要旨
From the purification of exhaust gases to the large scale industrial production of fertilizers, heterogeneous catalysis is of fundamental importance in various branches of our modern society. A central goal in catalysis research is to understand and control the influence of various experimental parameters on the performance of the reaction. The key to reaching this goal is a systematic way of experimentation both in terms of material synthesis and catalytic performance testing. Statistical design of experiments (DoE) is a mathematical toolbox, which can be used to maximize the information output of a given experimental budget. While traditional DoE is widely applied in industry, academic catalysis research often falls behind. In this thesis, a set of statistical tools especially tailored to tackle problems in chemical kinetics and catalysis is presented by bringing together classical DoE theory with modern statistical learning and optimization methods.
Having a closer look at the catalyst surface, the interplay of various adsorption, diffusion and reaction processes taking place during catalytic reactions can result in a complex kinetic phase diagram. Characteristic for such phase diagrams are transitions with abrupt changes in apparent kinetics. This challenges traditional DoE approaches with their underlying smoothness assumption. The established approaches for modeling the kinetics of catalytic reactions that can cope with such phase transitions suffer from the fact that a detailed understanding of the mechanism is required. Further, these models often also rely on a large number of parameters that are experimentally hardly accessible. Here, making uninformed assumptions can introduce systematic deficiencies into the resulting model.
For the investigation of novel catalytic reactions, for which detailed knowledge of the underlying mechanism is not available, a novel data driven regime identification algorithm is proposed.
In order to reduce the bias through a priori model assumptions, an algorithm which systematically analyzes the influence of process parameters on the reaction rate to identify effective rate laws without prior knowledge was developed. The proposed method determines relevant model terms from a polynomial ansatz employing well established statisticalmethods. For the optimization of the model parameters special emphasis is put on the robustness of the results by taking not only the quality of the fit but also the distribution of errors into account in a multi-objective optimization. The flexibility of this approach is demonstrated based on synthetic kinetic data sets from microkinetic models. It could be shown that the kinetics of both the classical HBr reaction and a prototypical catalytic cycle are automatically reproduced based on very limited data sets.
While such rate laws give a reasonable representation of the reaction within one kinetic regime, the low order polynomial approximation will break down approaching phase transitions. Thus, a kinetic regime can also be understood as the range of validity for such an effective regime model. By using local experimental designs in combination with automatically identified kinetic rate laws a local kinetic fingerprint can be created. This way, regions of distinct kinetic behavior are mapped out based on empirically observed data. Combining
this local information with unsupervised learning and support vector classification models, a global multi-regime kinetic model free of any prior assumptions on the reaction mechanism can be obtained.
Both classical experimental designs as well as space filling sampling techniques are designed for smooth functions of the input parameters. Therefore, the discontinuous behavior at the phase transition requires an alternative sampling approach in order to maximizemthe efficiency in terms of experimental data. Going beyond established DoE approaches, a modified adaptive experimental design approach is introduced, especially tailored towards modeling experimental regions containing phase transitions. By incorporating the presence of such discontinuities into the model assumption, the position of the real phase transition can iteratively be approached. The potential of this approach is illustrated investigating artificial data sets from a microkinetic model for CO oxidation over RuO2. Further, the formulation of this adaptive procedure, which strives for algorithmic equipollence between sets of interrelated continuous and categorical factors opens a wide field of applications going beyond the investigation of chemical kinetics.
