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An earlier molecular simulation and density-functional theory (DFT) study by Uline and Corti (2007, Phys. Rev. Lett. 99, 076102) of bubble formation in the pure-component superheated Lennard-Jones (LJ) liquid revealed that liquid-to-vapor nucleation is more appropriately described by an "activated instability". As the free energy barrier is surmounted, the reversible work of forming a bubble with n particles inside a spherical volume v, or 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 most 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, recent molecular simulation and DFT work (Uline and Corti, 2008, J. Chem. Phys. 129, 234507) focused on droplet formation in the pure-component supercooled LJ vapor to determine if any of the key features of W(n,v) discussed above also arise for vapor-to-liquid nucleation. While the structure of the free energy surface is similar to those obtained in some previous studies of cluster formation, one major and important difference arises for large enough clusters: each constant n profile terminates at a limit of stability as the droplet is compressed (for smaller radii, 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 studies. 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 also, 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. Overall, a new picture of homogeneous droplet nucleation and growth emerges from this work.

Recently, additional DFT and molecular simulations studies have been performed to probe further the formation of droplets and bubbles in the supercooled and superheated LJ fluid, respectively. We showed that a locus of instabilities and a flat ridge appears in W(n,v) for all metastable conditions, from the binodal to the spinodal. We also demonstrated that certain features of the free energy surface, such as the radius of the bubble or droplet at its limit of stability, scale in a nearly temperature independent manner when plotted versus a parameter that quantifies the extent of penetration into the metastable region. Hence, certain aspects of nucleation and growth are “common” to all metastability conditions. Nevertheless, other important aspects of W(n,v) failed to show this same scaling behavior, suggesting that a “universal surface” does not exist.

We also extended the our DFT method to the analysis of nucleation within water-like fluids. Using a model system that captures certain known features of water, W(n,v) for bubble formation in superheated water was generated. While the values of W were quite different at the limits of stability, as compared to the LJ fluid, the radii of these limiting bubbles were insensitive to the choice of the intermolecular potential. The implications of this result for nucleation within a broader range of technologically relevant fluids are currently being investigated.

In addition, we developed a novel method for deriving the collisions dynamics for particles that interact via discontinuous potentials (Uline and Corti, 2008, J. Chem. Phys. 129, 014107). By invoking the conservation of the extended Hamiltonian, we generated molecular dynamics (MD) algorithms for simulating the hard-sphere and square-well fluids within the isothermal-isobaric (NpT) ensemble. (The square-well interaction is a “simple” potential that is widely used in molecular simulation studies of, for example, systems comprised of polymers and/or proteins. To the authors’ knowledge, our MD algorithm represents the first such algorithm to be developed for the simulation of square-well fluids at constant pressure.) Consistent with the recent rigorous reformulation of the NpT ensemble partition function, the equations of motion impose a constant external pressure via the introduction of a shell particle of known mass [Uline and Corti, J. Chem. Phys.,123, 164101 and 164102 (2005)], which serves to define uniquely the volume of the system. The particles are also connected to a temperature reservoir through the use of a chain of Nosé-Hoover thermostats, the properties of which are not affected by a hard-sphere or square-well collision. (This widely used thermostating method has so far only been applied to systems interacting via continuous potentials. Here we showed that this thermostat can also be easily introduced into the simulation of systems interacting via discontinuous potentials.) By using the Liouville operator formalism and the Trotter expansion theorem to integrate the equations of motion, the update of the thermostat variables can be decoupled from the update of the positions of the particles and the momenta changes upon a collision. Hence, once the appropriate collision dynamics for the isobaric-isenthalpic (NpH) equations of motion are known, the adaptation of the algorithm to the NpT ensemble is straightforward.