Model-Free:Vyazovkin
The model-free Vyazovkin method is created for analysis of dynamic measurements with different heating rates.
The Vyazovkin analysis is an integral isoconversional method, where the measurements are analyzed for multiple conversion levels. At least two dynamic measurements with positive heating rates are required.
The determination of the activation energy is using the points at the same conversion (0.01, 0.02, …, 0.99, 1.00) from the measurements at different heating rates. There is no assumption about the reaction type.
Short Theory
Known kinetic equation
has the following view for the constant heating rate β:
For different heating rates βi and βj at the same degree of conversion αk, the following can be written:
Here Tki is the temperature at which the conversion αk is reached for the heating rate β i.
And finally the following function should be minimized:
This last equation is used for calculations.
The calculated Correlation Ris explained in section Statistics.
Activation Energy
Pressing
shows the calculated activation energy including error bar – if the checkbox Show Error Bars is activated:
Pre-Exponential Factor
Pressing
shows the calculated pre-exponential including error bar – if the checkbox Show Error Bars is activated:
Master Plot
Pressing
shows the calculated ratio f(α)/f(0.5):
The ratio f(α)/f(0.5) is useful for the graphical estimation of the reaction type for single-step processes.
Conversion Fit
Pressing
shows experimental and simulated values, where the simulation is done based on the results of the Vyazovkin analysis:
Advantages
Advantages of this method:
-for multiple-step reactions without parallel reaction steps
-each reaction point is evaluated
Disadvantages
Disadvantages of this method:
-suitable only for dynamic measurements
- for parallel and independent reactions, the Vyazovkin method gives the mean values ofEa
Related Literature
S. Vyazovkin, A. K. Burnham, J. M.Criado, L. A. Pérez-Maqueda, C.Popescu, N.Sbirrazzuoli, ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data,ThermochimicaActa 520 (2011) 1-19, doi:10.1016/j.tca.2011.03.034(Eqs 3.11-3.12)