(704a) Optimizing the Formation of Solid Solutions with Colloids of Different Shapes

A key challenge to engineer ordered solids from the co-assembly of two differently-shaped building blocks is to predict the key particle characteristics that lead to maximal mutual ordered-phase compatibility (MaxOC). While both entropy disparity, as captured by the relative size of the components, and energetic inter-species selectivity affect MaxOC, it is the former whose effect is less intuitive and the main focus of this work. Such MaxOC predictive rules are formulated and validated by using Monte Carlo simulation results for hard-core mixtures of octahedra and spheres and of other previously studied mixtures. Specifically, it is proposed that component size ratios should maximize their “substitutional symmetry” and hence minimize the combined free-energy cost associated with mutating a host-particle into a guest-particle in each of the solid phases. For the hard-core mixtures examined, packing entropy stabilizes substitutionally disordered solid solutions but not stoichiometric compounds. Additional molecular simulations were hence used to demonstrate, consistent with recent experimental findings, that such compounds can be formed by strengthening the inter-species compatibility via orientation-dependent attractions.