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Using a power-law relation between three-dimensional nucleation rate J and dimensionless supersaturation ratio S, and the theory of regular solutions to describe the temperature dependence of solubility, a novel Nývlt-like equation of metastable zone width of solution relating maximum supercooling ΔT max with cooling rate R is proposed in the form: ln(ΔT max /T 0 ) = Φ + βlnR, with intercept Φ = {(1−m)/m}ln(ΔH s /R G T lim ) + (1/m)ln(f/KT 0 ) and slope β = 1/m. Here T 0 is the initial saturation temperature of solution in a cooling experiment, ΔH s is the heat of dissolution, R G is the gas constant, T lim is the temperature of appearance of first nuclei, m is the nucleation order, and K is a new nucleation constant connected with the factor f defined as the number of particles per unit volume. It was found that the value of the term Φ for a system at saturation temperature T 0 is essentially determined by the constant m and the factor f. The value of the factor f for a solute−solvent system at initial saturation temperature T 0 is determined by solute concentration c 0 . Analysis of the experiment data for four different solute-water systems according to the above equation revealed that: (1) the values of Φ and m for a system at a given temperature depend on the method of detection of metstable zone width, and (2) the value of slope β = 1/m for a system is practically a temperature-independent constant characteristic of the system, but the value of Φ increases with an increase in saturation temperature T 0 , following an Arrhenius-type equation with an activation energy E sat . The results showed, among others, that solubility of a solute is an important factor that determines the value of the nucleation order m and the activation energy E sat for diffusion. In general, the lower the solubility of a solute in a given solvent, the higher is the value of m and lower is the value of E sat .

Experimental data on the maximum supercooling ΔT max, a measure of metastable zone width, for solutions saturated at a temperature T 0, as a function of cooling rate R are analyzed, for some solute−solvent systems chosen as examples, using Nývlt’s semiempirical approach and a new approach based on the classical theory of three-dimensional nucleation combined with the formation of n-sized embryos from monomers according to the law of mass action. Instead of a linear relation between ln(ΔT max) and lnR of the Nývlt’s approach, the new approach predicts a linear dependence of (T 0/ΔT max)2 on lnR with slope F 1 and intercept F. The quantity F 1/F is independent of saturation temperature T 0, characteristic of a solute−solvent and is associated with the growth of the stable three-dimensional nuclei to visible entities. The value of F 1 is determined by thermodynamic and solvation processes, while that of F is governed by thermodynamic and kinetic parameters as well as processes associated with solvation of solute ions/molecules and their transport in the solution. Limitations of Nývlt’s approach and advantages of the new approach in terms of its physical basis are exposed. It is pointed out that the new approach can also be extended to explain the value of metastable zone width by the isothermal method and to explain the effect of saturation temperature and impurities on metastable zone width.

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