DENSITY FUNCTIONAL THEORY OF INTERACTING HARD SPHERES: THE FORMATION OF COMPLEX FRANK-KASPER PHASES

Abstract

Understanding the phase behaviour of colloidal systems is relevant to designing new colloid-based nanostructured materials. One common platform for studying the colloidal system is the model of hard spheres. Over the last few decades, different hard-sphere models have been developed. We study the phase behaviour of three hard-sphere models: the lattice gas model, the local density approximation model, and the white bear version of the fundamental measure theory, with short-range attractive and long-range repulsive (SALR) interactions. The competition between the attraction and repulsion results in the formation of clusters composed of many particles, whereas the spatial arrangement of these clusters leads to the formation of long-range ordered phases. Phase diagrams containing the commonly observed body-center-cubic (BCC) and hexagonally close-packed (HCP) phases, as well as the novel Frank-Kasper $\sigma$ and A15 phases, have been constructed using the density functional theory applied to hard spheres with SALR interactions. Similar phase transition sequences have been predicted for the three hard-sphere models, implying a universality of the observed phase behaviour for hard spheres interacting with SALR potentials. However, the details of the phase diagrams could vary significantly. The results obtained from our study shed light on understanding the emergence of complex phases from simple systems.