered structure formed by patchy particles at finite temperature.…”

“…The global enthalpy minimum for this pressure value corresponds to, as previously reported in [12,5,8], a bcc-like structure that consists of two interpenetrating, but virtually non-interacting diamond lattices. This structure emerges in two different, but closely related versions: the particles of one diamond sublattice can be located exactly in the centers of the voids of the six-particle rings making up the other diamond sublattice ("b" in Figure 1) or the positions of the particles in each sublattice can be slightly shifted against each other ("a" in Figure 1).…”

“…The ordered equilibrium structures at zero temperature and the (pressure vs. temperature) phase diagram obtained via the combined approach outlined above have been shown and discussed in [8]. Several aspects that could not be presented in this rather concise presentation are discussed in detail in the present contribution.…”

“…Figures 1 and 2 visualize the ordered structures that correspond to the lowest-lying local enthalpy minima for P ⋆ = 2.5 and P ⋆ = 4.5, respectively (these values where chosen as particularly interesting based on the knowledge of the (P ⋆ , T ⋆ )-phase diagram [8]). The top panel shows, along with the respective enthalpy values, the two relevant contributions to this quantity, namely the lattice sum and the packing fractions as bars.…”

“…The spatial extent of the patches is characterized by a parameter, for which we have chosen the same value as in [5,8].…”