Model-Free: Numerical Optimization
Numerical Optimization optimizes the activation energy and pre-exponential factor numerically to achieve the best agreement between simulated and experimental curves. At least two measurements are required.
Numerical determination of activation energy and pre-exponential factor using the points at the same conversion (0.01, 0.02, …, 0.99) from the measurements at different heating rates or different isothermal conditions. There is no assumption about the reaction type.
Analysis
Analysis shows a graphic of Log(ConversionRate) vs. inverse temperatures of the points at the same conversion. Linear fit curves are shown for each conversion value specified:
Any of these isoconversional lines can be shown selecting All, None, Default or Custom:
Activation energy and pre-exponential results are found from the slope and intersect of these linear fits.
The calculated Correlation R is 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:
The chart presents decimal logarithm of pre-exponential factor.
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 Numerical Optimization:
In this case, a good match between data and simulated values is observed. This indicates that the analysis based on Numerical Optimization is reliable in this case.
Advantages
Advantages of this method:
- for multiple-step reactions without parallel reaction steps
- each reaction point is evaluated
- suitable for dynamic and isothermal measurements
Disadvantages
Disadvantages of this method:
- for parallel and independent reactions, Numerical Optimization gives the mean values of Ea