Isoconversional methods of thermal analysis yield activation energies that lack physical meaning for Turnbull-Fisher kinetics: Case study of crystallization of piperine from the melt

Differential scanning calorimetry (DSC) is a useful tool for studying the nucleation rate-limited kinetics of crystallization from the melt. However, applying popular isoconversional methods of thermal analysis to such calorimetric data often yields incorrect values of the activation energy, Ea. Against this backdrop, we investigate 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] to demonstrate that the Turnbull-Fisher (T-F) equation describing nucleation kinetics generates meaningful Ea values, across the entire temperature range, only when it is decoupled from isoconversional or Arrhenius analysis. This is accomplished by digitizing, replotting, and subsequently analyzing the Tammann dataset through application of the T-F equation, alone, the T-F equation used in conjunction with isoconversional analysis, and, lastly, the T-F equation combined with the Arrhenius equation. While the latter two methodologies are discussed thoroughly in a recent work [Vyazovkin S, Sbirrazzuoli N. Non-isothermal crystallization kinetics by DSC: Practical overview. Processes. 2023;11:1438], our goal is to reveal that the fundamental problem with those approaches that results in reporting of negative activation energies is that they are reliant on the assumption of Arrhenius kinetics. That is because T-F kinetics can exhibit both Arrhenius (at large supercooling from the melt) and non-Arrhenius (at moderate supercooling) behavior, depending on the temperature. Consistent with the predictions of classical nucleation theory (CNT), Ea values for nucleation rate-limited conversions are generally positive even though the specific rate often increases at higher degrees of cooling. Reports of negative activation energies are simply a mathematical artifact caused by ignoring the mismatch between Arrhenius and T-F kinetics.