(300h) Determining The Metastable Limit Of Nucleation From Gauge-CELL Monte Carlo Simulations

The phenomenon of primary homogeneous nucleation continues to be mysterious because it is a dynamic evolution of many non-equilibrium steps. Of greatest interest is the metastable limit, the lowest supersaturation at which nucleation is spontaneous, because predicting the metastable limit allows the design and optimization of nucleation experiments. Toward that goal, we elucidate the non-equilibrium thermodynamics of nucleation with a recent simulation technique, Gauge-Cell Monte Carlo, which collects the non-equilibrium chemical potentials of all nucleation steps into an N-µ isotherm. From this isotherm we calculate accurately the solubility, the surface tension, and critically the metastable limit of the model mixture. We construct several isotherms for a large number solutes, with solubilities ranging from 1% to 0.0001%,  at temperatures from 0°C to 100°C.  We find a correlation for all these isotherms which show convergence on a simple relationship: 1/(metastable limit) ~ L*·log(solubility); where L* is a characteristic length related to the number of nuclei that are generated, representing the average inter-nuclear distance at nucleation. This heuristic equation is sufficiently general, and accurately describes all our simulation results, thus shedding light on the most relevant variables to the nucleation phenomenon and suggesting how to design and optimizating new nucleation studies. We additionally examine the interplay between stable and unstable clustering; describe how the "critical nucleus" depends on environmental conditions, and assess the free energy barriers to nucleation for several isotherms.