Modelling quantitative composition activity relationships (QCARs) for heterogeneous catalysts by kriging and a multilevel B-spline approach

The main focus of this work lies in the mathematical modelling of quantitative composition activity relationships (QCARs) for heterogeneous catalysts tested for the oxidation of propene to acrolein. The use of combinatorial chemistry approaches together with high-throughput screening techniques also plays an important role here. One the one hand, the thesis tries to give a validation of the used synthesis and screening processes and on the other hand it is checked how well QCARs can be realized by the two applied interpolation techniques: Kriging and multilevel B-Splines. Following a sol-gel procedure approximately 2400 catalysts have been prepared and tested with the help of high-throughput synthesis and screening approaches. The samples include two complete pentanary composition spreads (elements Cr, Mn, Co, Te and Ni) having 10-%-wise variations in composition together with further refinements. The screening for catalytic activity itself has been realized in a high- throughput reactor system for sequential testing. An indicative sign of a potentially good catalyst candidate has been a large GC signal for acrolein in the product gas composition. For the analysis of data, new visualization techniques needed to be developed and introduced into the field of heterogeneous catalysis since common visualization approaches could not cope with more than three dimensional data sets. Another challenge has been the calculation of activities of 5%-wise variations given the 10%-wise samples by Kringing and B-Splines. Since the underlying functional relationship between composition and catalytic activity is not known, a direct evaluation of both interpolation techniques cannot be easily given.Das Hauptaugenmerk dieser Arbeit richtet sich auf die mathematische Modellierung von Zusammensetzung-Aktivität-Beziehungen für heterogene Katalysatoren in der Oxidation von Propen. Der Einsatz von Methoden der Kombinatorischen Chemie und Hochdurchsatzansätzen sowohl zur Herstellung als auch zum Testen dieser Katalysatorproben spielt dabei eine entscheidende Rolle. Die Arbeit versucht, zum einen eine Validierung der verwendeten Synthese- und Screeningverfahren zu geben, zum anderen aber auch zu prüfen, wie gut eine Beschreibung von Zusammensetzung-Aktivität-Beziehungen mit zwei mathematischen Interpolationsverfahren (Kriging, multilevel B-Splines) möglich ist. Im experimentellen Teil der Arbeit wurden rund 2400 Katalysatoren, zusammengesetzt aus den Elementen Cr, Mn, Co, Te und Ni, synthetisiert und auf ihre Aktivität hin getestet. Dabei wurden zwei komplette pentanäre Datensätze hergestellt (10%-ige Variation der Zusammensetzung). Alle Proben wurden in einer Hochdurchsatz-Screening Apparatur auf ihre Aktivität hinsichtlich der Oxidation von Propen (Zielprodukt Acrolein) untersucht. Als Kriterium für Aktivität wurden GC Signale aller interessanten Produkte aufgenommen. Hohe GC Signale entsprachen einer hohen Aktivität der Katalysatoren für das entsprechende Produkt. Zum Auswerten der Daten waren neue Visualisierungskonzepte zu entwickeln, wie sie im Bereich der heterogenen Katalyse noch nicht verwendet wurden. Mit Hilfe des Kriging- und B-Spline- Ansatzes konnten die Aktivitäten von Katalysatoren mit engeren Rasterungen im Suchraum geschätzt und mit experimentellen Werten verglichen werden. Dies lieferte neben der Reproduzierbarkeitsanalyse auch einen Vergleich der zwei verwendeten Modellierungsmethoden, wie es ansonsten mangels Kenntnis des wahren zugrundeliegenden funktionalen Zusammenhangs nicht möglich ist

Visualization of High-Dimensional Combinatorial Catalysis Data

The role of various techniques for visualization of high-dimensional data is demonstrated in the context of combinatorial high-throughput experimentation (HTE). Applying visualization tools, we identify which constituents of catalysts are associated with final products in a huge combinatorially generated data set of heterogeneous catalysts, and catalytic activity regions are identified with respect to pentanary composition spreads of catalysts. A radial visualization scheme directly visualizes pentanary composition spreads in two-dimensional (2D) space and catalytic activity of a final product by combining high-throughput results from five slate libraries. A glyph plot provides many possibilities for visualizing high-dimensional data with interactive tools. For catalyst discovery and lead optimization, this work demonstrates how large multidimensional catalysis data sets are visualized in terms of quantitative composition activity relationships (QCAR) to effectively identify the relevant key role of compositions (i.e., lead compositions) of catalysts

Die Modellierung von Zusammensetzung-Aktivitäts-Beziehungen von heterogenen Katalysatoren mit Hilfe eines Kriging- und eines B-Spline-Ansatzes

The main focus of this work lies in the mathematical modelling of quantitative composition activity relationships (QCARs) for heterogeneous catalysts tested for the oxidation of propene to acrolein. The use of combinatorial chemistry approaches together with high-throughput screening techniques also plays an important role here. One the one hand, the thesis tries to give a validation of the used synthesis and screening processes and on the other hand it is checked how well QCARs can be realized by the two applied interpolation techniques: Kriging and multilevel B-Splines. Following a sol-gel procedure approximately 2400 catalysts have been prepared and tested with the help of high-throughput synthesis and screening approaches. The samples include two complete pentanary composition spreads (elements Cr, Mn, Co, Te and Ni) having 10-%-wise variations in composition together with further refinements. The screening for catalytic activity itself has been realized in a high- throughput reactor system for sequential testing. An indicative sign of a potentially good catalyst candidate has been a large GC signal for acrolein in the product gas composition. For the analysis of data, new visualization techniques needed to be developed and introduced into the field of heterogeneous catalysis since common visualization approaches could not cope with more than three dimensional data sets. Another challenge has been the calculation of activities of 5%-wise variations given the 10%-wise samples by Kringing and B-Splines. Since the underlying functional relationship between composition and catalytic activity is not known, a direct evaluation of both interpolation techniques cannot be easily given.Das Hauptaugenmerk dieser Arbeit richtet sich auf die mathematische Modellierung von Zusammensetzung-Aktivität-Beziehungen für heterogene Katalysatoren in der Oxidation von Propen. Der Einsatz von Methoden der Kombinatorischen Chemie und Hochdurchsatzansätzen sowohl zur Herstellung als auch zum Testen dieser Katalysatorproben spielt dabei eine entscheidende Rolle. Die Arbeit versucht, zum einen eine Validierung der verwendeten Synthese- und Screeningverfahren zu geben, zum anderen aber auch zu prüfen, wie gut eine Beschreibung von Zusammensetzung-Aktivität-Beziehungen mit zwei mathematischen Interpolationsverfahren (Kriging, multilevel B-Splines) möglich ist. Im experimentellen Teil der Arbeit wurden rund 2400 Katalysatoren, zusammengesetzt aus den Elementen Cr, Mn, Co, Te und Ni, synthetisiert und auf ihre Aktivität hin getestet. Dabei wurden zwei komplette pentanäre Datensätze hergestellt (10%-ige Variation der Zusammensetzung). Alle Proben wurden in einer Hochdurchsatz-Screening Apparatur auf ihre Aktivität hinsichtlich der Oxidation von Propen (Zielprodukt Acrolein) untersucht. Als Kriterium für Aktivität wurden GC Signale aller interessanten Produkte aufgenommen. Hohe GC Signale entsprachen einer hohen Aktivität der Katalysatoren für das entsprechende Produkt. Zum Auswerten der Daten waren neue Visualisierungskonzepte zu entwickeln, wie sie im Bereich der heterogenen Katalyse noch nicht verwendet wurden. Mit Hilfe des Kriging- und B-Spline- Ansatzes konnten die Aktivitäten von Katalysatoren mit engeren Rasterungen im Suchraum geschätzt und mit experimentellen Werten verglichen werden. Dies lieferte neben der Reproduzierbarkeitsanalyse auch einen Vergleich der zwei verwendeten Modellierungsmethoden, wie es ansonsten mangels Kenntnis des wahren zugrundeliegenden funktionalen Zusammenhangs nicht möglich ist

DOI 10.1007/s00894-005-0068-9 ORIGINAL PAPER

Abstract Little is known about the relationship between the function and structure of materials. Materials (solids with a function) are complex entities and a better knowledge of the parameters that contribute to function is desirable. Here, we present modeling approaches that correlate chemical composition with function of heterogeneous catalysts. The complete composition space of the mixed oxides of Ni–Cr–Mn and of Ni–Co–Mo–Mn (10 % spacing) have been measured for the oxidation of propene to acroleine. The data have been collected, visualized and modeled. Different mathematical approaches such as Support Vector Machines, multilevel Bsplines approximation and Kriging have been applied to model this relationship. High-throughput screening data of ternary and quaternary composition spreads are approximated to locate catalysts of high activity within the search space. For quaternary systems, slice plots offer a good tool for visualization of the results. Using these approximation techniques, the composition of the most active catalysts can be predicted. The study documents that distinct relationships between chemical composition and catalytic function exist and can be described by mathematical models

Visualization of High-Dimensional Combinatorial Catalysis Data

The role of various techniques for visualization of high-dimensional data is demonstrated in the context of combinatorial high-throughput experimentation (HTE). Applying visualization tools, we identify which constituents of catalysts are associated with final products in a huge combinatorially generated data set of heterogeneous catalysts, and catalytic activity regions are identified with respect to pentanary composition spreads of catalysts. A radial visualization scheme directly visualizes pentanary composition spreads in two-dimensional (2D) space and catalytic activity of a final product by combining high-throughput results from five slate libraries. A glyph plot provides many possibilities for visualizing high-dimensional data with interactive tools. For catalyst discovery and lead optimization, this work demonstrates how large multidimensional catalysis data sets are visualized in terms of quantitative composition activity relationships (QCAR) to effectively identify the relevant key role of compositions (i.e., lead compositions) of catalysts.Reprinted with permission from ACS Combinatorial Chemistry 11 (2009): 385–392, doi:10.1021/cc800194j. Copyright 2009 American Chemical Society.</p

Modelling Quantitative Composition Activity Relationships (QCARs) for Heterogeneous Catalysts

First of all, I want to express my gratitude to Prof. Dr. W. F. Maier for giving me the opportunity to join his team and to start my work in a field being completely new to me. I am very thankful for all his support, his open mind and his encouraging ideas throughout the whole thesis. Second, I thank Prof. Dr. M. Springborg for his time and interest in this thesis. Especially, I would like to thank Prof. Dr. K. Rajan at Iowa State University, USA, for his kind invitations to join his work group and to visit him in Troy and Ames. I am very grateful to my dear colleague and friend Dr. Changwon Suh at Iowa State University who helped me to deepen my understanding of Principal Component Analysis and high-dimensional visualization techniques. Our collaboration has always been a great pleasure. I would like to thank Prof. Dr. F. Hamprecht at IWR in Heidelberg for his kind advice in the application of Kriging and the discussions we had. Moreover, I want to thank all my colleagues and friends in Saarbrücken for the friendly and positive atmosphere during my PhD-time and all the wonderful moment