(457c) Coarse-Grained Description of Phase Behavior in 38-Member Clusters of Lennard-Jones Particles

Small clusters of Lennard-Jones particles are a well studied system with interesting phase behavior.  The behavior found in these clusters has common features with the phase behavior, thermodynamics, and kinetics governing protein folding, glass formation, and other intriguing phenomena in complex systems.  The 38-member Lennard-Jones particle cluster (LJ₃₈) is especially interesting, as it has octahedral as well as different icosahedral minimum-energy configurations, leading to both solid-solid and solid-fluid phase coexistence.

In this presentation, we report results of a systematic investigation of the phase behavior of the LJ₃₈ cluster.  To study this phase behavior, we conducted Monte Carlo (MC) simulations and employed windowed Monte Carlo-umbrella sampling (MC-US) to generate free-energy landscapes (FELs).  We constructed these FELs over a broad temperature range to develop a comprehensive picture of the thermodynamically stable configurations as well as the transitions observed between them.  The FELs were generated within a coarse-grained framework, which employs diffusion mapping data mining techniques and is able to capture the phase behavior of interest over the temperature range examined.  The reduced dimensionality of the coarse-grained description and the choice of coarse variables (order parameters) used in this coarse graining are addressed in detail.  By analyzing the resulting FELs, we predict the conditions for the stability of different crystalline configurations and the coexistence between these crystalline configurations and the fluid-like states.  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 thermodynamic system smallness inherent to these LJ₃₈ clusters.