Studies on the freezing of pure liquids - II. The kinetics of homogeneous nucleation in supercooled liquids

Abstract

A modified form of Turnbull & Fisher’s equation for the rate of nueleation in pure liquids is derived from the more general solution of Frenkel to the non-equilibrium steady -state kinetic problem . Recent developments in relaxation theory, based on the Zeldovich— Frenkel formulation of the time-dependent flow of embryos over the size variable g , show that under certain conditions the nucleation time lag may be exceedingly sensitive to the initial state of the condensing system. Frisch’s integral for the nucleation time lag is evaluated for two initial distributions of embryo size. The results, which are of general form, are used to derive expressions for the time lag in supercooled liquids. Methods are given for estimating certain parameters required in the computation of time lags in supercooled liquids.

The crystal-fluid interfacial free energy and nucleation rate of NaCl from different simulation methods

“…Contrary to γ cf , the nucleation rate can be directly measured experimentally. [34][35][36] By means of our seeding simulations, CNT, and calculations of the attachment rate of particles to the critical cluster, we estimate the nucleation rate and find a good agreement between numerical simulations and experiments.…”

“…In Fig. 11(b), we also include the only available experimental data for the nucleation of NaCl from its melt [34][35][36] (blue triangle). Remarkably, the experimental data are fully consistent with the predictions of the model.…”

Seeding approach to crystal nucleation

“…Whereas the nucleation rate can be measured experimentally, [2][3][4][5][6] a microscopic description of the crystal nucleus remains elusive to current experimental techniques, due to the small size (∼nm) and short life (∼ns) of the nucleus. 7 To overcome this experimental shortcoming two different approaches are pursued.…”

Vapor condensation under nonequilibrium conditions

“…- (1) where F is the number of single vapor molecules, Ng is the number of g-molecule nuclei present, and Tf is the free energy change associated with the condensation of an individual nucleus. Since embryos smaller than the critical size cannot exist in the metastable vapor phase, he further assumed that the rate of condensation will be proportional to the number of nuclei present at any time.…”

“…To accomplish this purpose, the plan of approach is as follows: (1) to assume a plausible mechanism by which condensation can occur, (2) to derive a rate expression, based on this mechanism, for the homogeneous nucleation of the general vapor, (3) to elucidate this general expression for the different types of vapor important in nuclear reactor technology, (4) to account for the effect of surfaces and seeding (heterogeneous nucleation) on ths rate of condensation, and (5) to apply the nucleation theory developed to water vapor and compare the results with experimental data.…”