(704f) Inverse Materials Design from Phase Transitions in Shape Space

Since the development of the theory of atoms, packing arguments have been used in an attempt to explain and predict the structure of condensed matter. For atomic and even surfactant systems packing provides a useful heuristic rationalizing structure. However, studies prompted by the recent explosion of new nanoparticles show that packing arguments often fail in two ways. First packing arguments fail to predict the emergence of ordered mesophases. Second, packing arguments fail to predict particles likely to assemble dense packing structures at finite pressure. Though the formation of local dense packing motifs in order to maximize shape entropy has been proposed to explain why global packing arguments fail, there is no quantitative measure of how and when packing arguments fail. Here we use a recently proposed digital alchemy framework to distinguish between finite pressure assembly behavior and the onset of infinite pressure packing behavior through Alchemical Monte Carlo (Alch-MC) simulation. We study families of FCC-, BCC-, and SC- forming symmetric convex polyhedra and find for FCC a first-order shape-shape phase transition in shape space from an “assembly” regime to a “packing” regime. In the assembly regime we determine optimal shapes, as well as the most and least sensitive aspects of shapes for crystal formation. In the packing regime, we find that the optimal packing shape fails to predict the thermodynamically preferred shape up to packing fractions of 99% and that vertex truncation of these convex polyhedra generally optimizes the particle shape. We report parallel results for a family of simple cubic formers and body-centered cubic formers.