Homogeneous Nucleation in a Miscibility Gap System. A Critical Test of Nucleation Theory

Abstract

A critical test of the classical nucleation theory applied to condensed phases has been carried out for the liquid miscibility gap system, methylcyclohexane-perfluoromethylcyclohexane (C7H14–C7F14). The densities of, and the interfacial free energies between the coexisting liquid phases have been measured as a function of temperature. The interfacial free energy is found to vary as the 32 power of the critical temperature Tc, less the experimental temperature, and these data are used to calculate the gradient energy parameter κ in the Cahn-Hilliard theory of nucleation. The magnitudes of the relevant parameters are such that the Cahn-Hilliard theory reduces to the classical theory for the present system. These data, together with literature data on the thermodynamic properties of the bulk solutions, enable the degree of undercooling for a sensible nucleation rate to be calculated from classical theory. The experimentally determined undercoolings necessary to nucleate the C7H14-rich phase from the solution are found to be much greater than those predicted by the classical theory by factors ranging from 8.5 at 10 deg below Tc to 340 at 0.3 deg below Tc. These very large discrepancies are attributable to the breakdown of the traditional approximation in the classical nucleation theory that the number of molecules involved in the embryo population is a negligible fraction of the number of molecules in the system. When this approximation is avoided, the very complicated expression that results can be evaluated for the present case, leading to reasonable agreement between the predicted and the observed undercoolings. This is believed to constitute a satisfactory verification of the ``corrected'' classical theory of nucleation for condensed systems. The ``embryo population'' factor can be neglected in homogeneous nucleation in solidification and condensation (except near the critical temperature) and in most of the corresponding cases of heterogeneous nucleation. However, it is extremely important for nucleation in miscibility gap systems, or in any system in which the properties of the parent and daughter phases become identical at a critical temperature.