Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making direct connection between building block attributes and bulk behavior is both necessary for rationally engineering materials, and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building block attributes to bulk behavior through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure, and to determine which building block attributes are most important to control for self assembly, through a set of novel thermodynamic response functions, moduli and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature, and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self assemble diamond, FCC, and icosahedral quasicrystal structures, Mendeleev's tabular organization of the elements[1, 2] by atomic valence [3] has served for more than 140 years as a heuristic that relates properties of the atomic elements to how they arrange in bulk structures. However, attempts to understand how properties of bulk structures relate to atomic properties predate Mendeleev and, in fact, modern science [4], and are complicated by the fact that the chemical manipulation of atoms is prohibited by the quantization of both electrical charge and angular momentum. Fortunately for Mendeleev, this quantization constrains Nature to only about 80 stable elements, and limits elemental properties and bulk behaviors so that the elements can be tabulated by valence. In fact, starting with technetium [5] in the 1930s, new atomic elements have only been produced artificially (as suggested by the etymology of the name "technetium" [6]) by α-particle bombardment, fusion, or other nuclear techniques that finally realized the ancient alchemists' goal of transmuting the elements.In contrast, an inexhaustible array of new "elements" can be synthesized as patchy particles. [7,8] However, the exploding diversity of patchy particles [8][9][10] or, more generally, colloidal "elements" means that there are now so many types to synthesize and study that synthesizing them all and determining their bulk behavior is no longer possible in practice. This fundamental impracticality means that, for colloid science to progress,...

Depletion interactions arise from entropic forces, and their ability to induce aggregation and even ordering of colloidal particles through self-assembly is well established, especially for spherical colloids. We vary the size and concentration of penetrable hard sphere depletants in a system of cuboctahedra, and we show how depletion changes the preferential facet alignment of the colloids and thereby selects different crystal structures. Moreover, we explain the cuboctahedra phase behavior using perturbative free energy calculations. We find that cuboctahedra can form a stable simple cubic phase, and, remarkably, that the stability of this phase can only be rationalized by considering the effects of both the colloid and depletant entropy. We corroborate our results by analyzing how the depletant concentration and size affect the emergent directional entropic forces and hence the effective particle shape. We propose the use of depletants as a means of easily changing the effective shape of self-assembling anisotropic colloids.

We show how directional entropic forces (which are set by particle shape) give rise to distinct behaviors in entropic systems with translational order and orientational disorder.