Comparison Study of Master Kinetics Curve and Three Kinetic models
Date Issued
2011
Date
2011
Author(s)
Wang, Shao-Yu
Abstract
Master kinetics curve (MKC) is a new kinetic model derived from general chemical reaction rate equations and has only been studied for several years. The major difference between the MKC and other kinetic models is that it needs no assumptions regarding kinetic parameters. Instead, the establishment of the MKC is based on real experimental data. Thus, the MKC has several advantages, such as convenient to use, accurate to predict and a variety of potential applications. Previous researches have proved that MKC is capable of studying the kinetics of crystallization, thermal decomposition and sintering. However, some of the researches also showed that the predictions of the MKC, and in particular the parameter “apparent activation energy”, are not identical with the values determined by other kinetic methods. Therefore, it is necessary to study and understand these differences to make MKC into a universal kinetic model.
To compare the differences between the MKC and other kinetic models, three different kinetic models were chosen. The three models are the master sintering model (MSC), the Ozawa method and the Avrami equation. MSC is a well-established sintering model in the sintering field; it describes the whole densification process of a sintering. The Ozawa method is a kinetic model which greatly simplifies the determination procedure of kinetic parameters from thermogravimetric research. The Avrami equation is a phase transformation kinetic model which describes the relationship between reaction time and the extent of phase transformation; it is capable of determining the mechanism. In order to acquire enough data and reduce experimental errors, synthetic data and real data from early research are used for comparisons of the different models in this research.
The results showed that MKC and MSC have similar behavior in regard to prediction. The term 1/T of MSC introduces small deviations between these two models. If the reaction temperature increases, the deviations become slightly larger; however, these differences do not significantly change the predicted results.
The comparison between the MKC and the Ozawa method showed that the data from the 0th order and 1st order reactions can be perfectly merged by MKC’s fitting. However, the 2nd order and 3rd order reactions can only be partially merged by MKC analysis. These results can be explained by the reaction rates: 0th order and 1st order reactions have a slower reaction rate at the initial stage of reaction, and they are the same as an S-curve’s behavior (the S-curve has a slow reaction rate at the initial and final stages of reaction). However, the 2nd and 3rd order reactions have the highest reaction rate at the initial stage of reaction; they obviously differ from the characteristic of an S-curve. Consequently, the MKC cannot analyze all types of reactions by only using an S-shaped curve. Nevertheless, it is possible to merge these reaction data by other shaped curves.
The comparison between the MKC and the Avrami equation showed that the data only merged in the middle section of reactions. Predictions made by the MKC at both low and high temperatures are impossible. Data errors, especially the errors of reaction extent, might be the reason for the erroneous predictions. Due to the characteristic of an S-curve, errors of reaction extent might cause significant deviations to both ends of the curve rather than to the middle section. Likewise, these deviations give poor predictions at both low and high temperatures.
In this research, 1% to 5% errors were randomly added to three different variables of a MKC, i.e., time, temperature and reaction extent, in order to determine the relative influence of the variables on the models. From the results, we found that reaction extent affects MKC the most because the reaction extent is a parameter directly affecting the data fitting at the y axis. In comparison, time and temperature have to be integrated into the function log(Σ) at the x axis to affect the fitting. Therefore, the reaction extent requires greater accuracy than the other two variables.
In addition, we also used a different number of sets of data for the analysis of MKC in order to determine the minimum sets of data required to obtain a reasonable result. It shows that MKC can obtain a reasonable fitting curve by only three sets of data. This result also implies that, regardless of the accuracy of the data, MKC has the capability to describe the general trend of data. Thus it is important to ensure the accuracy of the data.
In conclusion, since MKC does not have to determine kinetic parameters and can analyze different reactions by different shaped curves, MKC definitely has the potential to become a universal kinetic model with a variety of applications and still remain convenient to use.
Subjects
master kinetics curve
MKC
Ozawa method
Avrami equation
kinetic models
chemical kinetics
Type
thesis
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