Kinetics and Catalysis of the Water-Gas-Shift Reaction: A Microkinetic and Graph Theoretic Approach

The search for environmentally benign energy sources is becoming increasingly urgent. One such technology is fuel cells, e.g., the polymer electrolyte membrane (PEM) fuel cell which uses hydrogen as a fuel and emits only H2O. However, reforming hydrocarbon fuels to produce the needed hydrogen yields reformate streams containing CO2 as well as CO, which is toxic to the PEM fuel cell at concentrations above 100ppm. As the amount of CO permitted to reach the fuel cell increases, the performance of the PEM fuel cell decreases until it ultimately stops functioning. The water-gas-shift (WGS) reaction, CO + H2O \u3c-\u3e H2 + CO2, provides a method for extracting the energy from the toxic CO by converting it into usable H2 along with CO2 which can be tolerated by the fuel cell. Although a well established industrial process, alternate catalysts are sought for fuel cell application. Catalyst selection for the WGS reaction has, until recently, been based on trial-and-error screening of potential catalysts due to a lack of fundamental understanding of the catalyst\u27s functioning. For this reason, we embarked on a deeper understanding of the molecular events involved in the WGS reaction such that a more systematic and theory-guided approach may be used to design and select catalysts more efficiently, i.e., rational catalyst design. The goal of this research was to develop a comprehensive predictive microkinetic model for the WGS reaction which is based solely on a detailed mechanism as well as theories of surface-molecule interactions (i.e., the transition-state theory) with energetic parameters determined a priori. This was followed by a comparison of the experimental results of sample catalysts to validate the model for various metal-based catalysts of interest including Cu, Fe, Ni, Pd, Pt, Rh, and Ru. A comprehensive mechanism of the plausible elementary reaction steps was compiled from existing mechanisms in the literature. These were supplemented with other likely candidates which are derivatives of those identified in the literature. Using established theories, we predicted the kinetics of each of the elementary reaction steps on metal catalysts of interest. The Unity Bond Index-Quadratic Exponential Potential Method (UBI-QEP) was used to predict the activation energies in both the forward and reverse direction of each step based solely on heats of chemisorption and bond dissociation energies of the species involved. The Transition State Theory (TST) was used to predict the pre-exponential factors for each step assuming an immobile transition state; however, the pre-exponential factors were adjusted slightly to ensure thermodynamic consistency with the overall WGS reaction. In addition, we have developed a new and powerful theoretical tool to gain further insight into the dominant pathways on a catalytic surface as reactants become products. Reaction Route (RR) Graph Theory incorporates fundamental elements of graph theory and electrical network theory to graphically depict and analyze reaction mechanisms. The stoichiometry of a mechanism determines the connectivity of the elementary reaction steps. Each elementary reaction step is viewed as a single branch with an assumed direction corresponding to the assumed forward direction of the elementary reaction step. The steps become interconnected via nodes which reflect the quasi-steady state conditions of the species represented by the node. A complete RR graph intertwines a series of routes by which the reactants may be converted to products. Once constructed, the RR graph may be converted into an electrical network by replacing, in the steady-state case, each elementary reaction step branch with a resistor and including the overall reaction as a power source where rate and affinity correspond to current and voltage, respectively. A simplification and reduction of the mechanism may be performed based on results from a rigorous De Donder affinity analysis as it correlates to Kirchhoff\u27s Voltage Law (KVL), akin to thermodynamic consistency, coupled with quasi-steady state conditions, i.e., conservation of mass, analyzed using Kirchhoff\u27s Current Law (KCL). Hence, given the elementary reaction step resistances, in conjunction with Kirchhoff\u27s Laws, a systematic reduction of the network identifies the dominant routes, e.g., the routes with the lowest resistance, along with slow and quasi-equilibrium elementary reaction steps, yielding a simplified mechanism from which a predictive rate expression may possibly be derived. Here, we have applied RR Graph Theory to the WGS reaction. An 18-step mechanism was employed to understand and predict the kinetics of the WGS reaction. From the stoichiometric matrix for this mechanism, the topological features necessary to assemble the RR graph, namely the intermediate nodes, terminal nodes, empty reaction routes and full reaction routes, were enumerated and the graph constructed. The assembly of the RR graph provides a comprehensive overview of the mechanism. After reduction of the network, the simplified mechanism, comprising the dominant pathways, identified the quasi-equilibrium and rate-determining steps, which were used to determine the simplified rate expression which predicts the rate of the complete mechanism for different catalysts. Experimental investigations were conducted on the catalysts of interest to validate the microkinetic model derived. Comparison of the experimental results from the industrially employed catalysts (e.g., Cu, Ni, Fe, etc.) shows that the simplified microkinetic model sufficiently predicts the behavior of the WGS reaction for this series of catalysts with very good agreement. Other catalysis tested (Pt, Pd, Rh and Ru), however, had sufficient methanation activity that a direct comparison with WGS kinetics could not be made. In summary, we have developed a comprehensive approach to unravel the mechanism and kinetics of a catalytic reaction. The methodology described provides a more fundamental depiction of events on the surface of a catalyst paving the way for rational analysis and catalyst design. Illustrated here with the WGS reaction as an example, we show that the dominant RRs may be systematically determined through the application of rigorous fundamental constraints (e.g. thermodynamic consistency and mass conservation) yielding a corresponding explicit a priori rate expression which illustrates very good agreement not only with the complete microkinetic mechanism, but also the experimental data. Overall, RR graph theory is a powerful new tool that may become invaluable for unraveling the mechanism and kinetics of complex catalytic reactions via a common-sense approach based on fundamentals

Kinetic model construction using chemoinformatics

Kinetic models of chemical processes not only provide an alternative to costly experiments; they also have the potential to accelerate the pace of innovation in developing new chemical processes or in improving existing ones. Kinetic models are most powerful when they reflect the underlying chemistry by incorporating elementary pathways between individual molecules. The downside of this high level of detail is that the complexity and size of the models also steadily increase, such that the models eventually become too difficult to be manually constructed. Instead, computers are programmed to automate the construction of these models, and make use of graph theory to translate chemical entities such as molecules and reactions into computer-understandable representations. This work studies the use of automated methods to construct kinetic models. More particularly, the need to account for the three-dimensional arrangement of atoms in molecules and reactions of kinetic models is investigated and illustrated by two case studies. First of all, the thermal rearrangement of two monoterpenoids, cis- and trans-2-pinanol, is studied. A kinetic model that accounts for the differences in reactivity and selectivity of both pinanol diastereomers is proposed. Secondly, a kinetic model for the pyrolysis of the fuel “JP-10” is constructed and highlights the use of state-of-the-art techniques for the automated estimation of thermochemistry of polycyclic molecules. A new code is developed for the automated construction of kinetic models and takes advantage of the advances made in the field of chemo-informatics to tackle fundamental issues of previous approaches. Novel algorithms are developed for three important aspects of automated construction of kinetic models: the estimation of symmetry of molecules and reactions, the incorporation of stereochemistry in kinetic models, and the estimation of thermochemical and kinetic data using scalable structure-property methods. Finally, the application of the code is illustrated by the automated construction of a kinetic model for alkylsulfide pyrolysis

A new formulation for symbolic regression to identify physico-chemical laws from experimental data

A modification to the mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed with the aim of identification of physical models from noisy experimental data. In the proposed formulation, a binary tree in which equations are represented as directed, acyclic graphs, is fully constructed for a pre-defined number of layers. The introduced modification results in the reduction in the number of required binary variables and removal of redundancy due to possible symmetry of the tree formulation. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the numbers of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was proven to be successful in identifying the correct physical models describing the relationship between shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of chemical reactions. Future work will focus on addressing the limitations of the present formulation and solver to enable extension of target problems to larger, more complex physical models.EPSRC EP/R009902/

Multi-Scale Modeling and Simulation of Cell Signaling and Transport in Renal Collecting Duct Principal Cells

The response of cells to their environment is driven by a variety of proteins and messenger molecules. In eukaryotes, their distribution and location in the cell is regulated by the vesicular transport system. The transport of aquaporin 2 between membrane and storage region is a crucial part of the water reabsorption in renal principal cells, and its malfunction can lead to Diabetes insipidus. To understand the regulation of this system, I aggregated pathways and mechanisms from literature and derived models in a hypothesis-driven approach. Furthermore, I combined the models to a single multi-scale model to gain insight into key regulatory mechanisms of aquaporin 2 recycling. To achieve this, I developed a computational framework for the modeling and simulation of cellular signaling systems. The framework integrates reaction and difusion of biochemical entities on a microscopic scale with mobile vesicles, membranes, and compartments on a cellular level. The simulation uses an adaptive step-width approach that e ciently regulates the agent-based simulation of macroscopic components with the numerical integration of mass action kinetics and grid-based nite diference methods. A reaction network generation algorithm was designed, that, in combination with a highly-modular modeling approach, allows for fast model prototyping. The analysis of the aquaporin 2 model system rationalizes that the compartmentalization of cAMP in renal principal cells is a result of the protein kinase A signalosome and can only occur if speci c cellular components are observed in conjunction. Endocytotic and exocytotic processes are inherently connected and can be regulated by the same protein kinase A signal.:Abstract 1. Introduction 1.1. Eukaryotic Signaling 1.2. Modeling and Simulation of Cellular Processes 1.3. Aquaporin 2 recycling 1.4. Motivation and Aims 1.5. Outline I. Background 2. Modeling and Simulation of Complex Signaling Pathways 2.1. Multi-scale Modeling 2.1.1. Approaches to Multi-scale Modeling 2.1.2. Reduction of Computational Complexity 2.2. Models of Chemical Reaction Networks 2.2.1. Reactions and Reaction Rates 2.2.2. Numerical Solutions 2.2.3. Reaction Network Generation 2.3. Models of Intracellular Transport 2.3.1. Undirected Transport 2.3.2. Directed Transport 3. Aquaporin 2 Recycling in Renal Principal Cells 3.1. The Physiology of Water Homeostasis 3.2. Molecular Mechanisms of the Vasopressin Response 3.2.1. The Vasopressin Receptor 3.2.2. cAMP Regulation of Protein Kinase A 3.2.3. Endo- and Exocytosis 3.3. Models of Water Transport in Renal Principal Cells II. Results & Discussion 4. Multi-scale Simulation of Cellular Signaling Pathways 4.1. Scale Separation and Bridging 4.2. Micro-scale Simulation Approach 4.2.1. Difusion and Discretization of the Simulation Space 4.2.2. Reaction Kinetics 4.3. Rule-based Reaction Network Generation 4.3.1. Definition of the Data Model 4.3.2. Design of Rule Based Reactions 4.3.3. Automated Generation of Reaction Networks 4.4. Macro-scale Simulation Approach 4.4.1. Agent-based Simulation of Discrete Entities 4.4.2. Modules for Displacement-based Behavior 4.5. Modularization and Error Estimation 4.5.1. Determination of the Numerical Error 4.5.2. Modularization of Concentration-based Events 4.5.3. Determination of the Displacement-based Error 5. Aquaporin 2 Recycling Model and Simulation 5.1. Model of Allosteric PKA Phosphorylation 5.1.1. Model Design 5.1.2. Simulation Results and Discussion 5.1.3. Conclusions 5.2. cAMP Compartmentalization in the Vesicle Storage Region 5.2.1. Model Design 5.2.2. Simulation Results and Discussion 5.2.3. Conclusions 5.3. Clathrin-mediated Endocytosis 5.3.1. Model Design 5.3.2. Simulation Results and Discussion 5.3.3. Conclusions 5.4. Intracellular Transport and Recycling 5.4.1. Model Design 5.4.2. Simulation Results and Discussion 6. Conclusion 6.1. Modeling and simulation approach 6.2. Insights into the AQP2 recycling model III. Appendix A. Code Availability B. Module Overview Bibliograph

Modelling Early Transitions Toward Autonomous Protocells

This thesis broadly concerns the origins of life problem, pursuing a joint approach that combines general philosophical/conceptual reflection on the problem along with more detailed and formal scientific modelling work oriented in the conceptual perspective developed. The central subject matter addressed is the emergence and maintenance of compartmentalised chemistries as precursors of more complex systems with a proper cellular organization. Whereas an evolutionary conception of life dominates prebiotic chemistry research and overflows into the protocells field, this thesis defends that the 'autonomous systems perspective' of living phenomena is a suitable - arguably the most suitable - conceptual framework to serve as a backdrop for protocell research. The autonomy approach allows a careful and thorough reformulation of the origins of cellular life problem as the problem of how integrated autopoietic chemical organisation, present in all full-fledged cells, originated and developed from more simple far-from-equilibrium chemical aggregate systems.Comment: 205 Pages, 27 Figures, PhD Thesis Defended Feb 201