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Solid-state kinetic models: basics and mathematical fundamentals.

Ammar Khawam1, Douglas R Flanagan

  • 1Division of Pharmaceutics, College of Pharmacy, University of Iowa, Iowa City, Iowa 52242, USA.

The Journal of Physical Chemistry. B
|September 1, 2006
PubMed
Summary

This study reviews solid-state kinetic models, classifying them by mechanism (nucleation, geometrical contraction, diffusion, reaction order) and detailing their mathematical development for better understanding.

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Area of Science:

  • Solid-state chemistry
  • Chemical kinetics

Background:

  • Numerous solid-state kinetic models have been developed over the last century.
  • Some models lack theoretical justification or are fundamentally incorrect.
  • Current models are categorized based on their underlying mechanistic principles.

Purpose of the Study:

  • To provide a comprehensive summary of commonly employed solid-state kinetic models.
  • To present the mathematical development of these models.
  • To clarify the classification of models based on mechanistic grounds.

Main Methods:

  • Literature review of solid-state kinetic models.
  • Classification of models based on mechanistic categories: nucleation, geometrical contraction, diffusion, and reaction order.
  • Detailed presentation of the mathematical derivations for each model type.

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Main Results:

  • Identification and categorization of prevalent solid-state kinetic models.
  • Explanation of the theoretical basis and mathematical formulation for each model.
  • Distinction between mechanistically sound models and those lacking theoretical rigor.

Conclusions:

  • A clear framework for understanding and applying solid-state kinetic models is presented.
  • The mathematical underpinnings of nucleation, geometrical contraction, diffusion, and reaction order models are elucidated.
  • This work serves as a valuable resource for researchers in solid-state kinetics.