Friedman Analysis

Friedman analysis is the model-free (isoconversional) method of kinetic analysis calculating dependence of activation energy E(α) on degree of conversion α.

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.

Friedman analysis belongs to the group of differential model-free methods where firstly, the derivative from main kinetic equation (1) must be found and then the logarithm must be taken.

Derivative and then logarithm for Friedman analysis:

If the points with the same degree of conversion (isoconversional points) will be taken from experiments performed at different temperature conditions then values ln[A(α)f(α)] will be the same for all of them and Eq(2) will look like the straight line

y=b+ax (3)

where:

y=ln(dα/dt)
b= ln[A(α)f(α)]
a=E/R
x=-1/T .

The Friedman plot y(x) looks as set of straight lines for different α values, where for each α the activation energy can be found from the slope and pre-exponent from the intercept for known(or assumed) f(α).

Advantages and disadvantages of this method and a comparison table with other methods.

Fig.2 Friedman plot containing straight lines for different conversion values α.

Fig.4 Friedman pre-exponent A(α) (for the assumption of first-order reaction).

Fig.5 Comparison between experiments (symbols) and simulation (solid lines) for Friedman dependences E(α) and A(α).

Example

Decomposition of La(OH)₃:

Experimental data
Friedman plot
Activation energy E(α)
Pre-exponent A(α) (for the assumption of first-order reaction)
Comparison between experiments and simulations for Friedman dependences E(α) and A(α).

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

Reference

H.L Friedman: J. Polymer Lett.4 (1966)323

https://onlinelibrary.wiley.com/doi/abs/10.1002/polc.5070060121