A novel self‐consistent Nývlt‐like equation for metastable zone width determined by the polythermal method

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 Δ T max with cooling rate R is proposed in the form: ln(Δ T max / T 0 ) = Φ + β ln R , with intercept Φ = {(1– m )/ m }ln(Δ H 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, Δ H 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 . (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)