Systematically extending classical nucleation theory

Abstract

The foundation for any discussion of first order phase transitions is classical nucleation theory (CNT). CNT, developed in the first half of the twentieth century, is based on a number of heuristically plausible assumptions and the majority of theoretical work on nucleation is devoted to refining or extending these ideas. Ideally, one would like to derive CNT from a more fundamental description of nucleation so that its extension, development and refinement could be developed systematically. In this paper, such a development is described based on a previously established (Lutsko 2012 J. Chem. Phys. 136 034509) connection between CNT and fluctuating hydrodynamics. Here, this connection is described without the need for artificial assumptions such as spherical symmetry. The results are illustrated by application to CNT with moving clusters (a long-standing problem in the literature) and the construction of CNT for ellipsoidal clusters.CNT provides the language used in all discussions of nucleation however, its accuracy has long been a subject of debate. Recent experiments on the homogeneous nucleation of argon droplets from vapor have reported nucleation rates 10-20 orders of magnitude higher than those predicted by CNT [6,7]. The rates observed for water are in better agreement at low temperatures but deviates as temperature increases [8]. Recent large-scale simulations of droplet nucleation in a Lennard-Jones system show smaller deviations in the nucleation rate compared to CNT, 8-13 orders of magnitude, but that the agreement was better for the size of the critical nucleus [9]. This is largely in agreement with earlier studies such as [10]. Note that this discussion pertains to absolute values for nucleation rates and not to the less demanding test of fitting the functional dependence of the rate on supersaturation. Another distinction is that sometimes the quantities required in CNT, such as the rate at which molecules attach to a cluster, are taken directly from simulation and in this case, good agreement with CNT is often found (as discussed, e.g. in [9] above and in the case of crystallization, in e.g. [11]). While such tests provide confirmation of some of the underlying concepts of CNT, it simply makes more precise the origin of the discrepancies with CNT. Similarly, the introduction of e.g. size-dependent surface tensions can also improve the theoretical predictions at the expense of having to import these from simulation or by determining them via direct fitting of the nucleation data (see, e.g., [12] for a recent example). All of these are useful procedures for improving CNT. The theoretical challenge is to link CNT to more fundamental theories from which these refinements emerge naturally, without empirical input.While CNT is the basis for a large part of the work on nucleation, it is clearly a crude approximation and, indeed, has internal inconsistencies. For example, in the capillary model for the free energy the density of the mother phase outside the cluster is assumed to be constant but in the tra...

Density functional theory of gas–liquid phase separation in dilute binary mixtures

“…We treat a neutral binary mixture in DFT [21][22][23][24], where the first species is a solvent and the second one is a dilute solute. The number densities n 1 (r) and n 2 (r) are coarse-grained smooth functions of space.…”

“…In the literature [22][23][24], φ ij (r) has often been set equal to the attractive part of the Lennard-Jones potential characterized by the parameters d ij and ǫ ij . For r > 2 1/6 d ij it is expressed as…”

“…In the previous papers on dynamical DFT [24,[34][35][36], the shear viscosity was introduced to include the hydrodynamic interaction among colloidal particles.…”

“…In this paper, we investigate two-phase states of dilute binary mixtures at T = 300 K using the density functional theory (DFT) [3,[21][22][23][24] on the basis of the Carnahan-Starling model for binary mixtures [25,26]. As in the case of O 2 in water, we determine the model parameters in Ref.…”

“…Within the scheme of DFT, some attempts have been made to describe dynamics of colloidal particles in solvent without [32,33] and with [24,[34][35][36] the hydrodynamic interaction. We also mention dynamic van der Waals theory with gradient entropy and energy [37], which is a generalization of the original van der Waals theory [38].…”