46998-AC6
A New Picture of Homogeneous Bubble Nucleation in Superheated Liquids
Earlier studies by Punnathanam and Corti (2002, Ind. Eng. Chem. Res. 41, 1113; 2003, J. Chem. Phys. 119, 10224) (2002) suggested that cavities (spherical regions devoid of particle centers) play an important role in the process of homogeneous bubble nucleation in superheated liquids. Specifically, the existence of a critical cavity (a limiting upper-bound on the size of a cavity for which the superheated liquid remained stable) necessarily implied that the free energy surface, or reversible work W(n,v), of bubble formation, is very different from previous constructions of this surface (where n is the number of particles inside an embryo with a given spherical volume v.) For example, this stability limit arising at the critical cavity, or terminus of the n=0 profile, was conjectured to be "felt" throughout W(n,v) (Uline and Corti, 2007, Phys. Rev. Lett. 99, 076102). Molecular simulation and density-functional theory (DFT), which constrained the number of particles located inside a bubble for a fixed radius, validated this new picture of bubble formation for the pure-component Lennard-Jones (LJ) liquid, revealing that liquid-to-vapor nucleation is more appropriately described by an "activated instability" (Uline and Corti, 2007). As the free energy barrier is surmounted, W(n,v) abruptly ends along a locus of instabilities, where a stability limit is reached for each n. Further growth of the post-critical bubbles must therefore proceed via a mechanism appropriate for an unstable system. DFT also suggested that many plausible transition pathways exist for a pre-critical bubble to cross the activation barrier, which appears as a flat ridge. This ridge is in marked contrast to the prediction of classical nucleation theory (CNT), where a well-defined saddle point in (n,v)-space provides the likely transition path between a pre-critical embryo and its growth to the new, bulk phase.
While the full implications of this new and intriguing picture of bubble formation have yet to be determined, we have recently focused on droplet formation in supercooled vapors to determine if any of the key features of W(n,v) discussed above also arise for vapor-to-liquid nucleation. Initially, one suspects that the critical cavity and its effects should play no role in droplet nucleation; many advances in recent years have placed the analysis of droplet formation on a more rigorous foundation, none of which have predicted the onset of an unstable growth phase. Nevertheless, we extended the constrained DFT method of Uline and Corti (2007) to the analysis of cluster formation in the pure component LJ supercooled vapor. While the structure of the free energy surface is similar to those obtained in some previous methods, one major and important difference arises for large enough clusters: each constant n profile terminates at a limit of stability, λsl, as the droplet is compressed (for λ<λsl, the density-profile outside of the cluster did not converge to a vapor-like density profile; these instabilities were also shown to correspond to true thermodynamic limits of stability, as verified by the vanishing of the lowest eigenvalue generated from the second-functional derivative of the grand potential). These limits of stability also reside at the same location as the bottom of the valley (or local minima) that appeared beyond the nucleation barrier in previous theoretical work. Consequently, a valley no longer develops beyond the free energy barrier. Instead, the free energy surface channels the post-critical droplets to a locus of instabilities, whereby further growth must occur by a mechanism consistent with an unstable system. As was found for bubble formation, droplet nucleation is, quite surprisingly, more aptly described as an "activated instability".
Furthermore, for large droplets, maxima develop in the resulting constant n work profiles. These maxima, which form a flat ridge since they all correspond to the same value of W, coincide with mechanical and chemical equilibrium between the droplet and surrounding vapor (a locus of unstable equilibrium points). Consequently, a true saddle point no longer appears in (n,v)-space, and many transition pathways are now possible for clusters to surmount the nucleation barrier. Molecular simulations performed at constant temperature and pressure verified all key aspects of the free energy surface obtained via our DFT method.
In conclusion, a new picture of homogeneous droplet nucleation and growth emerges from our DFT and simulation studies. In particular, a locus of instabilities appears on the free energy surface for droplet formation, suggesting that nucleation and growth is again more appropriately viewed as an "activated instability". Once a stability limit is reached, the further growth of the droplet must be described by a mechanism suitable for an unstable fluid. Additional investigations are of course needed to verify this new molecular-based picture. In particular, future work is directed towards identifying the signature of such an unstable growth phase, and whether such a process can be (or already has been) seen within molecular simulation.
