Kinetics of chemical reactions : decoding complexity

Cover
Title Page
Copyright
Preface to First Edition
Preface to Second Edition
Contents
Chapter 1 Introduction
	1.1 Overview
	1.2 Decoding Complexity in Chemical Kinetics
	1.3 Three Types of Chemical Kinetics
		1.3.1 Applied Kinetics
		1.3.2 Detailed Kinetics
		1.3.3 Mathematical Kinetics
	1.4 Challenges and Goals. How to Kill Chemical Complexity
		1.4.1 "Gray-Box" Approach
		1.4.2 Analysis of Kinetic Fingerprints
		1.4.3 Non-steady-state Kinetic Screening
	1.5 What Our Book is Not About. Our Book Among Other Books on Chemical Kinetics
	1.6 The Logic in the Reasoning of This Book
	1.7 How Chemical Kinetics and Mathematics are Interwoven in This Book
	1.8 History of Chemical Kinetics
	References
Chapter 2 Chemical Reactions and Complexity
	2.1 Introduction
	2.2 Elementary Reactions and the Mass-Action Law
		2.2.1 Homogeneous Reactions
		2.2.2 Heterogeneous Reactions
		2.2.3 Rate Expressions
	2.3 The Reaction Rate and Net Rate of Production of a Component – A Big Difference
	2.4 Dimensions of the Kinetic Parameters and Their Orders of Magnitude
	2.5 Conclusions
	Nomenclature
	References
Chapter 3 Kinetic Experiments: Concepts and Realizations
	3.1 Introduction
	3.2 Experimental Requirements
	3.3 Material Balances
	3.4 Classification of Reactors for Kinetic Experiments
		3.4.1 Steady-state and Non-steady-state Reactors
		3.4.2 Transport in Reactors
		3.4.3 Ideal Reactors
			3.4.3.1 Batch Reactor
			3.4.3.2 Continuous Stirred-tank Reactor
			3.4.3.3 Plug-flow Reactor
		3.4.4 Ideal Reactors with Solid Catalyst
			3.4.4.1 Batch Reactor
			3.4.4.2 Continuous Stirred-tank Reactor
			3.4.4.3 Plug-flow Reactor
			3.4.4.4 Pulse Reactor
		3.4.5 Determination of the Net Rate of Production
	3.5 Formal Analysis of Typical Ideal Reactors
		3.5.1 Batch Reactor
			3.5.1.1 Irreversible Reaction
			3.5.1.2 Reversible Reaction
			3.5.1.3 How to Distinguish Parallel Reactions from Consecutive Reactions
		3.5.2 Steady-state Plug-flow Reactor
		3.5.3 Non-steady-state Continuous Stirred-tank Reactor
			3.5.3.1 Irreversible Reaction
			3.5.3.2 Reversible Reaction
		3.5.4 Thin-zone TAP Reactor
	3.6 Kinetic-model-free Analysis
		3.6.1 Steady State
		3.6.2 Non-steady State
			3.6.2.1 Continuous Stirred-tank Reactor
			3.6.2.2 Plug-flow Reactor
	3.7 Diagnostics of Kinetic Experiments in Heterogeneous Catalysis
		3.7.1 Gradients at Reactor and Catalyst-pellet Scale
		3.7.2 Experimental Diagnostics and Guidelines
			3.7.2.1 Test for External Mass-transfer Effect
			3.7.2.2 Test for Internal Mass-transport Effect
			3.7.2.3 Guidelines
		3.7.3 Theoretical Diagnostics
			3.7.3.1 External Mass Transfer
			3.7.3.2 External Heat Transfer
			3.7.3.3 Internal Mass Transport
			3.7.3.4 Internal Heat Transport
			3.7.3.5 Non-steady-state Operation
	Nomenclature
	References
Chapter 4 Chemical Book-keeping: Linear Algebra in Chemical Kinetics
	4.1 Basic Elements of Linear Algebra
	4.2 Linear Algebra and Complexity of Chemical Reactions
		4.2.1 Atomic Composition of Chemical Components: Molecules "Consist of" Atoms
			4.2.1.1 Molecular Matrix
			4.2.1.2 Linear Algebra and Laws of Mass Conservation
			4.2.1.3 Key Components and Their Number
		4.2.2 Stoichiometry of Chemical Reactions: Reactions "Consist of" Chemical Components
			4.2.2.1 Stoichiometric Matrix
			4.2.2.2 Difference and Similarity Between the Conservation Law for Chemical Elements and the Kinetic Mass-Conservation Law
			4.2.2.3 Similarity and Difference Between the Number of Key Components and the Number of Key Reactions
		4.2.3 Detailed Mechanism of Complex Reactions: Complex Reactions "Consist of" Elementary Reactions
			4.2.3.1 Mechanisms and Horiuti Numbers
			4.2.3.2 Matrices and Independent Routes of Complex Reactions
	4.3 Concluding Remarks
	4.A Book-Keeping Support in Python/SymPy
		4.A.1 Skeleton Code Generation
		4.A.2 Matrix Augmentation and Reduction
	Nomenclature
	References
Chapter 5 Steady-State Chemical Kinetics: A Primer
	5.1 Introduction to Graph Theory
	5.2 Representation of Complex Mechanisms as Graphs
		5.2.1 Single-route Mechanisms
		5.2.2 Single-route Mechanism with a Buffer Step
		5.2.3 Two-route Mechanisms
		5.2.4 Number of Independent Reaction Routes and Horiuti's Rule
	5.3 How to Derive the Reaction Rate for a Complex Reaction
		5.3.1 Introduction
		5.3.2 Kinetic Cramer's Rule and Trees of the Chemical Graph
		5.3.3 Forward and Reverse Reaction Rates
		5.3.4 Single-route Linear Mechanism – General Case
		5.3.5 How to Find the Kinetic Equation for the Reverse Reaction: The Horiuti–Boreskov Problem
		5.3.6 What About the Overall Reaction – A Provocative Opinion
	5.4 Derivation of Steady-State Kinetic Equations for a Single-Route Mechanism – Examples
		5.4.1 Two-step Mechanisms
			5.4.1.1 Michaelis–Menten Mechanism
			5.4.1.2 Water–Gas Shift Reaction
			5.4.1.3 Liquid-phase Hydrogenation
		5.4.2 Three-step Mechanisms
			5.4.2.1 Oxidation of Sulfur Dioxide
			5.4.2.2 Coupling Reaction
		5.4.3 Four-step Mechanisms
		5.4.4 Five-step Mechanisms
		5.4.5 Single-route Linear Mechanisms with a Buffer Step
	5.5 Derivation of Steady-State Kinetic Equations for Multi Route Mechanisms: Kinetic Coupling
		5.5.1 Cycles Having a Common Intermediate
		5.5.2 Cycles Having a Common Step
		5.5.3 Cycles Having Two Common Steps
		5.5.4 Different Types of Coupling Between Cycles
	Nomenclature
	References
Chapter 6 Steady-state Chemical Kinetics: Machinery
	6.1 Analysis of Rate Equations
		6.1.1 Dependence of Parameters on Temperature and Number of Identifiable Parameters
		6.1.2 Simplifying Assumptions
			6.1.2.1 Fast Step
			6.1.2.2 Rate-limiting Step
			6.1.2.3 Quasi-equilibrated Step(s)
			6.1.2.4 Irreversible Step(s)
			6.1.2.5 Dependence of the Reaction Rate on Concentrations
	6.2 Apparent Kinetic Parameters: Reaction Order and Activation Energy
		6.2.1 Definitions
		6.2.2 Two-step Mechanism of an Irreversible Reaction
			6.2.2.1 Apparent Partial Reaction Order
			6.2.2.2 Apparent Activation Energy
		6.2.3 More Examples
			6.2.3.1 Apparent Partial Reaction Order
			6.2.3.2 Apparent Activation Energy
		6.2.4 Some Further Comments
	6.3 How to Reveal Mechanisms Based on Steady-state Kinetic Data
		6.3.1 Assumptions
		6.3.2 Direct and Inverse Problems of Kinetic Modeling
		6.3.3 Minimal and Non-minimal Mechanisms
			6.3.3.1 Two-step Catalytic Mechanisms
			6.3.3.2 Three-step Catalytic Mechanisms
			6.3.3.3 Four-step Catalytic Mechanisms
			6.3.3.4 Five-step Catalytic Mechanisms
			6.3.3.5 Summary
		6.3.4 What Kind of Kinetic Model Do We Need to Describe Steady-state Kinetic Data and to Decode Mechanisms?
			6.3.4.1 Kinetic Resistance
			6.3.4.2 Analysis of the Kinetic Resistance in Identifying and Decoding Mechanisms and Models
			6.3.4.3 Concentration Terms of the Kinetic Resistance and Structure of the Detailed Mechanism
			6.3.4.4 Principle of Component Segregation
	6.4 Concluding Remarks
	Nomenclature
	References
Chapter 7 Linear and Nonlinear Relaxation: Stability
	7.1 Introduction
		7.1.1 Linear Relaxation
		7.1.2 Relaxation Times and Steady-state Reaction Rate
			7.1.2.1 Relaxation Times and Kinetic Resistance
			7.1.2.2 Temkin's Rule. Is it Valid?
		7.1.3 Further Comments
	7.2 Relaxation in a Closed System − Principle of Detailed Equilibrium
	7.3 Stability – General Concept
		7.3.1 Elements of the Qualitative Theory of Differential Equations
		7.3.2 Local Stability – Rigorous Definition
		7.3.3 Local Stability – System with two Variables
			7.3.3.1 Real Roots
			7.3.3.2 Imaginary Roots
		7.3.4 Self-sustained Oscillations and Global Dynamics
	7.4 Simplifications of Non-steady-state Models
		7.4.1 Abundance and Linearization
		7.4.2 Fast Step − Equilibrium Approximation
		7.4.3 Rate-limiting Step Approximation
		7.4.4 Quasi-steady-state Approximation
	Nomenclature
	References
Chapter 8 Nonlinear Mechanisms: Steady State and Dynamics
	8.1 Critical Phenomena
	8.2 Isothermal Critical Effects in Heterogeneous Catalysis: Experimental Facts
		8.2.1 Multiplicity of Steady States
		8.2.2 Self-sustained Oscillations of the Reaction Rate in Heterogeneous Catalytic Reactions
		8.2.3 Diversity of Critical Phenomena and Their Causes
	8.3 Ideal Simple Models: Steady State
		8.3.1 Parallel and Consecutive Adsorption Mechanisms
		8.3.2 Impact Mechanisms
		8.3.3 Simplest Mechanism for the Interpretation of Multiplicity of Steady States
		8.3.4 Hysteresis: Influence of Reaction Reversibility
		8.3.5 Competition of Intermediates
	8.4 Ideal Simple Models: Dynamics
		8.4.1 Relaxation Characteristics of the Parallel Adsorption Mechanism
		8.4.2 Catalytic Oscillators
			8.4.2.1 Simplest Catalytic Oscillator
			8.4.2.2 Relaxation of Self-sustained Oscillation: Model
			8.4.2.3 Other Catalytic Oscillators
		8.4.3 Fine Structure of Kinetic Dependences
	8.5 Structure of Detailed Mechanism and Critical Phenomena: Relationships
		8.5.1 Mechanisms Without Interaction Between Intermediates
		8.5.2 Horn–Jackson–Feinberg Mechanism
	8.6 Nonideal Factors
	8.7 Conclusions
	Nomenclature
	References
Chapter 9 Kinetic Polynomials
	9.1 Linear Introduction to the Nonlinear Problem: Recap
	9.2 Nonlinear Introduction
	9.3 Principles of the Approach: Quasi-Steady-State Approximation. Mathematical Basis
		9.3.1 Introduction
		9.3.2 Examples
	9.4 Kinetic Polynomials: Derivation and Properties
		9.4.1 Resultant Reaction Rate: A Necessary Mathematical Basis
		9.4.2 Properties of the Kinetic Polynomial
		9.4.3 Examples of Kinetic Polynomials
			9.4.3.1 Impact Mechanism
			9.4.3.2 Adsorption Mechanism
	9.5 Kinetic Polynomial: Classical Approximations and Simplifications
		9.5.1 Rate-limiting Step
		9.5.2 Vicinity of Thermodynamic Equilibrium
		9.5.3 Thermodynamic Branch
	9.6 Application of Results of the Kinetic-Polynomial Theory: Cycles Across an Equilibrium
	9.7 Critical Simplification
		9.7.1 Critical Simplification: A Simple Example
		9.7.2 Critical Simplification and Limitation
		9.7.3 Principle of Critical Simplification: General Understanding and Application
	9.8 Concluding Remarks
	9.A Appendix
	Nomenclature
	References
Chapter 10 Temporal Analysis of Products: Principles, Applications, and Theory
	10.1 Introduction
	10.2 Characteristics of TAP
		10.2.1 The TAP Experiment
		10.2.2 Description and Operation of a TAP Reactor System
		10.2.3 Basic Principles of TAP
	10.3 Position of TAP Among Other Kinetic Methods
		10.3.1 Uniformity of the Active Zone
			10.3.1.1 Continuous Stirred-tank Reactor
			10.3.1.2 Plug-flow Reactor
			10.3.1.3 TAP Reactor
		10.3.2 Domain of Conditions
		10.3.3 Possibility of Obtaining Relevant Kinetic Information
		10.3.4 Relationship Between Observed Kinetic Characteristics and Catalyst Properties
		10.3.5 Model-Free Kinetic Interpretation of Data
		10.3.6 Summary of the Comparison
		10.3.7 Applications of TAP
	10.4 Qualitative Analysis of TAP Data: Examples
		10.4.1 Single-pulse TAP Experiments
		10.4.2 Pump-probe TAP Experiments
		10.4.3 Multipulse TAP Experiments
	10.5 Quantitative TAP Data Description. Theoretical Analysis
		10.5.1 One-Zone Reactor
			10.5.1.1 Diffusion Only
			10.5.1.2 Irreversible Adsorption
			10.5.1.3 Reversible Adsorption
		10.5.2 Two- and Three-Zone Reactors
		10.5.3 Thin-Zone TAP Reactor Configuration
		10.5.4 Moment-Based Quantitative Description of TAP Experiments
			10.5.4.1 Moments and Reactivities
			10.5.4.2 From Moments to Reactivities
			10.5.4.3 Experimental Procedure
			10.5.4.4 Summary
	10.6 Kinetic Monitoring: Strategy of Interrogative Kinetics
		10.6.1 State-by-state Kinetic Monitoring. Example: Oxidation of Furan
		10.6.2 Strategy of Interrogative Kinetics
	10.7 Theoretical Frontiers
		10.7.1 Global Transfer Matrix Equation
		10.7.2 Y Procedure
			10.7.2.1 Principles of the Solution
			10.7.2.2 Exact Mathematical Solution
			10.7.2.3 How to Reconstruct the Active Zone Concentration and Net Rate of Production in Practice
			10.7.2.4 Numerical Experiments
			10.7.2.5 Summary of the Y Procedure
		10.7.3 Probabilistic Theory of Single-particle TAP Experiments
	10.8 Conclusions: What Next?
	Nomenclature
	References
Chapter 11 Joint Kinetics
	11.1 Events and Invariances
	11.2 Single Reaction
		11.2.1 Batch Reactor
			11.2.1.1 Basics
			11.2.1.2 Point of Intersection
			11.2.1.3 Swapping the Equilibrium
		11.2.2 Continuous Stirred-tank Reactor
			11.2.2.1 Basis
			11.2.2.2 Point of Intersection
		11.2.3 Invariances
	11.3 Multiple Reactions
		11.3.1 Events: Intersections and Coincidences
		11.3.2 Mathematical Solutions of Kinetic Models
			11.3.2.1 Batch Reactor
			11.3.2.2 Continuous Stirred-tank Reactor
		11.3.3 First Stage: Occurrence of Single Kinetic Events
		11.3.4 Second Stage: Coincidences: Ordering Events by Pairs
		11.3.5 End Products Intersection: Intersection of B and C
		11.3.6 Invariances
	Nomenclature
	References
Chapter 12 Decoding the Past
	12.1 Chemical Time and Intermediates. Early History
	12.2 Discovery of Catalysis and Chemical Kinetics
	12.3 Guldberg and Waage's Breakthrough
	12.4 Van't Hoff's Revolution: Achievements and Contradictions
		12.4.1 Undisputable Achievements
		12.4.2 Contradictions
	12.5 Post-Van't Hoff Period: Reaction is Not a Single-act Drama
	12.6 All-in-all Confusion. Attempts at Understanding
	12.7 Out of Confusion: Physicochemical Understanding
	12.8 Towards Mathematical Chemical Kinetics
	Nomenclature
	References
Chapter 13 Decoding the Future
	13.1 A Great Achievement, a Great Illusion
	13.2 A New Paradigm for Decoding Chemical Complexity
		13.2.1 Advanced Experimental Kinetic Tools
		13.2.2 New Mathematical Tools. Chemical Kinetics and Mathematics
	References
Index
EULA