I am analyzing themogravimetric data (TGA) to determine kinetic parameters of thermal reaction of oil using Coats and Redfern method.
A plot of either ln{[(1-(1-a)1-n]/[T2(1-n)]} against 1/T or for n= 1, In{-ln(1-a)]/T2} against 1/T should yield a straight line with a slope ( -E/R) for the correct value of n.
Where a = fraction of the reactant decomposed at time t. Therefore, (1-a) = the remaining weight percent of the reactant.
The value of E obtained graphically is then used to calculate the pre-exponential factor.
I am validating my calculation using the data extracted from the work of Kamal N. Jha and Bela Verkoczy (The attached file "The Role of Thermal Analysis Techniques in the In-Situ Combustion Process"). In the attached calculation file (.xls), the calculated slopes are from 765 to 1074 for the temperature range of 140~360 oC. By multiplying the slopes to R (8.314 J/mol.K), the activation energy are from 6360~8930 J/mol. The results are much smaller than the values in the study of Jha and Verkoczy. Please refer to the excel file for your review.
I would like to hear your opinions and suggestions about this topic.
please see the attached file, you can used the described method. it is important to define the conversion correctly.
also you can see the folowing thesis:
https://www.researchgate.net/publication/268420889_Cross_Linked_Sulphonated_Polyether_ether_ketone_for_the_Development_of_Polymer_Electrolyte_Membrane_Fuel_Cell
Thank you for your answer, Dr. Abdul Al Lafi.
I am trying the recommended method. I will show you the results when the calculation completed.
In principle, the recommended method is similar to the method suggested by Coats and Redfern.
I need to get opinions and suggestions on my calculation using Coats and Redfern method.
If possible, please help me to find out the mistakes in my calculation.
Thank you very much!
As I have noticed you have used TG% *0.01 and not elpha which is the degree of conversion and defined as wi-w0/wi-wf
so could you please check that. hope it would help
I have updated the calculation sheet with alpha.
The alpha (a) is defined by:
a=(wi-wt)/wi-wf)
where wi, wt, and wf are the weight of sample at the initial, at time t, and final time, respectively.
In my calculation, the alpha was defined as:
a=(100-%TGt)/(100-%TGf)
The updated results show a slightly change compared to the previous results when alpha was not applied. The estimated activation energies are very small compared to that reported by Kamal N. Jha and Bela Verkoczy.
Please give me your opinions on this.
Thank you for your answer, Dr. F. Fraga
I have found two of your papers related to calculation of activation energy using Coats and Redfern method:
(1) Thermogravimetric study of the decomposition process of the system BADGE (n=0)/1,2 DCH
(2) Mechanism and Activation Energies in Different Blends of Poly-(-caprolactone) with Polyethyleneglycol (PEG) and Polyvinyl Alcohol (PVA)
In the first paper, different functions of the integral function of conversion [g(alpha)] were used. In principle, the plot of ln[g(alpha)] and 1000/T should yield a straight line. I have also applied the same method but the results are very different from the reference results. It might be error in one of the steps in my calculations. However, I cannot find out where is the error.
I cannot find the second paper. Could you please give me the full text of the second paper?
If possible, could you please give me an example of your calculation of activation energy? I would like to validate my calculation results. It is very important to me to do the next steps in my study
Could you please explain more details about your suggestion, Dr. F. Fraga?
I have attached a figure of TG-DTG data below. Could you please point out which temperature range should I choose for kinetic analysis so that the kinetic results can represent for the whole range of 140~360 oC?
Thank you very much!
Ridwan Hadi Kusuma We have not touched this topic for a long time. Now we are waiting for a new project to work with.
Dear Viet Nguyen-Le,
A plot of either ln{[(1-(1-a)1-n]/[T2(1-n)]} against 1/T or for n= 1, In{-ln(1-a)]/T2} against 1/T should yield a straight line with a slope ( -E/R) for the correct value of n.
Where a = fraction of the reactant decomposed at time t. Therefore, (1-a) = the remaining weight percent of the reactant.The value of E obtained graphically is then used to calculate the pre-exponential factor.
To improve the accuracy of the values predicted by CR techniques, it is advisable to correlate minimum level the activation energy within 0.15% of its assumed values and the frequency factor of 1% accuracy.
Refer the site given below;
Ashish
Dear Viet Nguyen-Le,
A plot of either ln{[(1-(1-a)1-n]/[T2(1-n)]} against 1/T or for n= 1, In{-ln(1-a)]/T2} against 1/T should yield a straight line with a slope ( -E/R) for the correct value of n.Where a = fraction of the reactant decomposed at time t. Therefore, (1-a) = the remaining weight percent of the reactant.The value of E obtained graphically is then used to calculate the pre-exponential factor.
To improve the accuracy of the values predicted by CR techniques, it is advisable to correlate minimum level the activation energy within 0.15% of its assumed values and the frequency factor of 1% accuracy. Refer the site given below;
Ashish
The TGA was performed T0 to Tf. However, I want to ask, if we are calculating activation energy in between a range of temperature(T1 and T2), what will be the fraction of mass.
i.e. mo=initial mass( will it be mass taken at starting of TGA or at T1?), m= mass at temperature(will it be mass taken at T2?), m infinity= final mass(will it be mass at the end temperature of TGA of mass at T2). please make it clear
There are many methods that are used to determine the values of the n and E parameters based on the TG curve. The only problem is that n is not an order of the process and E is not the activation energy. These are actually lumped parameters. It is best to try to separate steps that can be treated as elementary reactions and determine E values for them. Deconvolution of the DTG curve may help.
Dear Viet Nguyen-Le,
Were you able to find the solution to this issue?
Thanks,
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