How can Activation Energy be calculated from a TPR profile data of a sample treated at constant heating rate. Does a shift in a TPR peak imply change in activation energy if the shift occurs at similar heating rates?
Arrhenius equation can NOT be directly used for a non-stationary process kinetics.
You can only apply Arrhenius to the values of reactions rate CONSTANTS, which may be estimated from measurements of the reaction rate at THE SAME reaction conditions (except for T) and at THE SAME conversion extent. This approach is exactly what Ozawa-Flynn-Wall method does.
First of all, you have to measure TPR (or thermal curves of some other process) at several heating rates (e.g. 1, 3, 5 and 10 K/min). So, you have to perform a SERIES of TPR measurements.
Then you can only calculate the APPARENT activation energy of the process.
Three main methods can be used: Kissinger, Friedman and Ozawa-Flynn-Wall.
The first one is based on the shift of the peak maximum position at changing the heating rate and gives you one value of apparent Ea as
ln([heating rate]/[maximum temperature]^2)= - Ea/(R[maximum temperature]).
Kissinger is far from being precise, but is works well even if you have problems with accurate subtraction of baselines.
The two others are more complicated to describe here, you may find OFW method as ASTM E698. http://www.astm.org/Standards/E698.htm. OFW will give you dependence of apparent activation energy on the extent of the process. This is very helpful when you have a two-stage process (for example, when the transport stage of diffusion of cations from the oxide to the surface is followed by the chemical stage of its reduction.
Please note that all these methods were developed for calorimetric thermal analysis.
However, I believe that you can use them for TPR.
Answering you second question - NO. According to my experience (DSC of copper-containing oxides reduction), reduction processes can have very different apparent activation energies and still occur at nearly the same temperature. At that, processes occuring at different temperatures can have similar activation energies.
Run your reaction under two different T conditions and use Arrhenius equation
Arrhenius equation can NOT be directly used for a non-stationary process kinetics.
You can only apply Arrhenius to the values of reactions rate CONSTANTS, which may be estimated from measurements of the reaction rate at THE SAME reaction conditions (except for T) and at THE SAME conversion extent. This approach is exactly what Ozawa-Flynn-Wall method does.
This is for TGA, but I think the basics are the same: H. E. Kissinger Anal. Chem. 29 (1957) 1702
In answer to your second question ... When all else in your measurement system is exactly the same and the overall activation energy of a given process changes, the position of the peak that you measure in TPR for that process will shift. The focus is on OVERALL activation energy, which itself is comprised of a combination of activation energies from each of the molecular steps in the process.
I agree with Khassin's suggestion, using the ASTM E698, so that a referred method can be used for the comparison can be made.
Sure, Alex KHASSIN provided best answers. Est' esche UMY v ROSSII.
Dear Lebohang: From thermodesorption (TG curve) the activation energy can be determined by using either the Coats-Redfern procedure (1) or the Piloyan-Novikova equation (2) both of them are Arrhenius-like expressions. In the first procedure, reaction order can also be estimated. You can probably adapt these methods to your TPR results, taking into account the suggestions given in previous answers by Khassin.
(1) A. W. Coats and J.P. Redfern, Nature 201, 68 (1964)
(2) G. O. Piloyan and O.S. Novikova, Inorganic Materials 2, 1109 (1966) and Russian J. of Chem. 12, 313 (1967)
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