(196a) The Influence of Critical Cavities on Homogeneous Bubble Nucleation: a New Picture of Bubble Formation?
A recent study of cavity formation in model superheated liquids (Punnathanam and Corti, 2003, J. Chem. Phys. 119, 10224) verified the existence of a so-called critical cavity: superheated liquids containing cavities (spherical regions devoid of particle centers) greater than the critical size were found to be thermodynamically unstable. In addition, the size of the critical cavity was found to be a lower bound to the size of the critical bubble (the saddle point on the free energy surface of bubble formation), while the reversible work of forming the critical cavity was found to be a tight upper bound to the reversible work of forming the critical bubble (a crucial quantity appearing in the expression for the rate of bubble nucleation). Taken together, these two bounds plausibly suggest that the free energy surface of bubble formation, characterized by a bubble with a given number of particles n contained within a given volume v, should be quite different from the standard description of this surface. For example, one suspects that for any n each bubble will have its own critical size, larger than both the radius of the critical cavity and the critical radii for smaller n, beyond which any attempted increase in the volume of the bubble will cause the superheated liquid to become unstable. Consequently, a line of instabilities should appear beyond the bubble nucleation activation barrier. If, in turn, these instabilities are found to reside near the saddle point on the free energy surface, the molecular mechanism of bubble nucleation and growth may be quite different from previous descriptions.
To investigate in more detail the above conjecture, we adapt density functional theory (DFT) to calculate the (n, v) free energy surface of reversible bubble formation for the pure component superheated Lennard-Jones liquid. The new DFT calculations, which constrain the number of particles located inside the bubble for a fixed radius, confirm that after the free energy barrier has been surmounted the free energy surface abruptly ends along a locus of instabilities. In contrast to the classical picture of bubble nucleation, in which the surface continues indefinitely and describes the rapid, though reversible, growth beyond the barrier, the DFT results suggest that liquid-to-vapor liquid nucleation is more appropriately described by an ?activated instability?. We also present molecular simulation results that validate the DFT predictions. Furthermore, the free energy surface reveals that the saddle point, which still corresponds to the critical bubble, is not the only pathway a bubble embryo may take in order to cross the activation barrier. The ridge corresponding to the maximum free energy for each n that leads to the critical bubble is not steep, suggesting that an embryo will more likely than not surmount the barrier along pathways that do not pass through the saddle point. We discuss the implications of this flat ridge for the mechanism of bubble nucleation near the thermodynamic spinodal.