Toward a molecular theory of homogeneous bubble nucleation: II. Calculation of the number density of critical nuclei and the rate of nucleation.

In the present paper, we develop a method to calculate the rate of homogeneous bubble nucleation within a superheated L-J liquid based on the (n,v) equilibrium embryo free energy surface introduced in the first paper (DOI: 10.1021/jp404149n). We express the nucleation rate as the product of the concentration of critical nuclei within the metastable liquid phase and the relevant forward rate coefficient. We calculate the forward rate coefficient of the critical nuclei from their average lifetime as determined from MD simulations of a large number of embryo trajectories initiated from the transitional region of the metastable liquid configuration space. Therefore, the proposed rate coefficient does not rely on any predefined reaction coordinate. In our model, the critical nuclei belong to the region of the configuration space where the committor probability is about one-half, guaranteeing the dynamical relevance of the proposed embryos. One novel characteristic of our approach is that we define a limit for the configuration space of the equilibrium metastable phase and do not include the configurations that have zero committor probability in the nucleation free energy surface. Furthermore, in order to take into account the transitional degrees of freedom of the critical nuclei, we develop a simulation-based approach for rigorously mapping the free energy of the (n,v) equilibrium embryos to the concentration of the critical nuclei within the bulk metastable liquid phase.