(128f) Characterization of Phase Behavior In Thermodynamically Small Systems Using Windowed Monte Carlo Umbrella Sampling

The adjective “thermodynamically small,” or “small” for brevity, describes a system that cannot be considered infinite in the sense of traditional macroscopic thermodynamics.  Small systems have been the subject of theoretical study over the past two decades and have seen a recent surge in interest because of their relevance to bio- and nano-technology and increasing accessibility to experiment.  The nature of phases and the transitions between them are of particular interest for small systems.  In this presentation, we report results of a systematic investigation of the phase behavior of colloidal systems, which interact via a hard core + depletion attraction potential, as a function of system size and the inter-particle interaction strength.  To describe the various phases that may be present, we carry out a set of windowed Monte Carlo Umbrella Sampling (MC-US) simulations to generate Free Energy Landscapes (FELs).  Each MC-US landscape is a function of the radius of gyration, which serves as a proxy for system density.  This set of FELs samples various values of the system size and potential strength.  These computed FELs provide a description of the phase behavior of this system, and allow us to describe the effects of interaction strength and system size as the system approaches the bulk thermodynamic limit.  For small clusters of colloidal crystals, we also explore the possibility of formation of so-called “magic clusters” that correspond to certain extrema of the free energy as a function of cluster size for given crystalline phase.  This exploration is carried out for every crystalline phase that can be stabilized over a broad range of the interaction strength.