Special attention is paid to the problem of the chemical reaction complexity with theoretical and methodological concepts illustrated throughout by numerous examples taken from heterogeneous catalysis combustion and enzyme processes.
Of great interest to graduate students in both chemistry and chemical engineering.
Table of Contents
Preface to First Edition xv
Preface to Second Edition xix
1 Introduction 1
1.1 Overview 1
1.2 Decoding Complexity in Chemical Kinetics 2
1.3 Three Types of Chemical Kinetics 2
1.3.1 Applied Kinetics 3
1.3.2 Detailed Kinetics 3
1.3.3 Mathematical Kinetics 3
1.4 Challenges and Goals. How to Kill Chemical Complexity 4
1.4.1 “Gray-Box” Approach 4
1.4.2 Analysis of Kinetic Fingerprints 5
1.4.3 Non-steady-state Kinetic Screening 6
1.5 What Our Book is Not About. Our Book among Other Books on Chemical Kinetics 6
1.6 The Logic in the Reasoning of This Book 7
1.7 How Chemical Kinetics and Mathematics are Interwoven in This Book 7
1.8 History of Chemical Kinetics 8
References 12
2 Chemical Reactions and Complexity 17
2.1 Introduction 17
2.2 Elementary Reactions and the Mass-Action Law 19
2.2.1 Homogeneous Reactions 19
2.2.2 Heterogeneous Reactions 21
2.2.3 Rate Expressions 22
2.3 The Reaction Rate and Net Rate of Production of a Component - A Big Difference 23
2.4 Dimensions of the Kinetic Parameters and Their Orders of Magnitude 24
2.5 Conclusions 26
Nomenclature 26
References 28
3 Kinetic Experiments: Concepts and Realizations 29
3.1 Introduction 29
3.2 Experimental Requirements 29
3.3 Material Balances 30
3.4 Classification of Reactors for Kinetic Experiments 31
3.4.1 Steady-state and Non-steady-state Reactors 31
3.4.2 Transport in Reactors 31
3.4.3 Ideal Reactors 32
3.4.3.1 Batch Reactor 32
3.4.3.2 Continuous Stirred-tank Reactor 33
3.4.3.3 Plug-flow Reactor 34
3.4.4 Ideal Reactors with Solid Catalyst 34
3.4.4.1 Batch Reactor 34
3.4.4.2 Continuous Stirred-tank Reactor 35
3.4.4.3 Plug-flow Reactor 35
3.4.4.4 Pulse Reactor 35
3.4.5 Determination of the Net Rate of Production 36
3.5 Formal Analysis of Typical Ideal Reactors 36
3.5.1 Batch Reactor 36
3.5.1.1 Irreversible Reaction 36
3.5.1.2 Reversible Reaction 38
3.5.1.3 How to Distinguish Parallel Reactions from Consecutive Reactions 40
3.5.2 Steady-state Plug-flow Reactor 43
3.5.3 Non-steady-state Continuous Stirred-tank Reactor 43
3.5.3.1 Irreversible Reaction 43
3.5.3.2 Reversible Reaction 44
3.5.4 Thin-zone TAP Reactor 45
3.6 Kinetic-model-free Analysis 46
3.6.1 Steady State 46
3.6.2 Non-steady State 47
3.6.2.1 Continuous Stirred-tank Reactor 47
3.6.2.2 Plug-flow Reactor 48
3.7 Diagnostics of Kinetic Experiments in Heterogeneous Catalysis 49
3.7.1 Gradients at Reactor and Catalyst-pellet Scale 49
3.7.2 Experimental Diagnostics and Guidelines 49
3.7.2.1 Test for External Mass-transfer Effect 51
3.7.2.2 Test for Internal Mass-transport Effect 51
3.7.2.3 Guidelines 52
3.7.3 Theoretical Diagnostics 52
3.7.3.1 External Mass Transfer 53
3.7.3.2 External Heat Transfer 54
3.7.3.3 InternalMass Transport 56
3.7.3.4 Internal Heat Transport 59
3.7.3.5 Non-steady-state Operation 59
Nomenclature 59
References 62
4 Chemical Book-keeping: Linear Algebra in Chemical Kinetics 65
4.1 Basic Elements of Linear Algebra 65
4.2 Linear Algebra and Complexity of Chemical Reactions 67
4.2.1 Atomic Composition of Chemical Components: Molecules “Consist of” Atoms 68
4.2.1.1 Molecular Matrix 68
4.2.1.2 Linear Algebra and Laws of Mass Conservation 68
4.2.1.3 Key Components and Their Number 70
4.2.2 Stoichiometry of Chemical Reactions: Reactions “Consist of” Chemical Components 72
4.2.2.1 Stoichiometric Matrix 72
4.2.2.2 Difference and Similarity between the Conservation Law for Chemical Elements and the KineticMass-Conservation Law 74
4.2.2.3 Similarity and Difference between the Numbers of Key Components and the Number of Key Reactions 74
4.2.3 DetailedMechanism of Complex Reactions: Complex Reactions “Consist of” Elementary Reactions 75
4.2.3.1 Mechanisms and Horiuti Numbers 75
4.2.3.2 Matrices and Independent Routes of Complex Reactions 80
4.3 Concluding Remarks 83
4.A Book-Keeping Support in Python/SymPy 83
4.A.1 Skeleton Code Generation 83
4.A.2 Matrix Augmentation and Reduction 84
Nomenclature 88
References 90
5 Steady-State Chemical Kinetics: A Primer 93
5.1 Introduction to Graph Theory 93
5.2 Representation of Complex Mechanisms as Graphs 94
5.2.1 Single-route Mechanisms 95
5.2.2 Single-route Mechanism with a Buffer Step 97
5.2.3 Two-route Mechanisms 97
5.2.4 Number of Independent Reaction Routes and Horiuti’s Rule 99
5.3 How to Derive the Reaction Rate for a Complex Reaction 101
5.3.1 Introduction 101
5.3.2 Kinetic Cramer’s Rule and Trees of the Chemical Graph 104
5.3.3 Forward and Reverse Reaction Rates 110
5.3.4 Single-route LinearMechanism - General Case 111
5.3.5 How to Find the Kinetic Equation for the Reverse Reaction: The Horiuti-Boreskov Problem 112
5.3.6 What About the Overall Reaction - A Provocative Opinion 114
5.4 Derivation of Steady-State Kinetic Equations for a Single-Route Mechanism - Examples 116
5.4.1 Two-step Mechanisms 117
5.4.1.1 Michaelis-Menten Mechanism 117
5.4.1.2 Water-Gas Shift Reaction 118
5.4.1.3 Liquid-phase Hydrogenation 119
5.4.2 Three-step Mechanisms 120
5.4.2.1 Oxidation of Sulfur Dioxide 120
5.4.2.2 Coupling Reaction 121
5.4.3 Four-step Mechanisms 122
5.4.4 Five-step Mechanisms 124
5.4.5 Single-route Linear Mechanisms with a Buffer Step 125
5.5 Derivation of Steady-State Kinetic Equations for Multi Route Mechanisms: Kinetic Coupling 126
5.5.1 Cycles Having a Common Intermediate 127
5.5.2 Cycles Having a Common Step 129
5.5.3 Cycles Having Two Common Steps 130
5.5.4 Different Types of Coupling between Cycles 131
Nomenclature 132
References 133
6 Steady-state Chemical Kinetics:Machinery 137
6.1 Analysis of Rate Equations 137
6.1.1 Dependence of Parameters on Temperature and Number of Identifiable Parameters 138
6.1.2 Simplifying Assumptions 140
6.1.2.1 Fast Step 140
6.1.2.2 Rate-limiting Step 141
6.1.2.3 Quasi-equilibrated Step(s) 141
6.1.2.4 Irreversible Step(s) 142
6.1.2.5 Dependence of the Reaction Rate on Concentrations 143
6.2 Apparent Kinetic Parameters: Reaction Order and Activation Energy 143
6.2.1 Definitions 143
6.2.2 Two-step Mechanism of an Irreversible Reaction 145
6.2.2.1 Apparent Partial Reaction Order 145
6.2.2.2 Apparent Activation Energy 146
6.2.3 More Examples 147
6.2.3.1 Apparent Partial Reaction Order 147
6.2.3.2 Apparent Activation Energy 152
6.2.4 Some Further Comments 153
6.3 How to Reveal Mechanisms Based on Steady-state Kinetic Data 154
6.3.1 Assumptions 154
6.3.2 Direct and Inverse Problems of Kinetic Modeling 155
6.3.3 Minimal and Non-minimal Mechanisms 155
6.3.3.1 Two-step Catalytic Mechanisms 156
6.3.3.2 Three-step Catalytic Mechanisms 156
6.3.3.3 Four-step Catalytic Mechanisms 157
6.3.3.4 Five-step Catalytic Mechanisms 158
6.3.3.5 Summary 158
6.3.4 What Kind of Kinetic Model Do We Need to Describe Steady-state Kinetic Data and to Decode Mechanisms? 159
6.3.4.1 Kinetic Resistance 159
6.3.4.2 Analysis of the Kinetic Resistance in Identifying and Decoding Mechanisms and Models 160
6.3.4.3 Concentration Terms of the Kinetic Resistance and Structure of the Detailed Mechanism 160
6.3.4.4 Principle of Component Segregation 164
6.4 Concluding Remarks 165
Nomenclature 166
References 167
7 Linear and Nonlinear Relaxation: Stability 169
7.1 Introduction 169
7.1.1 Linear Relaxation 171
7.1.2 Relaxation Times and Steady-state Reaction Rate 173
7.1.2.1 Relaxation Times and Kinetic Resistance 173
7.1.2.2 Temkin’s Rule. Is it Valid? 174
7.1.3 Further comments 176
7.2 Relaxation in a Closed System − Principle of Detailed Equilibrium 177
7.3 Stability - General Concept 180
7.3.1 Elements of the Qualitative Theory of Differential Equations 180
7.3.2 Local Stability - Rigorous Definition 182
7.3.3 Local Stability - System with two Variables 184
7.3.3.1 Real Roots 186
7.3.3.2 Imaginary Roots 187
7.3.4 Self-sustained Oscillations and Global Dynamics 188
7.4 Simplifications of Non-steady-state Models 190
7.4.1 Abundance and Linearization 190
7.4.2 Fast Step − Equilibrium Approximation 191
7.4.3 Rate-limiting Step Approximation 191
7.4.4 Quasi-steady-state Approximation 192
Nomenclature 198
References 200
8 Nonlinear Mechanisms: Steady State and Dynamics 203
8.1 Critical Phenomena 203
8.2 Isothermal Critical Effects in Heterogeneous Catalysis: Experimental Facts 205
8.2.1 Multiplicity of Steady States 205
8.2.2 Self-sustained Oscillations of the Reaction Rate in Heterogeneous Catalytic Reactions 207
8.2.3 Diversity of Critical Phenomena and Their Causes 207
8.3 Ideal Simple Models: Steady State 209
8.3.1 Parallel and Consecutive Adsorption Mechanisms 209
8.3.2 Impact Mechanisms 210
8.3.3 Simplest Mechanism for the Interpretation of Multiplicity of Steady States 212
8.3.4 Hysteresis: Influence of Reaction Reversibility 218
8.3.5 Competition of Intermediates 223
8.4 Ideal Simple Models: Dynamics 227
8.4.1 Relaxation Characteristics of the Parallel Adsorption Mechanism 227
8.4.2 Catalytic Oscillators 234
8.4.2.1 Simplest Catalytic Oscillator 234
8.4.2.2 Relaxation of Self-sustained Oscillation: Model 239
8.4.2.3 Other Catalytic Oscillators 239
8.4.3 Fine Structure of Kinetic Dependences 242
8.5 Structure of Detailed Mechanism and Critical Phenomena: Relationships 244
8.5.1 Mechanisms without Interaction between Intermediates 245
8.5.2 Horn-Jackson-Feinberg Mechanism 247
8.6 Nonideal Factors 250
8.7 Conclusions 251
Nomenclature 251
References 253
9 Kinetic Polynomials 263
9.1 Linear Introduction to the Nonlinear Problem: Recap 263
9.2 Nonlinear Introduction 266
9.3 Principles of the Approach: Quasi-Steady-State Approximation. Mathematical Basis 267
9.3.1 Introduction 267
9.3.2 Examples 269
9.4 Kinetic Polynomials: Derivation and Properties 270
9.4.1 Resultant Reaction Rate: A Necessary Mathematical Basis 270
9.4.2 Properties of the Kinetic Polynomial 272
9.4.3 Examples of Kinetic Polynomials 273
9.4.3.1 Impact Mechanism 273
9.4.3.2 Adsorption Mechanism 274
9.5 Kinetic Polynomial: Classical Approximations and Simplifications 276
9.5.1 Rate-limiting Step 276
9.5.2 Vicinity of Thermodynamic Equilibrium 278
9.5.3 Thermodynamic Branch 279
9.6 Application of Results of the Kinetic-polynomial Theory: Cycles across an Equilibrium 282
9.7 Critical Simplification 289
9.7.1 Critical Simplification: A Simple Example 289
9.7.2 Critical Simplification and Limitation 295
9.7.3 Principle of Critical Simplification: General Understanding and Application 296
9.8 Concluding Remarks 297
9.A Appendix 298
Nomenclature 299
References 301
10 Temporal Analysis of Products: Principles, Applications, and Theory 307
10.1 Introduction 307
10.2 Characteristics of TAP 309
10.2.1 The TAP Experiment 309
10.2.2 Description and Operation of a TAP Reactor System 310
10.2.3 Basic Principles of TAP 312
10.3 Position of TAP among Other Kinetic Methods 314
10.3.1 Uniformity of the Active Zone 315
10.3.1.1 Continuous Stirred-tank Reactor 315
10.3.1.2 Plug-flow Reactor 315
10.3.1.3 TAP Reactor 315
10.3.2 Domain of Conditions 315
10.3.3 Possibility of Obtaining Relevant Kinetic Information 316
10.3.4 Relationship between Observed Kinetic Characteristics and Catalyst Properties 316
10.3.5 Model-Free Kinetic Interpretation of Data 317
10.3.6 Summary of the Comparison 318
10.3.7 Applications of TAP 318
10.4 Qualitative Analysis of TAP Data: Examples 318
10.4.1 Single-pulse TAP Experiments 319
10.4.2 Pump-probe TAP Experiments 322
10.4.3 Multipulse TAP Experiments 324
10.5 Quantitative TAP Data Description.Theoretical Analysis 326
10.5.1 One-Zone Reactor 327
10.5.1.1 Diffusion Only 327
10.5.1.2 Irreversible Adsorption 330
10.5.1.3 Reversible Adsorption 331
10.5.2 Two- and Three-Zone Reactors 332
10.5.3 Thin-Zone TAP Reactor Configuration 333
10.5.4 Moment-Based Quantitative Description of TAP Experiments 336
10.5.4.1 Moments and Reactivities 336
10.5.4.2 From Moments to Reactivities 342
10.5.4.3 Experimental Procedure 345
10.5.4.4 Summary 348
10.6 Kinetic Monitoring: Strategy of Interrogative Kinetics 348
10.6.1 State-by-state Kinetic Monitoring. Example: Oxidation of Furan 348
10.6.2 Strategy of Interrogative Kinetics 352
10.7 Theoretical Frontiers 353
10.7.1 Global Transfer Matrix Equation 353
10.7.2 Y Procedure 354
10.7.2.1 Principles of the Solution 355
10.7.2.2 Exact Mathematical Solution 358
10.7.2.3 How to Reconstruct the Active Zone Concentration and Net Rate of Production in Practice 359
10.7.2.4 Numerical Experiments 361
10.7.2.5 Summary of the Y Procedure 364
10.7.3 Probabilistic Theory of Single-particle TAP Experiments 366
10.8 Conclusions:What Next? 367
Nomenclature 368
References 371
11 Joint Kinetics 383
11.1 Events and Invariances 383
11.2 Single Reaction 384
11.2.1 Batch Reactor 384
11.2.1.1 Basics 384
11.2.1.2 Point of Intersection 386
11.2.1.3 Swapping the Equilibrium 387
11.2.2 Continuous Stirred-tank Reactor 388
11.2.2.1 Basis 388
11.2.2.2 Point of Intersection 388
11.2.3 Invariances 389
11.3 Multiple Reactions 391
11.3.1 Events: Intersections and Coincidences 391
11.3.2 Mathematical Solutions of Kinetic Models 393
11.3.2.1 Batch Reactor 393
11.3.2.2 Continuous Stirred-tank Reactor 394
11.3.3 First Stage: Occurrence of Single Kinetic Events 394
11.3.4 Second Stage: Coincidences: Ordering Events by Pairs 397
11.3.5 End Products Intersection: Intersection of B and C 402
11.3.6 Invariances 403
Nomenclature 405
References 406
12 Decoding the Past 407
12.1 Chemical Time and Intermediates. Early History 407
12.2 Discovery of Catalysis and Chemical Kinetics 407
12.3 Guldberg and Waage’s Breakthrough 409
12.4 Van’t Hoff’s Revolution: Achievements and Contradictions 409
12.4.1 Undisputable Achievements 409
12.4.2 Contradictions 410
12.5 Post-Van’t Hoff Period: Reaction is Not a Single-act Drama 411
12.6 All-in-all Confusion. Attempts at Understanding 411
12.7 Out of Confusion: Physicochemical Understanding 412
12.8 Towards Mathematical Chemical Kinetics 414
Nomenclature 418
References 419
13 Decoding the Future 425
13.1 A Great Achievement, a Great Illusion 425
13.2 A New Paradigm for Decoding Chemical Complexity 426
13.2.1 Advanced Experimental Kinetic Tools 427
13.2.2 New Mathematical Tools. Chemical Kinetics and Mathematics 428
References 430
Index 433
