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Sigmoidal Nucleation and Growth Curves Across Nature Fit by the Finke–Watzky Model of Slow Continuous Nucleation and Autocatalytic Growth: Explicit Formulas for the Lag and Growth Times Plus Other Key Insights
Ist Teil von
Journal of physical chemistry. C, 2017-03, Vol.121 (9), p.5302-5312
Ort / Verlag
United States: American Chemical Society
Erscheinungsjahr
2017
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Sigmoidal kinetic curves have been reported for a number of cooperative phenomena in nature. These curves may be fit by purely mathematical functions that, however, do not correspond to any physical model. The 1997 Finke–Watzky (F–W) two-step model of slow, continuous nucleation (A → B, rate constant k 1) and fast, autocatalytic growth (A + B → 2B, rate constant k 2) provides both a physical model and a mathematical solution. As a result, the F–W two-step kinetic model has been successfully applied to a large number of cooperative phenomena throughout nature that display sigmoidal kinetic curves. Herein, we derive formulas for the first, second, and third derivatives of the concentration of product versus time, [B] t , expressed in terms of the F–W parameters k 1, k 2, and the initial concentration of monomer, [A]0. Mathematical expressions are then derived for key empirical parameters in sigmoidal curves, including the induction period and (maximum) slope, which are then examined under the limit k 1 ≪ k 2[A]0 where nucleation and growth are well-separated in time. The resultant seven previously unavailable equations provide a better fundamental and intuitive understanding of sigmoidal curves across nature well-fit by the F–W two-step mechanism.