Power Law and Arrhenius Approaches to the Melting Kinetics of Superheated Crystals: Are They Compatible?

The melting kinetics of superheated crystals has been recently described via two entirely different approaches. One is based on a power law model proposed by Toda and co-workers. Another makes use of the traditional Arrhenius model. The present work explores the compatibility of these two approaches. By using the formalism of the Ozawa and Kissinger methods, it derives equations that allow one to use the power law parameters to estimate the activation energy of melting. The value estimated in such a manner is demonstrated to decrease with temperature (i.e., with the superheating) just as the activation energy determined via the Arrhenius treatment. It is noted that the decreasing dependence is consistent with the theories of nucleation and growth. Differential scanning calorimetry data on melting of superheated crystals of glucose are used to illustrate the similarity of the activation energies obtained via the two approaches. It is suggested that the equations derived can be used to supplement the power law treatment by estimating the activation energies, whose values can provide insights into the process of crystal melting, in particular, in its cooperative nature.