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

• Published in: Crystal research and technology (1979) 2009-03, Vol.44 (3), p.231-247
• Main Author: Sangwal, K.
• Format: Article
• Language: English
• Subjects: industrial crystallization; metastable zone width; nucleation kinetics; organic compounds; potassium compounds; supersaturated solutions
• ISSN: 0232-1300; 1521-4079
• DOI: 10.1002/crat.200800501

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 ΔTmax with cooling rate R is proposed in the form: ln(ΔTmax/T0) = Φ + β lnR, with intercept Φ = {(1–m)/m }ln(ΔHs/RGTlim) + (1/m)ln(f/KT0) and slope β = 1/m. Here T0 is the initial saturation temperature of solution in a cooling experiment, ΔHs is the heat of dissolution, RG is the gas constant, Tlim 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 T0 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 T0 is determined by solute concentration c0. 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 T0, following an Arrhenius‐type equation with an activation energy Esat. 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 Esat 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 Esat. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)