Dispersive kinetic models for isothermal solid-state conversions and their application to the thermal decomposition of oxacillin

The authors recently published works in which the use of two novel equations for modeling the dispersive kinetics observed in various solid-state conversions are described. These equations are based on the assumptions of a ‘Maxwell-Boltzmann (M-B)-like’ distribution of activation energies and a first-order rate law. In the present work, it is shown that it may be possible to expand the approach to include mechanisms other than first-order, i.e. some of those commonly encountered in the field of thermal analysis, thus obtaining ‘dispersive versions’ of these kinetic models. The application of these dispersive kinetic models to the slightly sigmoidal, isothermal conversion-time (x-t) data of Rodante and co-workers for the degradation of the antibiotic, oxacillin, is described. This is done in an effort to test the limitations of the proposed dispersive models in describing kinetic data which is not clearly sigmoidal (i.e. as shown in previous works). Finally, it is demonstrated that, using graphical analysis, the typically sigmoidal x-t plots of first-order dispersive processes are the direct result of (asymmetric) activation energy distributions that are either ‘∩-shaped’ (for heterogeneous conversions) or ‘∪-shaped’ (for homogeneous conversions) in appearance, i.e. when the activation energy is plotted as a function of conversion. This finding lends support to the founding hypothesis of the authors’ approach for modeling dispersive kinetic processes: the existence of ‘M-B-like’ distributions of activation energies.