(201f) Phase Behavior of Thermodynamically Small Assemblies of Colloidal Nanoparticles

Self and directed assembly into highly ordered configurations of small clusters of colloidal nanoparticles is an area of great technological and scientific interest; of particular technological importance is the assembly of such colloidal nanoparticle clusters into crystalline phases. These thermodynamically small systems range from ~10 to ~100 particles in size. The phase behavior of these small systems is inherently 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 colloidal systems, which interact via electrostatic repulsion and depletion attraction; this interparticle potential can be derived experimentally and used for accurate statistical mechanical analyses of the fundamental thermodynamics and kinetics of the colloidal clusters.

In order to study the coexisting configurations present in clusters of colloidal nanoparticles, we conducted Monte Carlo (MC) simulations based on experimentally derived interparticle potentials and employed windowed Monte Carlo-umbrella sampling (MC-US) to generate free-energy landscapes (FELs). We constructed these FELs over a wide range of interparticle interaction strength and cluster size and obtained a comprehensive picture regarding the possible stable configurations of such colloidal assemblies at equilibrium, as well as the phase-transition behavior observed between them. The FELs were generated with respect to the proper number and type of order parameters required to provide an adequate description of the underlying phase-transition dynamics; the determination of the dimensionality of the order-parameter space and the choice of order parameters for the analysis are described and discussed in detail. By analyzing these FELs, we can predict the conditions for the formation of stable crystalline nuclei for the assembly of crystalline phases of colloidal nanoparticles. The predicted conditions for critical crystalline cluster nucleation are used to mark the onset of crystallization for clusters of colloidal nanoparticles. This FEL analysis 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.