The noticeable weakness of the ‘single curve’ methods (determination of the kinetic parameters from single run recorded with one heating rate or isothermal condition only) has led to the introduction of ‘multi curve’ methods over the past few years, as discussed in the International ICTAC kinetics project.

Degradation reactions are often too complex to be described in terms of a single pair of Arrhenius parameters and the commonly applied set of reaction models. As a general rule, these reactions demonstrate profoundly multi-step characteristics. They can involve several processes with different activation energies and mechanisms. In such situation the reaction rate can be described only by complex equations, where the activation energy term is no more constant but is dependent on the reaction progress α (E ≠ const but E = E(α)).

The isoconversional methods were introduced by Friedman and Ozawa-Flynn-Wall. A detailed analysis of the various isoconversional methods (i.e. the isoconversional differential and integral methods) for the determination of the activation energy has been presented by Budrugeac. The convergence of the activation energy values obtained by means of a differential method (Friedman) with those resulted from using integral methods (Ozawa-Flynn-Wall) comes from the fundamentals of the differential and integral calculus.

The differential isoconversional method of Friedman is based on the Arrhenius equation:

f (α): the model function

A: the pre-exponential factor

E: the activation energy

T: the temperature

t: the time

Friedman has applied the logarithm of the conversion rate d α /dt as a function of the reciprocal temperature at any conversion α:

As f(α) is a constant in the last term at any fixed α, the logarithm of the conversion rate d α /dt over 1/T shows a straight-line dependence with the slope of m = -E/R.

By the extension of the expression


one can predict the reaction rate or reaction progress having determined  and using the following expression:

Acquisition of the Chemiluminescence signals of natural rubber oxidation under non-isothermal temperature profiles (5 different heating rates 0,059..0,005K/min) in synthetic air.
Acquisition of CL-data
Reaction progress (alpha) of natural rubber oxidation depending on the performed non-isothermal temperature profiles.
reaction progress
Arrhenius-Plot (Ln[da/dt] against the inverse temperature) of the experimental data (oxidation of natural rubber): differential isoconversional analysis for alpha = Xi (e.g. 60% of oxidation reaction progress).
isoconversional analysis
Energy of activation as a function of the reaction's progress (oxidation of unstabilised natural rubber): calculation according to the differential isoconversional approach.
activation energy

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