As the new method has been shown to be able to replicate the initial kinetic param-eters used to simulate a complex thermogram, it can now be used to understand the reduction processes occurring in real catalytic systems.
The catalytic materials used are a set CeO2 catalysts, which have been calcined at three temperatures, (400, 500, and 600◦C). CeO2 was chosen as the material of interest as it is a commonly used in the three way catalytic converter as an oxygen storage medium. TPR can be used to asses the ease at which oxygen can be removed from this material. By comparing these three materials information on the effect of preparation method on the functionality can be obtained. The CeO2 catalysts have been reduced at three heating rates (5, 10, and 15 K min−1) which allows the full kinetic analysis to be performed.
When studying figure 4.11 from thedEa/dαprofile it could be argued that there are one or two peaks in thedEa/dαprofile, indicating two or three processes. As noise is a large problem in experimental data, the analysis was performed using both two and three processes. Increasing the number of processes will always increase the quality of the fit. Therefore having a close estimate of the number of processes occurring, performing the analysis, and seeing which gives the best fit with the lowest number of peaks is the best practice.
Table 4.6: Coefficients calculated from regression algorithm
Peak A Ea m n γ p
1 9 49.5 0.46 0.45 0.141 0.69 2 114687 115.8 0.01 0.53 0.000 0.31
The first step was to use the least amount of processes as calculated from figure 4.11, estimated to be 2. This is based on the assumption that any peak in the
dEa/dα profile (e.g. at α = 0.25) indicates a change in reduction process (as the activation energies for two processes are expected to be different). Figure 4.12
Chapter 4 Kinetic Analysis and Modelling in Heterogeneous Catalysis
Figure 4.11: CeO2 catalyst calcined at 400◦C baseline corrected data, activation energy, anddEa/dα profiles respectively.
shows the calculated profiles, and table 4.6 shows the calculated parameters. When fitting the experimental data it was found that including the Kissinger method
(a) (b)
Figure 4.12: Experimental (Exp.) and simulated two process (Sim.) dα/dT and ac-tivation energy profiles overlaid for CeO2 calcined at 400◦C a) dα/dT profiles with deconvoluted peaks b) Activation energy profiles for Kissinger and Friedman meth-ods.
for analysing the curves in the regression algorithm was useful for comparing the curves. As the Friedman method is correlated to the shape of the curve, and the Kissinger is correlated to the temperatures of the reduction it makes sense to use a combination of the two as the target for the regression algorithm. From figure 4.12 it can be seen that the simulated activation energy profile misses a feature at approximatelyα = 0.25, therefore it is assumed that two processes do not replicate the real reduction profile accurately.
(a) (b)
Figure 4.13: Experimental (Exp.) and simulated three process (Sim.) dα/dT and activation energy profiles overlaid for CeO2 calcined at 500◦C a) dα/dT profiles with deconvoluted peaks b) Activation energy profiles for Kissinger and Friedman meth-ods.
Chapter 4 Kinetic Analysis and Modelling in Heterogeneous Catalysis
Table 4.7: Coefficients calculated from regression algorithm
Peak A Ea m n γ p
1 14 43.8 0.75 0.87 0.000 0.06 2 24 53.6 0.39 0.77 0.029 0.67 3 4918 90.8 0.53 0.73 0.012 0.27
Figure 4.13, and in particular figure 4.13b, clearly shows a much more accurate fit with three processes when compared with 4.12b, particularly when comparing the residuals between the peaks (res = |sim − exp|) which are calculated to be 96 and 203 respectively. As there could be one or two peaks in thedEa/dα profile, it can be assumed that the three-process model provides the best estimate for the deconvolved thermogram. Analysing the peaks, they all seem to reduce via similar kinetic models, with the m and n parameters having no distinct pattern with changing activation energyEa and Arrhenius pre-exponentialA. The one pattern that can be observed, is that with an increasing activation energy the activation energy scaling parameters γ also increases. While individually the kinetic parameters can be used to estimate some of the properties of the catalytic material, where the analysis really shines is when it is used to compare similar materials.
The next catalyst to be analysed was the CeO2calcined at 500◦C. ThedEa/dαdoes seem to show a small peak at0.2α, and therefore the first test should be performed using a two process regression model, similar to the previous catalyst.
Table 4.8: Coefficients calculated from regression algorithm
Peak A Ea m n γ p
1 6 45.2 0.55 0.47 0.233 0.48 2 573 80.4 0.26 0.52 0.015 0.52
Similar to the previous catalyst, the two process regression method does not accurately recreate the activation energy profile as seen in figure 4.15b, particularly in the region of 0.1α to 0.5α. The parameters in table 4.8 seem to be consistent with the ones calculated for the previous catalyst, table 4.6 indicating that similar processes are attempting to be modelled. Based on this assumption, a three process
Figure 4.14: a) CeO2catalyst calcined at 500◦C baseline corrected data b) activation energy c)dα/dT profiles respectively.
regression model will also be used, as even though the dEa/dα profile appears to be flat, there could be a small change hidden by the noise. As mentioned previously
Chapter 4 Kinetic Analysis and Modelling in Heterogeneous Catalysis
(a) (b)
Figure 4.15: Experimental (Exp.) and simulated two process (Sim.) dEa/dα and activation energy profiles overlaid for CeO2 calcined at 500◦C a) dα/dT profiles with deconvoluted peaks b) Activation energy profiles for Kissinger and Friedman meth-ods.
this method of assigning the number of reduction processes is subjective, and the
dEa/dαshould only be used a guideline, with the rule of thumb being using the least number of processes required to get an accurate fit.
(a) (b)
Figure 4.16: Experimental (Exp.) and simulated three process (Sim.) dEa/dα and activation energy profiles overlaid for CeO2 calcined at 500◦C a) dα/dT profiles with deconvoluted peaks b) Activation energy profiles for Kissinger and Friedman meth-ods.
Table 4.9: Coefficients calculated from regression algorithm
Peak A Ea m n γ p
1 8 42.5 0.66 1.01 0.026 0.12 2 53 60.3 0.51 0.76 0.089 0.69 3 605 76.5 0.67 0.67 0.009 0.19
Figure 4.16b clearly shows a much more accurate fit to the activation energy profile than figure 4.15b, and the parmaeters calculated in table 4.9 show a strong correlation to the ones calculated in table 4.7. At first glance this indicates that when the material is calcined at 400◦C and 500◦C there is little change in the actual structure of the catalyst.
The final catalyst to be analysed is the CeO2 which has been calcined at 600◦C.
It is important to note that the raw response for the catalyst calcined at 600◦C was much lower than the catalysts calcined at 400 and 500◦C. Assuming that all other experimental parameters have been kept consistent (e.g. equipment used, amount of catalyst, amount of gas) this would indicate that less material has been reduced overall as the total amount of H2 adsorbed is less. This alone would indicate that the thermal stability of the material has been increased by the high temperature calcination, subsequently indicating a possible phase change. This is further sup-ported by the emergence of a shoulder peak (figure 4.17) at high temperatures for the three thermograms. As the dEa/dα profile for the 600◦C calcined catalyst is ex-tremely noisy, it is difficult to get an initial estimate to the number of processes occuring during the reduction of the material. By applying what we have seen from the previous materials, where a three-process reduction method fits the main peak, assuming that the main peak seen in figure 4.17 is the same as the one seen in figure 4.11 and 4.14, and that the shoulder peak the emergence of a new phase, it can be assumed that a four-process model will fit the resulting data.
It was found that the complex nature of the activation energy profile caused large problems for the optimisation algorithm, and it was difficult to extract any kinetic information from the thermogram. This most likely arose from the low signal to noise ratio, and the fact that the baseline was highly complex in the original thermogram.
Attempting to model the entire thermogram was found to be unfeasible, and therefore no kinetic information could be obtained. Applying the principle that the second peak that appears in the reduction profile is the formation of a new phase,
Chapter 4 Kinetic Analysis and Modelling in Heterogeneous Catalysis
Figure 4.17: a) CeO2catalyst calcined at 600◦C baseline corrected data b) activation energy c)dα/dT profiles respectively
and that the main peak is the reduction of the same material seen in the material when it is calcined at 400 and 500◦C, the thermogram was split so that the only
(a) (b)
Figure 4.18: Experimental (Exp.) and simulated four process (Sim.) dEa/dα and activation energy profiles overlaid for CeO2 calcined at 600◦C a) dα/dT profiles with deconvoluted peaks b) Activation energy profiles for Kissinger and Friedman meth-ods.
peak being modelled was the secondary one.
(a) (b)
Figure 4.19: Experimental (Exp.) and simulated two process (Sim.) dEa/dα and activation energy profiles overlaid for CeO2 calcined at 600◦C zoomed on second peak a) dα/dT profiles with deconvoluted peaks b) Activation energy profiles for Kissinger and Friedman methods.
Table 4.10: Coefficients calculated from regression algorithm
Peak A Ea m n γ p
1 5319901 144.2 0.95 1.69 0.000 0.08
Using this method some kinetic parameters were able to be calculated for the secondary process. It would seem that the second phase has a much higher activation energy for reduction, which is to be expected, and the Arrhenius pre-exponentialA
Chapter 4 Kinetic Analysis and Modelling in Heterogeneous Catalysis
is much higher when compared to the other processes from the thermograms for the material reduced at 400 and 500◦C. The material reduced at 600◦C is presented as the extreme case when it comes to deconvolution of TPR thermograms, when the baseline is subjective, and the signal to noise ratio is very low.