Presents the theory and applications of Toroidal Capillary, Microchip, and Slab Electrophoresis to analytical chemists across a range of disciplines
Written by one of the developers of Toroidal Capillary Electrophoresis (TCE), this book is the first to present this novel analytical technique, in detail, to the field of analytical chemistry.
The exact expressions of separation efficiency, resolution, peak capacity, and many other performance indicators of the open and toroidal layouts are presented and compared.
Featuring numerous illustrations throughout, Open and Toroidal Electrophoresis: Ultra-High Separation Efficiencies in Capillaries, Microchips and Slabs offers chapters covering: Solvents and Buffer Solutions; Fundamentals of Electrophoresis; Open Layout; and Toroidal Layout. Confronting Performance Indicators is next, followed by chapters on High Voltage Modules and Distributors; Heat Removal and Temperature Control; and Detectors. The book finishes with an examination of the applications of Toroidal Electrophoresis.
The first book to offer a detailed account of Toroidal Electrophoresis - written by one of its creators
- Compares the toroidal layouts with the well-established open layouts of the three most used platforms (Capillary, Microchip, and Slab)
- Provides solutions to many of the experimental issues arising in electromigration techniques and discusses the voltage distributors and detectors that are compatible with the toroidal layouts
- Richly illustrated with a large number of useful equations showing the relationships between important operational parameters and the performance indicators
Open and Toroidal Electrophoresis is aimed at method developers and separation scientists working in clinical analysis, and food analysis, as well as those in pharmacology, disease biomarker applications, and nucleic acid analysis using the Capillary, Microchip, or slab Platform. It will also benefit undergraduate and graduate students of inorganic analytical chemistry, organic analytical chemistry, bioanalysis, pharmaceutical sciences, clinical sciences, and food analysis.
Table of Contents
Preface xiii
Acronyms xv
Symbols and Conventions xvii
Introduction xxi
1 Solvents and Buffer Solutions 1
1.1 Water as a Solvent 1
1.1.1 Temperature and Brownian Motion 1
1.1.2 Electric Permittivity of Water 2
1.1.3 Dissolution 3
1.1.4 Solvation 3
1.1.5 Dissociation 5
1.1.6 Ionization 7
1.1.7 Hydrophilicity, Hydrophobicity, and LogP 8
1.1.8 Gibbs Free Energy Change 9
1.1.9 Acid Ionization Constants 10
1.1.10 Concentration-pH and pa-pH Diagrams 12
1.1.11 Henderson-Hasselbalch Equation 13
1.1.12 Buffer Capacity 15
1.2 Binary Mixtures and Other Solvents 18
References 19
2 Fundamentals of Electrophoresis 21
2.1 Introduction 21
2.2 The Platforms 21
2.3 Electrophoresis 23
2.4 Electrophoresis of Single Molecules 27
2.5 Ionic Limiting Mobility 30
2.6 Bands, Fronts, Peaks, and Zones 32
2.6.1 Bands and Peaks 32
2.6.2 Fronts 37
2.6.3 Zones 38
2.7 The Isoelectric Point 38
2.7.1 Isoelectric Point of Molecules 38
2.7.2 Isoelectric Point of Nano and Microparticles 41
2.8 Turbulent and Laminar Flow 42
2.8.1 The Driving Forces of Fluid Flow 42
2.8.2 Turbulence 43
2.8.3 Laminar Flow in Cylindrical Capillaries 43
2.8.3.1 Pressure Driven Flow 43
2.8.3.2 Gravity Driven Flow 45
2.8.3.3 Capillary Action 45
2.8.4 Laminar Flow in Microchannels 46
2.8.4.1 Pressure Driven Flow 46
2.8.4.2 Gravity Driven Flow 49
2.9 Electroosmosis 50
2.9.1 EOF in Cylindrical Capillaries 50
2.9.1.1 Volumetric Flow Rate 53
2.9.1.2 Combined Pressure Driven Flow and EOF 53
2.9.2 EOF in Rectangular Microchannels 53
2.10 Supression of EOF 54
2.10.1 Protocols for EOF Suppression 54
2.10.2 Advantages of Suppressing EOF with Covalent Coatings 56
2.10.3 Measuring Small and Large EOF Velocities 56
2.11 Joule Effect and Heat Dissipation 57
2.12 Temperature Profiles 58
2.13 Molecular Diffusion and Band Broadening 62
2.14 Sample Stacking and Band Compression 64
2.15 Separation Modes 69
2.15.1 Affinity Electrophoresis 69
2.15.2 Electrochromatography 71
2.15.3 End-labeled Free-solution Electrophoresis 72
2.15.4 Free-Solution Electrophoresis 73
2.15.5 Isoelectric Focusing 76
2.15.6 Isotachophoresis 77
2.15.7 Microemulsion Electrokinetic Chromatography 79
2.15.8 Micellar Electrokinetic Chromatography 79
2.15.9 Sieving Electrophoresis 81
2.15.10 Suitable Separation Modes for Each Class of Analytes 82
References 84
3 Open Layout 89
3.1 Introduction 89
3.2 Capillary Electrophoresis 89
3.3 Microchip Electrophoresis 92
3.4 Slab Electrophoresis 94
3.5 Performance Indicators for Open Layouts 97
3.5.1 From Single Bands or Peaks 98
3.5.1.1 Number of Theoretical Plates 98
3.5.1.2 Number of Theoretical Plates per Unit Time Squared 99
3.5.1.3 Height Equivalent of a Theoretical Plate 99
3.5.2 From Two Neighboring Bands or Peaks 100
3.5.2.1 Resolution 104
3.5.2.2 Resolution per Unit Time 106
3.5.3 From n Bands and n Peaks 107
3.5.3.1 Band Capacity 107
3.5.3.2 Band Capacity per Unit of Time 108
3.5.3.3 Peak Capacity 108
3.5.3.4 Peak Capacity per Unit Time 109
References 109
4 Toroidal Layout 115
4.1 Introduction 115
4.2 Toroidal Capillary Electrophoresis 117
4.3 Toroidal Microchip Electrophoresis 120
4.4 Toroidal Slab Electrophoresis 121
4.5 Folding Geometries 121
4.6 Microholes and Connections 125
4.7 Reservoirs 126
4.8 Active and Passive Modes of Operation 127
4.8.1 The Gravimetric Method 128
4.8.2 The Hydrodynamic Method 129
4.8.3 The Electrokinetic Method 129
4.8.4 Using Microvalves or Microcaps 130
4.9 Performance Indicators for Toroidal Layouts 130
4.9.1 From Single Bands or Peaks 131
4.9.1.1 Number of Theoretical Plates 131
4.9.1.2 Number of Plates per Unit Time Squared 131
4.9.1.3 Height Equivalent of a Theoretical Plate 132
4.9.2 From Two Neighboring Bands or Peaks 132
4.9.2.1 Resolution 132
4.9.2.2 Resolution per Unit Time 133
4.9.3 From n Bands or n Peaks 133
4.9.3.1 Band Capacity 133
4.9.3.2 Band Capacity per Unit Time 134
4.9.3.3 Peak Capacity 134
4.9.3.4 Peak Capacity per Unit Time 135
References 136
5 Confronting Performance Indicators 137
5.1 Introduction 137
5.2 Performance Indicators from Experimental Data 137
5.3 Performance Indicators Predicted from Operational Parameters 139
References 146
6 High Voltage Modules and Distributors 147
6.1 Introduction 147
6.2 High Voltages in Open Layouts 147
6.3 High Voltages in Toroidal Layouts 148
6.3.1 The Ideal Toroidal Length 148
6.3.2 High Voltage Distribution Made by Four Modules 150
6.3.3 High Voltage Distribution Based on Relays 152
6.3.4 High Voltage Distribution Based on Sliding Switches 153
6.3.5 High Voltage Distribution Based on Rotating Switches 155
References 156
7 Heat Removal and Temperature Control 157
7.1 Introduction 157
7.2 Temperature Gradients are Unavoidable 159
7.3 Temperature has Multiple Effects 160
7.4 Electrical Insulators with High Thermal Conductivity 165
7.5 Cooling Strategies Used in Capillary Electrophoresis 167
7.5.1 Advantages of a Symmetric Cooling Geometry 170
7.6 Cooling Strategies Used in Microchip Electrophoresis 177
7.6.1 Advantages of a Symmetric Cooling Geometry 177
7.7 Cooling Strategies Used in Slab Electrophoresis 177
7.7.1 Advantages of a Rational Cooling Strategy 178
7.8 Shear Rate of the Coolant 178
7.9 Final Considerations 179
References 180
8 Detectors 181
8.1 Introduction 181
8.2 Fixed Point Detectors 182
8.3 Spatial Detectors (Scanners and Cameras) 184
8.4 Derivatization Reactions 185
8.4.1 Fluorogenic Reactions 186
8.4.2 Labeling Reactions 189
8.4.3 Improving Selectivity Through Derivatization 189
References 191
9 Applications of Toroidal Electrophoresis 193
9.1 Introduction 193
References 197
Appendix A Nomenclature 199
References 203
Appendix B Species Concentration in Buffer Solutions 205
B.1 Acids (HnA) 206
B.1.1 Monoprotic Acids (n = 1) 206
B.1.2 Diprotic Acids (n = 2) 206
B.1.3 Triprotic Acids (n = 3) 206
B.1.4 Tetraprotic Acids (n = 4) 206
B.2 Bases (B) 207
B.2.1 Monoprotonated Bases (n = 1) 207
B.2.2 Diprotonated Bases (n = 2) 207
B.2.3 Triprotonated Bases (n = 3) 207
B.2.4 Tetraprotonated Bases (n = 4) 207
References 208
Appendix C Electrophoresis 209
C.1 Free-Solution Electrophoretic Mobility 209
C.1.1 Classical Trajectories 210
C.2 Mobility Dependence on Temperature 212
C.3 Transient Regimes 213
C.3.1 Eletrophoretic Transient Regime (𝜏e) 214
C.3.2 Hardware Transient Regime (𝜏o) 214
References 216
Appendix D Electroosmosis 217
D.1 Slab and Microchips - Cartesian Coordinates 217
D.2 Capillaries - Cylindrical Coordinates 220
D.3 Zeta Potential 223
References 224
Appendix E Molecular Diffusion 227
E.1 The Diffusion Equation 227
E.2 The Propagator 229
E.3 Application of Propagators to Bands at Rest 230
E.4 Application of Propagators to Bands in Movement 232
E.5 Bands and Peaks 233
References 234
Appendix F Poiseuille Counter-flow 235
F.1 Introduction 235
F.2 Velocity Level Contours 236
F.3 Temperature Level Contours 237
F.4 Equalizing 𝑣max and Δ𝑣e 238
Reference 240
Appendix G Cyclic On-column Band Compression 241
G.1 Introduction 241
G.2 Effect of Cyclic Band Compression Events on Variance 242
G.3 Number of Theoretical Plates 243
G.4 Number of Theoretical Plates per Unit Time 244
G.5 Height Equivalent of a Theoretical Plate 244
G.6 Resolution 245
G.7 Resolution per Unit Time 246
G.8 Band Capacity 246
G.9 Band Capacity per Unit Time 247
G.10 Detailed Calculation of 𝜎2, Δx, fn, and hn 249
G.10.1 Peak Variance 249
G.10.1.1 Compression Events Before Each Detection 249
G.10.1.2 Compression Events After Each Detection 250
G.10.2 Inter-Peak Spacing (Δx) 251
G.10.2.1 Compression Events Before Each Detection 251
G.10.2.2 Compression Events After Each Detection 251
G.10.3 Calculation of the Values of hn 251
G.10.3.1 Compression Events Before Each Detection 252
G.10.3.2 Compression Events After Each Detection 252
References 253
Index 255
