Interpreting the Activated Rate Theory for Solid-Phase Crystallization: Comparing Lactose and Sucrose

Abstract

The activated rate theory (ART) for solid-phase crystallization has been interpreted to assess its key features with previous data for spray-dried lactose and new data for spray-dried sucrose. The theory implies that the kinetic parameters for the two sugars should be different due to the differences in their structural configurations. The activation enthalpy for solid-phase crystal growth has been found to be 39 ± 2 kJ/mol for lactose and 68 ± 4 kJ/mol for sucrose. These activation enthalpies are close to the values for liquid-phase crystallization (40 kJ mol−1 for lactose; 66–75 kJ mol−1 for sucrose) from previous literature, suggesting that the theory might apply to both liquid- and solid-phase crystallization. There are also physical arguments for suggesting that the activated state in the new theory has features of both solid- and liquid-phase crystallization. For lactose and sucrose, the crystal growth rate constants at 25°C have been found to be 1.4 × 10−4 s−1and 2.5 × 10−5 s−1, respectively, similar to the literature values of 1.3 × 10−4 s−1and 3 × 10−5 s−1, respectively. The difference in the thermodynamic parameters between the two sugars has been found to be significant, as expected from the differences in their structures. Interpreting the sucrose data in terms of the Williams-Landel-Ferry equation and the Avrami equation has shown their limitations and inconsistencies for the new sucrose data, as found previously for lactose. Key features of the ART are highlighted and discussed. These features include minimum activation enthalpies and maximum activation entropies at particular moisture contents for each sugar and minimum and maximum moisture contents below which crystallization is predicted to occur very slowly.