Single-step kinetics approximation employing non-Arrhenius temperature functions
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Solid-state reactions ordinarily demonstrate a tangled interplay of various chemical and physical processes. The single-step kinetics approximation resides in substituting a generally complex set of kinetic equations by the sole single-step kinetics equation. It enables to describe the kinetic hypersurface in a simple way irrespective of the complexity of the overall process. The kinetic hypersurface is the dependence of conversion on temperature and time. The functions describing the temperature and conversion components of the hypersurface should be separable. For a complex process, the adjustable parameters in the temperature function have no mechanistic significance so that there is no reason to be confined to the Arrhenius relationship. Two groups of isoconversional methods based on non-Arrhenius temperature functions are presented and the corresponding formulas for isothermal, integral, differential and incremental isoconversional methods are derived. As an example of the method using the explicit expression of the conversion function, the first-order kinetics is treated. Comparing with the methods based on the Arrhenius relationship, the greatest advantage of the methods presented here is that the problems with calculating the temperature integral are eliminated since the corresponding integrals can be expressed in a closed form.
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