Model-Free Analysis in Kinetics Neo

Model-free analysis: There is no assumption of the reaction type

Model-free analysis allows for determination of the activation energy of a reaction process without assuming a kinetic model for the process. Also, the reaction type is usually not required to calculate the activation energy. However, it is not possible to determine the number of reaction steps, their contribution to the total effect or the order in which they occur.

Model-free analysis is based on two assumptions:

1. The reaction can be described by only one kinetic equation for the degree of reaction α:

Model Free Formula

where E(α) is the activation energy depending on the conversion α, and A(α) is the pre-exponential factor.

2. The reaction rate at a constant value of conversion is only a function of temperature.

Model-Free Methods in Kinetics Neo

In Kinetics Neo, the following methods can be used:

  • ASTM E698,
  • ASTM E2890,
  • ASTM E1641,
  • Isothermal Arrhenius for time-to-event,
  • Dynamic Arrhenius for failure temperature (ASTM E2070D),
  • ASTM E2070(A) for isothermal data,
  • Friedman,
  • Ozawa-Flynn-Wall (OFW),
  • Kissinger-Akahira-Sunose (KAS),
  • Numerical Optimization (Kinetics Neo only).

The Model-Free Analysis Methods — Advantages and Disadvantages

The Friedman analysis is an isoconversional method whereas the Ozawa-Flynn-Wall (OFW) and Kissinger-Akahira-Sunose (KAS) analyses are integral isoconversional methods. In all methods, the measurements are analyzed for multiple conversion levels. Friedman requires at least two measurements.

In addition to two dynamic measurements, OFW and KAS require positive heating rates.

The Numerical Optimization uses digital simulation in determining the activation energy and pre-exponential factor to achieve the best agreement between simulated and experimental curves. At least two measurements are required.

In all of the methods, the activation energy is determined using the points at the same conversion (0.01, 0.02, …, 0.99) from the measurements at different heating rates or under different isothermal conditions (for Friedman and Numerical Optimization).

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Model-Free MethodsAdvantageDisadvantage
Methods based on a single conversion

ASTM E698
ASTM E1641
ASTM E2890

Isothermal Arrhenius

Dynamic Arrhenius

Only for one-step reactions; for complex reactions, the points are not on a straight line 

 

Only for dynamic measurements 

 

Only one point is evaluated; all other information is not used

Conversion-dependent methodsASTM E2070(A)

For multiple-step reactions without parallel reaction steps

 

Evaluation of each reaction point

Suitable for isothermal measurements only

 

For parallel and independent reactions, the mean values of Ea are given
Friedman

For multiple-step reactions without parallel reaction steps

 

Evaluation of each reaction point

Suitable for dynamic and isothermal measurements

 

For parallel and independent reactions, the mean values of Ea are given
Ozawa-Flynn- Wall (OFW)
For multiple-step reactions  without parallel reaction steps

 

Evaluation of each reaction point

Suitable only for dynamic runs

For parallel and independent reactions, the mean values of Ea are given

Kissinger-Akahira-Sunose (KAS)

For multiple-step reactions  without parallel reaction steps

Evaluation of each reaction point

Suitable only for dynamic runs

For parallel and independent reactions, the mean values of Ea are given

Numerical Optimization

For multiple-step reactions without parallel reaction steps

Evaluation of each reaction point

Suitable for dynamic and   isothermal measurements

For parallel and independent reactions, the mean values of Ea are given

Model-Free Methods — Results

  • Analysis graph with Y-axis:
    • log (heating rate),
    • log (heating rate/T2),
    • log dx/dt versus 1000/T,
    • log(time) versus 1000/T;
  • Plots of activation energy and pre-exponential factor vs. conversion;
  • Master plot for f(α);
  • Conversion fit.
Friedman analysis plot: log(reaction rate) vs. 1000/T. Lines are drawn through isoconversion points for the measurement with different heating rates.
Apparent activation energy vs. conversion, found from the slope of isoconversion lines from Friedman analysis plot.
Experimental points and simulated solid lines. For the simulation, the apparent activation energy is used as the function of conversion.
Isothermal Arrhenius Method (ASTM E2070 D): Values of Oxidation induction Time (OIT) at isothermal measurements with different temperatures, isoconversional line and calculated kinetic parameters.