(443b) Towards a Molecular Theory for Homogeneous Bubble Nucleation in Metastable Liquids

Homogeneous bubble nucleation refers to the process by which a first-order phase transition occurs within a bulk metastable liquid, in the absence of impurities or external perturbations. We report an equilibrium embryo definition for homogeneous bubble nucleation based on the following two order parameters: the number of particles n contained within a spherical volume v, which are in constrained equilibrium with the surrounding superheated liquid. The reversible work of formation, or the underlying free energy surface, of these (n,v) embryos within the superheated Lennard-Jones liquid is generated via several novel Monte Carlo simulation procedures. By doing so, we also emphasize several key aspects that any well-formulated equilibrium based theory of homogeneous nucleation must address. Namely, within the suggested embryo definition any configuration of the particles at a fixed location in space must be capable of being mapped onto one and only one point in the order parameter space. Moreover, the suggested equilibrium-based model must be able to identify the transitional configurations that, based on a committor probability analysis, are dynamically relevant to the nucleation process. Another novel characteristic of the developed theory is that we define a limit for the configuration space of the metastable phase. Hence, those configurations that have a zero committor probability are not included in the free energy surface. Finally, we develop a simulation-based algorithm that non-redundantly relates the number density of the critical nucleation sites to their free energies of formation (The critical nuclei are located close to the boundary of the metastable phase configuration space where the committor probability is about one half). In turn, this allows us to determine the forward rate coefficient of the critical nuclei based on their average life times calculated via MD simulation of a large number trajectories initiated from the transitional region of the configuration space. We compare our nucleation rate predictions to those obtained from other methods, and discuss the limitations of all of these approaches.