Vyazovkin Advanced Analysis

Vyazovkin Analysis is the model-free (isoconversional) method of kinetic analysis calculating dependence of activation energy E(α) on degree of conversion α for experiments with arbitrary temperature program, including also dynamic and isothermal conditions.

Vyazovkin Advanced method is different from Vyazovkinmethod.

It is always necessary to check if this model-free method is valid to be used and is applicable because of restrictions of model-free methods.

Vyazovkin analysis belongs to the group of integral model-free methods where firstly, the integral of main kinetic equation (1) over temperature must be found from begin of reaction to the current conversion α (Eq. 1):

\frac{d\alpha}{dt} = A(\alpha) \bullet f(\alpha) \bullet exp\left( \frac{- E(\alpha)}{RT} \right)

Integral over time for temperature program T(t) (Eq. 2):

\int_{0}^{\alpha}\frac{d\alpha}{A(\alpha) \bullet f(\alpha)} = \int_{t_{0}}^{t}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}

For different experiments with numbers i ang j at the same degree of conversion α, the following can be written (Eq. 3):

\int_{t_{0}}^{t_{\alpha i}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt} = \int_{t_{0}}^{t_{\alpha j}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}

And finally, the following function should be minimized to find activation energy E(α) [1,2] (Eq. 4):

\psi(\alpha) = \sum_{i}^{}{\sum_{j \neq i}^{}\frac{\int_{t_{0}}^{t_{\alpha i}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}}{\int_{t_{0}}^{t_{\alpha j}}{\exp\left( \frac{- E(\alpha)}{RT(t)} \right)dt}}}

Where t_αi is the time at which the conversion α is reached for the i-th measurement.

It is always necessary to simulate the curves by Vyazovkin method and compare them with experiment. This comparison helps to check if Vyazovkin method is suitable for analysis of the current reaction.

Kinetics Neo

This method is not used in Kinetics Neo. For dynamic data with constant heating rate please use Vyazovkin Analysis method in Kinetics Neo.

For arbitrary temperature program please use Friedman Analysis method in Kinetics Neo.

References

Vyazovkin, S.; Dollimore, D. Linear and Nonlinear Procedures in Isoconversional Computations of the Activation Energy of Nonisothermal Reactions in Solids. J. Chem. Inf. Comput. Sci.36(1), 42–45 (1996). https://doi.org/10.1021/ci950062m