In the previous section, the thermograms for CeO2 have been analysed using the new method outlined in this thesis. In this section the kinetic parameters and deconvolved curves are used to analyse the process for the reduction of CeO2. The kinetic parameters calculated for the two materials are shown below for clarity.
Table 4.11: Coefficients calculated from regression algorithm for CeO2 calcined at 400 and 500◦C
Peak A Ea m n γ p
400◦C: 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 0.27 500◦C: 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
The first step was to run the deconvolved peaks through Malek’s procedure, in order to see if a kinetic model can be applied to each reduction process. Table 4.12 shows the computed kinetic models for the various processes.
When comparing the reduction processes on each of the materials, the first pro-cess (Peak 1) does not seem to follow any explicit reduction model and hence de-faults to the SB(m,n) model. It is promising that the kinetic function predicted from Malek’s procedure in table 4.12 replicates the kinetic function calculated through the regression method in table 4.11, further supporting the validity of the regression method. Although the SB(m,n) model is not derived from any explicit reduction
Table 4.12: Kinetic models calculate from Malek’s procedure for CeO2 calcined at
method, some attempt has been made at trying to understand the kinetic param-eters m and n.[3] The parameter m has been indicated to relate to the influence of the reduced area of the material, with the n parameter indicating the influence of the oxide on the reduction process. The explicit values of the kinetic parame-ters are arbitrary, but when used in comparison for similar kinetic processes, more information can be divulged from them.
For process 1 (peak 1) the value for m decreases and the value of n increases for the CeO2 calcined at 500◦C when compared to the material calcined at 400◦C. This indicates both a decrease in the influence of the reduced material and an increase in the influence of the metal oxide on the reduction process. The very similar activation energy would indicate that chemically the same reduction process is occurring, and that this difference in influence is purely physical. This is backed up by the change in the Arrhenius pre-exponentialA which is lower in the 500◦C catalyst, which also correlates to a larger value for γ which indicates that as more of the material is reduced the reduction process becomes more difficult. Perhaps one could assume that the reduction for the first process is around a specific type of ceria grain, and in the catalyst calcined at 500◦C the grains are larger, as would be expected by higher temperature calcination. This would create a lower surface area (hence the lowered A value) and if the reduction occurs on the grain boundary, as the larger grain is reduced the distance between the grain boundary and the oxide increases which would increase the energy required for the reduction, which would not be seen
Chapter 4 Kinetic Analysis and Modelling in Heterogeneous Catalysis
in the smaller grains.
For the second process, which make up 67% and 69% of the materials respectively for the catalyst calcined at 400◦C follows a Johnson-Mehl-Avrami type reduction process, and at 500◦C does not follow any specific mechanism. This would indicate that the bulk of the material has changed when the calcination temperature is increased. This is further backed by the increase in the the kinetic coefficients A, Ea and the kinetic parameter m. As the influence of the metal is increased in the catalyst calcined at 500◦C, one can assume a polymorphic change where more Ce metal is present on the surface has occurred.
The final processes, both follow a Johnson-Mehl-Avrami reduction model, with the catalyst calcined at 500◦C having an increased value of M . The values of M have been shown to correlate to specific reduction processes[4], with a value of M ≈ 2 indicating a grain edge nucleation method, and a value of 3 > M > 4 indicating a decreasing nucleation rate. This is backed up by the decrease in the kinetic parameterA when M = 3.233, and the different activation energies indicating different reduction processes. As the P parameters seem to be correlated between process 1 and 3, perhaps process 3 is the reduction of the material on the grain boundary of the material reduced in process 1. As the size of the particles reduced in process 1 seem to have increased in the material calcined at 500◦C this would be reflected in less area for the material reduced in process 3.
Here the surface structure and possible changes in the material have been dis-cussed in great detail, of course it would be impossible to confirm these polymorphic changes in the material without some other form of characterisation (XRD, XAFS etc.), but the idea here is to show how much information it is possible to gain from what is usually considered to be a basic experiment with little to no kinetic informa-tion. Using the new methodology outlined in this thesis, the quality and quantity of information available from TPR thermograms has been greatly increased, and hopefully will prompt a more in-depth approach when it comes to kinetic analysis.
4.8 Summary
Similar to the previous chapter, there has been an initial focus on the development of software, with the aim of making the analysis of Temperature Programmed Re-actions more accessible. The current literature has been very poor in applying the described techniques either due to a lack of understanding or simply being unaware that they exist. It is hoped that by taking the very well established theory behind the non-isothermal analysis and creating a new technique for analysis, these methods will become more popular. It has been shown using simulated data that this new method can provide in-depth information about the reduction process of a material, with one of the major perks being an ability to ability to deconvolute a reduction processes with a high level of accuracy not possible with standard shape regres-sion techniques. The new methodology has been applied to various CeO2 materials which were calcined at varying temperatures, and it was found that for the samples calcined at 400 and 500◦C it was possible to deconvolve three different reduction processes, and therefore three different phases of the material. The differing kinetic parameters calculated from the regression model found that when increasing the calcination temperature from 400◦C to 500◦C there was some phase change in the material, but this could not be proved without further characterisation techniques.
The limitation of the methodology was demonstrated when studying the CeO2 sam-ple calcined at 600◦C, as if the reduction spectrum is not clean, and if the reduction process does not return to the baseline the assumptions made during the numerical integration (that the whole process is completed) are no longer true. A future study could perhaps be in attempt to counteract this problem by developing a technique of expanding TPR thermograms theoretically, as is seen in the TAP literature.
Bibliography
(1) J. Malek, Thermochimica acta, 1992, 200, 257–269.
(2) V. Gorbachev, Journal of Thermal Analysis and Calorimetry, 1983, 27, 151–
154.
(3) G. Munteanu, L. Ilieva, R. Nedyalkova and D. Andreeva, Applied Catalysis A: General, 2004, 277, 31–40.
(4) J. W. Christian, The Theory of Transformations in Metals and Alloys Ediz 2. an Advanced Textbook in Physical Metallurgy Parte 1. Equilibrium and General Kinetic Theory, Pergamon Press, 1975.
5.1 Hydrogenation of Levulinic Acid
The final set of work performed as part of this thesis was part of a of a larger project which was interested in the conversion of biomass into more readily usable materials. The particular reaction of interest was the hydrogenation of levulinic acid (LA) toγ-valerolactone (gVL). A Cu−ZrO2 catalyst had been developed which had been shown to be active for the hydrogenation of LA to gVL using 5 wt.%
LA/H2O, 0.025 g of Cu−ZrO2, 200◦C, and 35 bar H2. Throughout the experiment the conversion and selectivity for gVL was 100%. From a catalytic perspective this is fantastic, but from a perspective of kinetics it presents some problems:
• No idea of reaction mechanism
• No way to gauge rate determining step
• No understanding of role of catalyst
Chapter 5 Kinetic Analysis and Modelling in Heterogeneous Catalysis
To increase the quality of the catalyst, the most important step is understanding how the reactant interacts with the catalyst surface. As in-situ methods require highly specialised equipment and training, DFT and Molecular Dynamics was used to attempt to understand both the reaction mechanism and the catalytic system.