| Abstract
| - Many solid-state reactions and phase transformations performed under isothermal conditions give rise toasymmetric, sigmoidally shaped conversion−time (x−t) profiles. The mathematical treatment of such curves,as well as their physical interpretation, is often challenging. In this work, the functional form of a Maxwell−Boltzmann (M−B) distribution is used to describe the distribution of activation energies for the reagent solids,which, when coupled with an integrated first-order rate expression, yields a novel semiempirical equationthat may offer better success in the modeling of solid-state kinetics. In this approach, the Arrhenius equationis used to relate the distribution of activation energies to a corresponding distribution of rate constants for theindividual molecules in the reagent solids. This distribution of molecular rate constants is then correlated tothe (observable) reaction time in the derivation of the model equation. In addition to providing a versatiletreatment for asymmetric, sigmoidal reaction curves, another key advantage of our equation over other modelsis that the start time of conversion is uniquely defined at t = 0. We demonstrate the ability of our simple,two-parameter equation to successfully model the experimental x−t data for the polymorphic transformationof a pharmaceutical compound under crystallization slurry (i.e., heterogeneous) conditions. Additionally, weuse a modification of this equation to model the kinetics of a historically significant, homogeneous solid-state reaction: the thermal decomposition of AgMnO4 crystals. The potential broad applicability of our statistical(i.e., dispersive) kinetic approach makes it a potentially attractive alternative to existing models/approaches.
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