(717d) Effects of Interaction Range, Interaction Strength, and System Size on the Phase Behavior of Small Clusters of Colloidal Particles

Self and directed assembly of small clusters of colloidal particles is an area of great technological and scientific interest. Of particular technological importance is the assembly of clusters of colloidal particles into highly ordered crystalline structures. These clusters range from ~10 to ~100 particles in size and are termed thermodynamically small. The phase behavior of these small systems is qualitatively different from the typical thermodynamic behavior of bulk phases. Specifically, such colloidal assemblies exhibit coexistence of phases or configurations over a broad range of physical conditions. In this presentation, we report results of a systematic investigation of the phase behavior of thermodynamically small colloidal assemblies, which interact via electrostatic repulsion and Asakura-Oosawa (AO) depletion potentials. The interparticle potential has been validated experimentally and used for accurate statistical mechanical analyses of the fundamental thermodynamics and kinetics of the colloidal clusters.

In order to study the phase behavior of small clusters of colloidal particles, we conducted Monte Carlo (MC) simulations and employed windowed Monte Carlo-umbrella sampling (MC-US) to generate free-energy landscapes (FELs). The FELs were generated with respect to a well justified coarse-variable space, which has been shown to be able to capture both order-to-disorder and polymorphic structural transitions. The dimensionality of coarse-variable space was determined by analysis based on the machine learning technique of diffusion mapping on data sets generated by dynamical simulations of the colloidal clusters of interest. We constructed these FELs over a range of interparticle interaction strength, interaction range, and cluster size and obtained a comprehensive picture regarding the possible stable configurations of such colloidal assemblies at equilibrium, as well as the phase changes observed between them. In particular, we observe an order-to-disorder transition between fluid-like and crystalline phases as well as a polymorphic transition between relaxed face-centered cubic and relaxed hexagonal close-packed structures. The analysis of these FELs yields phase-diagram information, which can describe not only the bulk-like phase behavior (i.e., coexistence at a single point) but also the complex phase behavior arising from the system smallness inherent to these colloidal clusters.