Minimal Positive Design for Self-Assembly of the Archimedean Tilings

Molecular self-assembly is the spontaneous association of molecules under equilibrium conditions into stable, structurally well-defined aggregates joined by noncovalent bonds. Molecular self-assembly is ubiquitous in biological systems and underlies the formation of a wide variety of complex biological structures. Understanding self-assembly and the associated noncovalent interactions that connect complementary interacting molecular surfaces in biological aggregates is a central concern in structural biochemistry. Self-assembly is also emerging as a new strategy in chemical synthesis, with the potential of generating nonbiological structures with dimensions of 1 to 10(2) nanometers (with molecular weights of 10(4) to 10(10) daltons). Structures in the upper part of this range of sizes are presently inaccessible through chemical synthesis, and the ability to prepare them would open a route to structures comparable in size (and perhaps complementary in function) to those that can be prepared by microlithography and other techniques of microfabrication.

A challenging goal in materials chemistry and physics is spontaneously to form intended superstructures from designed building blocks. In fields such as crystal engineering and the design of porous materials, this typically involves building blocks of organic molecules, sometimes operating together with metallic ions or clusters. The translation of such ideas to nanoparticles and colloidal-sized building blocks would potentially open doors to new materials and new properties, but the pathways to achieve this goal are still undetermined. Here we show how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal-in this case a colloidal kagome lattice-through decoration of their surfaces with a simple pattern of hydrophobic domains. The building blocks are simple micrometre-sized spheres with interactions (electrostatic repulsion in the middle, hydrophobic attraction at the poles, which we call 'triblock Janus') that are also simple, but the self-assembly of the spheres into an open kagome structure contrasts with previously known close-packed periodic arrangements of spheres. This open network is of interest for several theoretical reasons. With a view to possible enhanced functionality, the resulting lattice structure possesses two families of pores, one that is hydrophobic on the rims of the pores and another that is hydrophilic. This strategy of 'convergent' self-assembly from easily fabricated colloidal building blocks encodes the target supracolloidal architecture, not in localized attractive spots but instead in large redundantly attractive regions, and can be extended to form other supracolloidal networks.

Many nanometre-sized building blocks will readily assemble into macroscopic structures. If the process is accompanied by effective control over the interactions between the blocks and all entropic effects, then the resultant structures will be ordered with a precision hard to achieve with other fabrication methods. But it remains challenging to use self-assembly to design systems comprised of different types of building blocks-to realize novel magnetic, plasmonic and photonic metamaterials, for example. A conceptually simple idea for overcoming this problem is the use of 'encodable' interactions between building blocks; this can in principle be straightforwardly implemented using biomolecules. Strategies that use DNA programmability to control the placement of nanoparticles in one and two dimensions have indeed been demonstrated. However, our theoretical understanding of how to extend this approach to three dimensions is limited, and most experiments have yielded amorphous aggregates and only occasionally crystallites of close-packed micrometre-sized particles. Here, we report the formation of three-dimensional crystalline assemblies of gold nanoparticles mediated by interactions between complementary DNA molecules attached to the nanoparticles' surface. We find that the nanoparticle crystals form reversibly during heating and cooling cycles. Moreover, the body-centred-cubic lattice structure is temperature-tuneable and structurally open, with particles occupying only approximately 4% of the unit cell volume. We expect that our DNA-mediated crystallization approach, and the insight into DNA design requirements it has provided, will facilitate both the creation of new classes of ordered multicomponent metamaterials and the exploration of the phase behaviour of hybrid systems with addressable interactions.