On the linear and integral models for metastable zone width determined by solution cooling method

From a consideration of fundamental concepts of metastable zone width (MSZW), as determined by the maximum undercooling Delta T-m that a solution saturated at temperature T-0 can withstand without crystallization as a function of cooling rate R-L, final equations of three deterministic approaches, namely: solute-supply, integral nucleation and integral nucleation-plus-growth models, based on classical three-dimensional nucleation theory are derived in a consistent manner, and then used to analyze the published experimental data of Delta T-m of glycine-water, glutaric acid-acetic acid and potassium tetraborate tetrahydrate-water systems saturated at different temperatures T-0. From analysis of the experimental data of MSZW of glycine-water system trends of variations in the values of the nucleation kinetic parameters of the equation of the classical nucleation theory, obtained by the determininstic integral nucleation model and the conventional stochastic theory, are compared and discussed. It was found that: (1) equation of the simple solute-supply approach satisfactorily explains the dependence of Delta T-m of solutions on cooling rate R-L at their different saturation temperature T-0, and enables to estimate nucleation parameters such as preexponential factor A and solid-solution interfacial solution gamma(eff) associated with nucleation, and (2) the values of gamma(eff) obtained from the MSZW data are relatively low and suggest the occurrence of crystallization by heterogeneous nucleation. Finally, the nature of nucleation encountered in MSZW measurements by the polythermal method is discussed.

Automated summary

Based on classical nucleation theory, final equations regarding the metastable zone width were derived using three deterministic approaches, which were then applied to analyze experimental data from different systems. The analysis compared and discussed trends in nucleation kinetic parameters values obtained from the deterministic integral nucleation model and the conventional stochastic theory. Results showed that the solute-supply approach could explain the dependency of solutions' Delta T-m values on cooling rate at different saturation temperatures and estimate nucleation parameters, while relatively low values of the solid-solution interfacial solution gamma(eff) suggested crystallization by heterogeneous nucleation. The nature of nucleation encountered in the MSZW measurements by the polythermal method was also discussed.