Isoconversional Methods of Thermal Analysis are Incompatible with Turnbull-Fisher Kinetics: Case Study of Crystallization of Piperine from the Melt

Differential scanning calorimetry (DSC) is a useful tool for studying nucleation rate-limited kinetics of crystallization from the melt. However, applying popular isoconversional methods of thermal analysis to such calorimetric data yields incorrect values of the effective activation energy, E_a. Investigating the classical dataset for the temperature-dependent rate of crystallization of piperine from the melt [Tammann, G. Ueber die Abhängigkeit der Zahl der Kerne, welche sich in verschiedenen unterkühlten Flüssigkeiten bilden, von der Temperatur. Z. Phys. Chem. 1898, 25, 441-479], we demonstrate that the Turnbull-Fisher (T-F) equation generates meaningful E_a values, across a broad temperature range, only when it is decoupled from isoconversional analysis. The problem with isoconversional methods is that they are reliant on Arrhenius kinetics, whereas T-F kinetics can exhibit either Arrhenius or non-Arrhenius behavior, depending on the temperature. Consistent with classical nucleation theory (CNT), E_a values for nucleation rate-limited conversions are positive even though the rate typically increases at higher degrees of cooling.