Homogeneous nucleation and growth in simple fluids. II. Scaling behavior, instabilities, and the (n,v) order...

The free energy of forming a droplet and a bubble with a given number of particles n inside a volume v within the pure component Lennard-Jones supercooled vapor and superheated liquid, respectively, is further explored using density-functional theory. Certain key aspects of the free energy surface for bubble formation, such as the radius of the bubble at a stability limit, are found to scale in a nearly temperature independent manner when plotted versus a parameter that quantifies the location of the given state point in the metastable region. The corresponding work at this stability limit exhibits scaling for small values of n, but shows a strong temperature dependence for large n. No aspect of the free energy surface for droplet formation shows scaling over the full range of metastability conditions, including the work of forming the critical droplet and the radius of a droplet at its stability limit. Hence, there is no "universal" surface for embryo formation in metastable fluids. We also generate by thermodynamic arguments alone droplet and bubble trajectories along the corresponding free energy surfaces that avoid by construction the locus of instabilities, which match quite well the results obtained from other approaches. We also discuss in greater detail the use of the (n,v) order parameter within an equilibrium-based description of embryo formation, focusing on why the density profile of the embryo is found to be discontinuous at the embryo surface and why stability limits are expected to develop at certain bubble radii.