(250b) Homogeneous Bubble Nucleation In Superheated Liquids: From the Underlying Free Energy Surface to the Dynamics of Nucleation and Growth

Homogeneous bubble nucleation refers to the process by which embryos of the vapor phase are formed due to spontaneous local density fluctuations in absence of any impurities, solid surfaces or external perturbations within a bulk superheated liquid. According to classical nucleation theory (CNT), if an embryo of the new phase is smaller than some critical size, the embryo collapses back into the metastable fluid; if the embryo exceeds this critical size, it grows to a macroscopic new phase. Recently, the reversible work of forming an embryo defined as a spherical volume v containing n particles in equilibrium with the surrounding superheated Lennard-Jones liquid was separately generated via Monte Carlo simulation and a density-functional theory (DFT) model [1]. Both methods consistently yielded (n,v) free energy surfaces that are considerably different than what is predicted by CNT. In particular, a locus of instabilities emerged whereby, for a given number of particles inside the embryo, an increase in the size of the spherical bubble beyond some critical volume resulted in the surrounding superheated liquid being unable to maintain its liquid-like equilibrium density far from the bubble surface. These stability limits are not captured by CNT due to its modeling of the vapor embryo and the surrounding liquid phase as two separate uniform phases with bulk properties.

While the above (n,v) free energy surface yielded new insights into the molecular-level mechanisms of bubble nucleation, some issues remain to be resolved before this surface can be used to generate consistent predictions of the rates of bubble nucleation. Specifically, the surface was found to describe embryos whose configurations were not accounted for in a fully non-redundant manner, i.e., different (n,v) points could be representative of the same equilibrium embryo. To eliminate these redundancies, we present a modification to our (n,v) embryo definition by introducing 1) a shell particle (a liquid-like particle residing in the spherical shell enclosing the volume v) that uniquely defines the volume of the embryo and 2) a bond-connectivity criterion that properly distinguishes between liquid-like and vapor-like particles (utilizing the same liquid-like/vapor-like definition proposed by ten Wolde and Frenkel [2]). With this latter definition, any particle that has less than five neighboring particles within a sphere of radius 1.5 particle diameters around it is labeled as vapor-like. Consequently, only vapor-like particles are now allowed to be present inside the spherical volume that is representative of a bubble or vapor-like embryo. In parallel, we present an approximate way to incorporate the shell particle and bond-connectivity criterion within our DFT formulation.  With these modifications, meaningful trajectories along the (n,v) surface can now be defined, where the embryo configurations are mapped to only one point in the (n,v) parameter space. Through this narrowing down of the possible pathways for reactive trajectories, the updated free energy surface strongly indicates that the emergence of a vapor-like embryo is overwhelmingly initiated by the formation of a cavity (a region void of particles), a result that is consistent with previous molecular simulation studies of the initial stages of bubble nucleation.

Finally, we discuss the relevance of the suggested (n,v) equilibrium embryo formulation as an appropriate order parameter for the study of the dynamics of bubble nucleation and growth in superheated liquids [3]. We show that this order parameter results in a relatively sharp transition of the committor probability of phase transition from zero to one. This provides us with the opportunity of accurately generating the transition configurations which almost have equal chance of growth or collapse. This new (n,v) equilibrium embryo formulation also provide us with  the chance of estimating the number density of the transition embryos  that serve as the dynamical bottleneck for the phase transition in the metastable liquid.  Having generated an ensemble of the transition configurations, we also present a new procedure to estimate how fast the system passes through the transition bottleneck, which when combined with knowledge of the probability of formation of a transition embryo yields a prediction of the rate of homogenous bubble nucleation in a model superheated liquid.

[1] M. J. Uline and D. S. Corti, Phys. Rev. Letters 99, 076102 (2007).

[2] P. R. ten Wolde and D. Frenkel, J. Chem. Phys. 109, 9901 (1998).

[3] K. Torabi and D. S. Corti, J. Chem. Phys. 133, 134505 (2010).