Application of solid-state kinetics to desolvation reactions

Most solid-state kinetic principles were derived from those for homogenous phases in the past century. Rate laws describing solid-state degradation are more complex than those in homogenous phases. Solid-state kinetic reactions can be mechanistically classified as nucleation, geometrical contraction, diffusion and reaction order models. Experimentally, solid-state kinetics are studied either isothermally or nonisothermally. Many mathematical methods have been developed to interpret experimental data for both heating protocols. These methods generally fall into one of two categories: model-fitting and model-free. Historically, model-fitting methods were widely used because of their ability to directly determine the kinetic triplet (i.e., frequency factor [A], activation energy [Ea] and model). However, these methods suffer from several problems among which is their inability to uniquely determine the reaction model. This has led to the decline of these methods in favor of isoconversional (model-free) methods that evaluate kinetics without modelistic assumptions. However, isoconversional methods do not compute a frequency factor nor determine a reaction model which are needed for a complete and accurate kinetic analysis. A new approach was proposed that combines the power of isoconversional methods with model-fitting methods. It is based on using isoconversional methods instead of traditional statistical model-fitting methods to select the reaction model. Once a reaction model has been selected, the activation energy and frequency factor can be determined for that model. This approach was investigated for simulated and real experimental data for desolvation reactions of sulfameter solvates. Controversies have arisen with regard to interpreting solid-state kinetic results which include variable activation energy, calculation methods and kinetic compensation effects. The concept of variable activation energy in solid-state reaction kinetics has caused considerable debate because this behavior has been viewed by some as a violation of basic chemical kinetic principles. Activation energy variation has been detected by isoconversional or "model-free" calculation methods which generate activation energy as a function of reaction progress. The relationship between calculation methods and artifactual variation in activation energy was investigated by employing model-fitting and isoconversional methods to analyze both simulated and experimental data. The experimental data was for the sulfameter-dioxolane solvate desolvation by TGA. It was shown that variable activation energy in simple reactions could be an artifact resulting from the use of isoconversional methods; this artifactual behavior can be seen in both isothermal and nonisothermal kinetic experiments. Therefore, care should be taken when interpreting kinetic results from isoconversional methods. If the variation in activation energy is artifactual, this variation can lead to a false mechanistic conclusion about a reaction being complex while, in fact, it is not. Artifactual variation can be reduced by careful experimental design and control of experimental variables in addition to experimental replication, so that averaged kinetic parameters and their confidence intervals can be estimated. The solid-state stability of several structurally related solvates of sulfameter (5-methoxysulfadiazine) was investigated by studying the kinetics of their desolvation reaction both isothermally and nonisothermally. Calculated kinetic parameters were compared and related to the crystal structure of these solvates. A relationship was established between desolvation kinetic parameters (e.g., activation energy) and the solvent size; the larger the solvent molecule, the higher its activation energy. The solid-state reaction models selected also corresponded to the single crystal structure of the sulfameter-solvate system in which the solvent molecules were in cavities. Finally, it was found that kinetic parameters obtained isothermally and nonisothermally were not in agreement. Therefore, kinetic results from one may not be extended to the other.