Activated Instability of Homogeneous Bubble Nucleation and Growth

For the superheated Lennard-Jones liquid, the free energy of forming a bubble with a given particle number and volume is calculated using density-functional theory. As conjectured, a consequence of known properties of the critical cavity [S. N. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10 224 (2003)], the free energy surface terminates at a locus of instability. These stability limits reside, however, unexpectedly close to the saddle point. A new picture of homogeneous bubble nucleation and growth emerges from our study, being more appropriately described as an “activated instability.”

Figure 1

The reversible work $W$ of forming a bubble with a given particle number $n$ and radius $\lambda$ within the superheated LJ liquid at $kT/\epsilon =0.8$ and ${\rho }_b{\sigma }^3=0.7$ (${\rho }_b{\sigma }^3$ at the spinodal and binodal are 0.647 and 0.855, respectively). The saddle point is located at $n\approx 10$, $\lambda /\sigma \approx 3.78$, and $W_b/\epsilon \approx 68.66$.

Figure 2

The bubble and surrounding liquid density profiles, relative to the bulk density ${\rho }_b$, for the saddle point in Fig. 1.

Figure 3

Three-dimensional view of $W(n/v)$ given in Fig. 1.

Figure 4

The reversible work $W$ of forming a bubble within the superheated LJ liquid at $kT/ϵ=0.8$ and $P{\sigma }^3/\epsilon =-0.329$ obtained from isothermal-isobaric Monte Carlo simulations (at the spinodal and binodal, $P{\sigma }^3/\epsilon$ are $\simeq -0.600$ and $\simeq 0.00617$, respectively [11]). $W$ at the limits of stability for $n=0$ and $n=2$ (which do not exhibit maxima) are $\sim 52.9$ and $\sim 52.1\mathrm{kT}$, respectively, while at the maxima for $n=5$, $n=10$, and $n=15$, $W\sim 52.6$, $\sim 52.7$, and $\sim 52.8\mathrm{kT}$, respectively. The saddle point resides around $n=5$.