Activated Instability of Homogeneous Bubble Nucleation and Growth

Abstract

For the superheated Lennard-Jones liquid, the free energy of forming a bubble with a given particle number and volume is calculated using density-functional theory. As conjectured, a consequence of known properties of the critical cavity [S. N. Punnathanam and D. S. Corti, J. Chem. Phys. 119, 10 224 (2003), the free energy surface terminates at a locus of instability. These stability limits reside, however, unexpectedly close to the saddle point. A new picture of homogeneous bubble nucleation and growth emerges from our study, being more appropriately described as an "activated instability."

Density functional theory of inhomogeneous liquids. III. Liquid-vapor nucleation

“…These would not appear to be physically equivalent to clusters of different sizes at fixed chemical potentials. Uline and Corti have used a similar method to explore bubble nucleation but without the adjustment of the density outside the clusters [10]. This circumvents the objection raised above, but the method has other problems: the generation of discontinuous density profiles and the appearance of spurious instabilities [17].…”

“…For example, such a constraint for a bubble could be (ρ l − ρ(r)) dr = ∆N which defines a profile to be of size ∆N if the total num-ber of atoms is ∆N less than in the uniform fluid. For reasons described elsewhere [17], this particular example of a constraint is not really useful but more realistic constraints have been constructed [9,10,18]. Note however the philosophy of this approach: a path through densityfunction space is defined by the parameter ∆N (or whatever parameters enter the constraint).…”

“…Recent years have seen tremendous progress in the development of simulation methods that circumvent the time and size limitations of simulations to allow for the study of rare events, such as homogeneous nucleation [4,5,6,7]. In parallel, various approaches to a theoretical description of nucleation have been formulated with varying degrees of success [8,9,10]. However, the theoretical description of nucleation is difficult because it is fundamentally a nonequilibrium process: the initial and final states are metastable and stable, respectively, but the transition between them involves a sequence of unstable configurations making the use of equilibrium statistical mechanics difficult.…”

Phase separation dynamics in a two-dimensional magnetic mixture

“…Using Eqs. (6) and (7), the ideal gas contribution becomes (11) where α denotes the thermal de Broglie wavelength of species α. The particle interactions enter into the excess part of the free energy functional, which can be written as…”

“…8 In addition to yielding the equilibrium phase diagram and microscopic fluid structure, DFT techniques have been successfully used to calculate nucleation barriers for state points in the metastable region of the phase diagrams. [9][10][11][12] Based on the success of these approaches, it seems very tempting to use DFT techniques also to tackle the non-equilibrium dynamics of the phase separation, including the growth of nuclei, the actual nucleation pathway, and coarsening processes during spinodal decomposition. Indeed, a) Electronic mail: lichtner@mailbox.tu-berlin.…”