# Comments on Some Problems concerning the evaluation of the by dfhercbml

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```									                              Comments on Review Article No. 20

"Some Problems Concerning the Evaluation of the Activation Energy from Non-
Isothermal Data for Reactions with Activation Parameters Dependent on the Degree of
Conversion"

Before entering into the complex mathematics quoted in this article, it is important to determine
whether the activation parameters do indeed vary with the degree of conversion, or if there is any
further variation due to another process. This can be achieved by plotting the left hand side of
the following equation against 1/T

(1)

where             is the rate of reaction at temperature T
and      f() is the value of the equation representing the process at temperature T
E is the activation energy of the process
A is the pre-exponential factor
R is the gas constant

If the slope of the resulting graph is constant, i.e. the curve is linear, then the slope has a value
-E/R and intercept ln A. This will only be the case if E and A are constant over the whole
reaction. The ln curve can be non linear if the incorrect function of  is chosen.

There are many instances where the ln plot can be non-linear, not necessarily due to variation of
E with the extent of reaction or the use of the incorrect function of . The author has recently
investigated many ln plots that are not linear even though the correct functions have been
chosen and some of these investigations have been published [1,2]. Furthermore, the ln plot for
a first order reaction in which the activation energy either increases or decreases with extent of
reaction shows little deviation from linearity until the very high temperature end of the curve.
[ref.1, Figs 15 and 17]

Similar deviations, although different in shape, can also be seen on ln plots for visibly
overlapping peaks, even though the E and A values for both reactions are constant. A sigmoid ln
plot can be produced by overlapping peaks which are not visible on the DTG curve when one
reaction peak lies wholly within the other peak, again even when the E and A values are
constant for both reactions.

It is interesting to note that the slope of the low temperature part of all the ln plots has a value of
-E/R, which is close to the initial value of the activation energy/gas constant even when E varies.
This is also true even if the incorrect f() has been chosen.

Hence non linearity of the ln curve can be due to a number of causes and not necessarily due to
the variation of E (or A) with the extent of the reaction. Hence it is most important that the data
be tested using the equation above and deciding from the shape of the ln plot the possible cause
of the variation in both the activation energy and the pre-exponential function.
Papers cited:
[1] F. W. Wilburn, Thermochim. Acta, 340-341 (1999), 77 - 87
[2] F. W. Wilburn, Thermochim. Acta, 354 (2000), 99 - 105

F. W. Wilburn

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