Peter J. Skrdla

Dispersive kinetic models (DKMs) based on the concept of a distribution of activation energies have shown much promise in describing complex reaction transients. In particular, DKMs exhibiting a time (t)-dependent rate coefficient, k, of approximately Gaussian functional form provide the most insight into the kinetics because they do not rely on unit-less, empirical parameters [P.J. Skrdla, J. Phys. Chem. A 113, 9329 (2009)]. The physical basis of the Gaussian behaviour is investigated using a dispersive simple harmonic oscillator (DSHO) description of Marcus-type reactions studied on the ultrafast timescale. The DSHO description is found to support the Gaussian t-dependence of k over relatively short time periods. Moreover, in cases where the transition state survives more than one vibration of the predominant reactive mode, a periodicity in k is observed that is also consistent with empirical observations.

Kinetic models for nucleation, denucleation, Ostwald ripening (OR), and nanoparticle (NP) aggregation are presented and discussed from a physicochemical standpoint, in terms of their role in current NP preparations. Each of the four solid-state mechanisms discussed predict a distinct time dependence for the evolution of the mean particle radius over time. Additionally, they each predict visually different particle size distributions (PSDs) under limiting steady-state (time-independent) conditions. While nucleation and denucleation represent phase transformation mechanisms, OR and NP aggregation do not. Thus, when modeling solid-state kinetics relevant to NP processing, either the time evolution of the mean particle radius or the fractional conversion data should be fit using appropriate models (discussed herein), without confusing/combining the two classes of models. Experimental data taken from the recent literature are used to demonstrate the usefulness of the models in real-world applications. Specifically, the following examples are discussed: the preparation of bismuth NPs, the synthesis of copper indium sulfide nanocrystals, and the aggregation of neurological proteins. Because the last process is found to obey reaction-limited colloid aggregation (RLCA) kinetics, potential connections between protein aggregation rates, the onset of neurological disease, and population lifespan dynamics are suggested by drawing a parallel between RLCA kinetics and Gompertz kinetics. The physical chemistry underpinning NP aggregation is investigated, and a detailed definition of the rate constant of aggregation, k_a, is put forth that provides insight into the origin of the activation energy barrier of aggregation. For the two nanocrystal preparations investigated, the initial kinetics are found to be well-described by the author’s dispersive kinetic model for nucleation-and-growth, while the late-stage NP size evolution is dominated by OR. At intermediate times, it is thought that the two mechanisms both contribute to the NP growth, resulting in PSD focusing as discussed in a previous work [Skrdla, P. J. J. Phys. Chem. C2012, 116, 214–225]. On the basis of these two mechanisms, a synthetic procedure for obtaining monodisperse NP PSDs, of small and/or systematically targeted mean sizes, is proposed.

The potential applications of dispersive kinetic models range from solid-state conversions to gas-phase chemical physics and to microbiology. Here, the derivation and application of two such models, for use in solid-state applications, is presented. The models are based on the concept of a Maxwell−Boltzmann distribution of activation energies. The ability of the models to fit/explain an assortment of asymmetric, sigmoidal conversion-versus-time transients presented in the recent literature, as well as to provide physicochemical interpretations of the kinetics via the two fit parameters, α and β, makes them a powerful tool for understanding nucleation/denucleation rate-limited processes that are involved in many phase transformations, dissolutions and crystallizations.