378248 Equilibrium Shape of Colloidal Crystals
Clusters of colloidal crystals exhibit a broad range of emergent, size dependent properties. Leveraging such properties requires a strong fundamental understanding of the thermodynamics and kinetics of colloidal clusters. A first step in developing this understanding is to accurately describe the equilibrium structure and morphology of these assemblies. In this presentation, we report the results of a generalized Wulff construction that can accurately describe the equilibrium, i.e., of minimum free energy, shape of a crystalline assembly of colloidal particles. The colloidal system that we consider is modeled according to an inter-particle interaction potential consisting of two terms, an electrostatic repulsion and an Asakura-Oosawa (AO) depletion attraction. This inter-particle potential has been validated experimentally and used for various accurate analyses of the thermodynamics and kinetics of these colloidal clusters, including disorder-to-order transitions as well as polymorphic transitions of colloidal crystalline clusters.
The generalized Wulff construction accounts for both surface and edge effects on the stable colloidal crystalline morphology through surface free energy contributions from surface facets and edges in the cluster morphology. The inputs to the generalized Wulff construction are the bulk crystal energy and free energy penalties associated with the formation of crystalline facets as well as edges between these facets. The bulk energy and free energy penalties are calculated for the relaxed structure of the stable crystalline assembly in the face-centered cubic phase. This approach differs from the conventional Wulff construction, which considers surface free energy effects on the equilibrium structure due to surface facets only. The result of this generalized approach is a minimum-free-energy configuration for given crystal size (volume or number of atoms). We carry out these calculations over a range of crystal sizes to probe size effects on the morphological stability of colloidal clusters. Based on the findings of this analysis, we can determine the existence of “magic” cluster sizes, for which the colloidal clusters exhibit improved stability, i.e., lower internal energy, compared to other clusters of similar size. Such analyses also provide useful information for the development of coarse-grained theories of colloidal crystal nucleation and growth.