Starting with the early alchemists, a holy grail of science has been to makedesired materials by modifying the attributes of basic building blocks.Building blocks that show promise for assembling new complex materials can besynthesized at the nanoscale with attributes that would astonish the ancientalchemists in their versatility. However, this versatility means that makingdirect connection between building block attributes and bulk behavior is bothnecessary for rationally engineering materials, and difficult because buildingblock attributes can be altered in many ways. Here we show how to exploit themalleability of the valence of colloidal nanoparticle "elements" to directlyand quantitatively link building block attributes to bulk behavior through astatistical thermodynamic framework we term "digital alchemy". We use thisframework to optimize building blocks for a given target structure, and todetermine which building block attributes are most important to control forself assembly, through a set of novel thermodynamic response functions, moduliand susceptibilities. We thereby establish direct links between the attributesof colloidal building blocks and the bulk structures they form. Moreover, ourresults give concrete solutions to the more general conceptual challenge ofoptimizing emergent behaviors in nature, and can be applied to other types ofmatter. As examples, we apply digital alchemy to systems of truncatedtetrahedra, rhombic dodecahedra, and isotropically interacting spheres thatself assemble diamond, FCC, and icosahedral quasicrystal structures,respectively.
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