LLOYD R. SNYDER, PHD, is a Principal at LC Resources in Walnut Creek, California. He is the author or coauthor of several books including An Introduction to Separation Science, Introduction to Modern Liquid Chromatography, Second Edition, and the bestselling Practical HPLC Method Development, Second Edition, all published by Wiley. JOHN W. DOLAN, PHD, is a Principal at LC Resources. He is author of the popular " LC Troubleshooting" column in LCGC Magazine and coauthor with Lloyd Snyder of Troubleshooting LC Systems.

"This book is clear, well written, and easy to understand despite the complexity of the subject." (Journal of the American Chemical Society, July 2007)

• Preface xvGlossary of Symbols and Terms xxi1 Introduction 11.1 The “General Elution Problem” and the Need for Gradient Elution 11.2 Other Reasons for the Use of Gradient Elution 41.3 Gradient Shape 71.4 Similarity of Isocratic and Gradient Elution 101.4.1 Gradient and Isocratic Elution Compared 101.4.2 The Linear-Solvent-Strength Model 131.5 Computer Simulation 181.6 Sample Classification 191.6.1 Sample Compounds of Related Structure (“Regular Samples”) 191.6.2 Sample Compounds of Unrelated Structure (“Irregular” Samples) 192 Gradient Elution Fundamentals 232.1 Isocratic Separation 232.1.1 Retention 232.1.2 Peak Width and Plate Number 242.1.3 Resolution 252.1.4 Role of Separation Conditions 272.1.4.1 Optimizing Retention [Term a of Equation (2.7)] 272.1.4.2 Optimizing Selectivity a [Term b of Equation (2.7)] 282.1.4.3 Optimizing the Column Plate Number N [Term c of Equation (2.7)] 282.2 Gradient Separation 312.2.1 Retention 322.2.1.1 Gradient and Isocratic Separation Compared for “Corresponding” Conditions 342.2.2 Peak Width 382.2.3 Resolution 392.2.3.1 Resolution as a Function of Values of S for Two Adjacent Peaks (“Irregular” Samples) 422.2.3.2 Using Gradient Elution to Predict Isocratic Separation 452.2.4 Sample Complexity and Peak Capacity 472.3 Effect of Gradient Conditions on Separation 492.3.1 Gradient Steepness b: Change in Gradient Time 502.3.2 Gradient Steepness b: Change in Column Length or Diameter 512.3.3 Gradient Steepness b: Change in Flow Rate 552.3.4 Gradient Range ∆Φ: Change in Initial Percentage B (Φ0) 582.3.5 Gradient Range ∆Φ: Change in Final Percentage B (Φf) 602.3.6 Effect of a Gradient Delay 632.3.6.1 Equipment Dwell Volume 662.3.7 Effect of Gradient Shape (Nonlinear Gradients) 672.3.8 Overview of the Effect of Gradient Conditions on the Chromatogram 712.4 Related Topics 722.4.1 Nonideal Retention in Gradient Elution 722.4.2 Gradient Elution Misconceptions 723 Method Development 743.1 A Systematic Approach to Method Development 743.1.1 Separation Goals (Step 1 of Fig. 3.1) 753.1.2 Nature of the Sample (Step 2 of Fig. 3.1) 783.1.3 Initial Experimental Conditions 793.1.4 Repeatable Results 793.1.5 Computer Simulation: Yes or No? 803.1.6 Sample Preparation (Pretreatment) 813.2 Initial Experiments 813.2.1 Interpreting the Initial Chromatogram (Step 3 of Fig. 3.1) 853.2.1.1 “Trimming” a Gradient Chromatogram 873.2.1.2 Possible Problems 883.3 Developing a Gradient Separation: Resolution versus Conditions 903.3.1 Optimizing Gradient Retention k* (Step 4 of Fig. 3.1) 923.3.2 Optimizing Gradient Selectivity a* (Step 5 of Fig. 3.1) 923.3.3 Optimizing the Gradient Range (Step 6 of Fig. 3.1) 953.3.3.1 Changes in Selectivity as a Result of Change in k* 963.3.4 Segmented (Nonlinear) Gradients (Step 6 of Fig. 3.1 Continued) 1003.3.5 Optimizing the Column Plate Number N* (Step 7 of Fig. 3.1) 1023.3.6 Column Equilibration Between Successive Sample Injections 1063.3.7 Fast Separations 1063.4 Computer Simulation 1083.4.1 Quantitative Predictions and Resolution Maps 1093.4.2 Gradient Optimization 1113.4.3 Changes in Column Conditions 1123.4.4 Separation of “Regular” Samples 1143.4.5 Other Features 1153.4.5.1 Isocratic Prediction (5 in Table 3.5) 1153.4.5.2 Designated Peak Selection (6 in Table 3.5) 1173.4.5.3 Change in Other Conditions (7 in Table 3.5) 1173.4.5.4 Computer-Selection of the Best Multisegment Gradient (8 in Table 3.5) 1173.4.5.5 “Two-Run” Procedures for the Improvement of Sample Resolution 1193.4.6 Accuracy of Computer Simulation 1193.4.7 Peak Tracking 1193.5 Method Reproducibility and Related Topics 1203.5.1 Method Development 1213.5.2 Routine Analysis 1223.5.3 Change in Column Volume 1233.6 Additional Means for an Increase in Separation Selectivity 1243.7 Orthogonal Separations 1273.7.1 Two-Dimensional Separations 1284 Gradient Equipment 1334.1 Gradient System Design 1334.1.1 High-Pressure vs Low-Pressure Mixing 1334.1.2 Tradeoffs 1354.1.2.1 Dwell Volume 1354.1.2.2 Degassing 1364.1.2.3 Accuracy 1374.1.2.4 Solvent Volume Changes and Compressibility 1374.1.2.5 Flexibility 1394.1.2.6 Independent Module Use 1404.1.3 Other System Components 1404.1.3.1 Autosampler 1404.1.3.2 Column 1404.1.3.3 Detector 1414.1.3.4 Data System 1414.1.3.5 Extra-Column Volume 1424.2 General Considerations in System Selection 1424.2.1 Which Vendor? 1434.2.2 High-Pressure or Low-Pressure Mixing? 1444.2.3 Who Will Fix It? 1444.2.4 Special Applications 1444.3 Measuring Gradient System Performance 1454.3.1 Gradient Performance Test 1464.3.1.1 Gradient Linearity 1464.3.1.2 Dwell Volume Determination 1474.3.1.3 Gradient Step-Test 1474.3.1.4 Gradient Proportioning Valve Test 1484.3.2 Additional System Checks 1494.3.2.1 Flow Rate Check 1494.3.2.2 Pressure Bleed-Down 1504.3.2.3 Retention Reproducibility 1504.3.2.4 Peak Area Reproducibility 1514.4 Dwell Volume Considerations 1515 Separation Artifacts and Troubleshooting 1535.1 Avoiding Problems 1545.1.1 Equipment Checkout 1575.1.1.1 Installation Qualification, Operational Qualification, and Performance Qualification 1575.1.2 Dwell Volume 1585.1.3 Blank Gradient 1585.1.4 Suggestions for Routine Applications 1585.1.4.1 Reagent Quality 1595.1.4.2 System Cleanliness 1595.1.4.3 Degassing 1595.1.4.4 Dedicated Columns 1595.1.4.5 Equilibration 1595.1.4.6 Priming Injections 1595.1.4.7 Ignore the First Injection 1605.1.4.8 System Suitability 1605.1.4.9 Standards and Calibrators 1605.1.5 Method Development 1605.1.5.1 Use a Clean and Stable Column 1605.1.5.2 Use Reasonable Mobile Phase Conditions 1615.1.5.3 Clean Samples 1625.1.5.4 Reproducible Runs 1625.1.5.5 Sufficient Equilibration 1625.1.5.6 Reference Conditions 1625.1.5.7 Additional Tests 1625.2 Method Transfer 1635.2.1 Compensating for Dwell Volume Differences 1635.2.1.1 Injection Delay 1635.2.1.2 Adjustment of the Initial Isocratic Hold 1645.2.1.3 Use of Maximum-Dwell-Volume Methods 1655.2.1.4 Adjustment of Initial Percentage B 1655.2.2 Other Sources of Method Transfer Problems 1685.2.2.1 Gradient Shape 1695.2.2.2 Gradient Rounding 1695.2.2.3 Inter-Run Equilibration 1695.2.2.4 Column Size 1695.2.2.5 Column Temperature 1695.2.2.6 Interpretation of Method Instructions 1705.3 Column Equilibration 1705.3.1 Primary Effects 1715.3.2 Slow Equilibration of Column and Mobile Phase 1735.3.3 Practical Considerations and Recommendations 1745.4 Separation Artifacts 1755.4.1 Baseline Drift 1765.4.2 Baseline Noise 1795.4.2.1 Baseline Noise: A Case Study 1805.4.3 Peaks in a Blank Gradient 1825.4.3.1 Mobile Phase Water or Organic Solvent Impurities 1825.4.3.2 Other Sources of Background Peaks 1855.4.4 Extra Peaks for Injected Samples 1855.4.4.1 t0 Peaks 1855.4.4.2 Air Peaks 1865.4.4.3 Late Peaks 1875.4.5 Peak Shape Problems 1885.4.5.1 Tailing and Fronting 1885.4.5.2 Excess Peak Broadening 1885.4.5.3 Split Peaks 1905.4.5.4 Injection Conditions 1915.4.5.5 Sample Decomposition 1935.5 Troubleshooting 1955.5.1 Problem Isolation 1965.5.2 Troubleshooting and Maintenance Suggestions 1975.5.2.1 Removing Air from the Pump 1975.5.2.2 Solvent Siphon Test 1975.5.2.3 Premixing to Improve Retention Reproducibility in Shallow Gradients 1985.5.2.4 Cleaning and Handling Check-Valves 1995.5.2.5 Replacing Pump Seals and Pistons 2005.5.2.6 Leak Detection 2005.5.2.7 Repairing Fitting Leaks 2005.5.2.8 Cleaning Glassware 2015.5.2.9 For Best Results with TFA 2015.5.2.10 Improved Water Purity 2015.5.2.11 Isolating Carryover Problems 2035.5.2.12 Troubleshooting Rules of Thumb 2045.5.3 Gradient Performance Test Failures 2065.5.3.1 Linearity (4.3.1.1) 2065.5.3.2 Step Test (4.3.1.3) 2065.5.3.3 Gradient-Proportioning-Valve Test (4.3.1.4) 2095.5.3.4 Flow Rate (4.3.2.1) 2115.5.3.5 Pressure Bleed-Down (4.3.2.2) 2125.5.3.6 Retention Reproducibility (4.3.2.3) 2125.5.3.7 Peak Area Reproducibility (4.3.2.4) 2135.5.4 Troubleshooting Case Studies 2135.5.4.1 Retention Variation – Case Study 1 2135.5.4.2 Retention Variation – Case Study 2 2185.5.4.3 Contaminated Reagents – Case Study 3 2205.5.4.4 Baseline and Retention Problems – Case Study 4 2246 Separation of Large Molecules 2286.1 General Considerations 2286.1.1 Values of S for Large Molecules 2296.1.2 Values of N* for Large Molecules 2356.1.3 Conformational State 2366.1.4 Homo-Oligomeric Samples 2386.1.4.1 Separation of Large Homopolymers 2416.1.5 Proposed Models for the Gradient Separation of Large Molecules 2426.1.5.2 “Critical Elution Behavior”: Biopolymers 2466.1.5.3 Measurement of LSS Parameters for Large Molecules 2476.2 Biomolecules 2486.2.1 Peptides and Proteins 2486.2.1.1 Sample Characteristics 2496.2.1.2 Conditions for an Initial Gradient Run 2496.2.1.3 Method Development 2536.2.1.4 Segmented Gradients 2596.2.2 Other Separation Modes and Samples 2616.2.2.1 Hydrophobic Interaction Chromatography 2626.2.2.2 Ion Exchange Chromatography 2646.2.2.3 Hydrophilic Interaction Chromatography 2666.2.2.4 Separation of Viruses 2676.2.3 Separation Problems 2716.2.4 Fast Separations of Peptides and Proteins 2746.2.5 Two-Dimensional Separations of Peptides and Proteins 2746.3 Synthetic Polymers 2756.3.1 Determination of Molecular Weight Distribution 2776.3.2 Determination of Chemical Composition 2787 Preparative Separations 2837.1 Introduction 2837.1.1 Equipment for Preparative Separation 2857.2 Isocratic Separation 2867.2.1 Touching-Peak Separation 2877.2.1.1 Theory 2877.2.1.2 Column Saturation Capacity 2897.2.1.3 Sample-Volume Overload 2927.2.2 Method Development for Isocratic Touching-Peak Separation 2927.2.2.1 Optimizing Separation Conditions 2957.2.2.2 Selecting a Sample Weight for Touching-Peak Separation 2977.2.2.3 Scale-Up 2987.2.2.4 Sample Solubility 3007.2.3 Beyond Touching-Peak Separation 3017.3 Gradient Separation 3027.3.1 Touching-Peak Separation 3067.3.2 Method Development for Gradient Touching-Peak Separation 3067.3.2.1 Step Gradients 3117.3.3 Sample-Volume Overload 3127.3.4 Possible Complications of Simple Touching-Peak Theory and Their Practical Impact 3127.3.4.1 Crossing Isotherms 3137.3.4.2 Unequal Values of S 3147.4 Severely Overloaded Separation 3157.4.1 Is Gradient Elution Necessary? 3167.4.2 Displacement Effects 3177.4.3 Method Development 3177.4.4 Separations of Peptides and Small Proteins 3187.4.5 Column Efficiency 3207.4.6 Production-Scale Separation 3208 other Applications of Gradient Elution 3238.1 Gradient Elution for LC-MS 3248.1.1 Application Areas 3258.1.2 Requirements for LC-MS 3258.1.3 Basic LC-MS Concepts 3268.1.3.1 The Interface 3268.1.3.2 Column Configurations 3288.1.3.3 Quadrupoles and Ion Traps 3288.1.4 LC-UV vs LC-MS Gradient Conditions 3308.1.5 Method Development for LC-MS 3328.1.5.1 Define Separation Goals (Step 1, Table 8.2) 3328.1.5.2 Collect Information on Sample (Step 2, Table 8.2) 3348.1.5.3 Carry Out Initial Separation (Run 1, Step 3, Table 8.2) 3398.1.5.4 Optimize Gradient Retention k* (Step 4, Table 8.2) 3398.1.5.5 Optimize Selectivity a* (Step 5, Table 8.2) 3398.1.5.6 Adjust Gradient Range and Shape (Step 6, Table 8.2) 3408.1.5.7 Vary Column Conditions (Step 7, Table 8.2) 3418.1.5.8 Determine Inter-Run Column Equilibration (Step 8, Table 8.2) 3418.1.6 Special Challenges for LC-MS 3418.1.6.1 Dwell Volume 3428.1.6.2 Gradient Distortion 3428.1.6.3 Ion Suppression 3438.1.6.4 Co-Eluting Compounds 3458.1.6.5 Resolution Requirements 3468.1.6.6 Use of Computer Simulation Software 3478.1.6.7 Isocratic Methods 3478.1.6.8 Throughput Enhancement 3478.2 Ion-Exchange Chromatography 3498.2.1 Theory 3498.2.2 Dependence of Separation on Gradient Conditions 3568.2.3 Method Development for Gradient IEC 3568.2.3.1 Choice of Initial Conditions 3568.2.3.2 Improving the Separation 3578.3 Normal-Phase Chromatography 3598.3.1 Theory 3598.3.2 Method Development for Gradient NPC 3608.3.3 Hydrophilic Interaction Chromatography 3618.3.3.1 Method Development for Gradient HILIC 3618.4 Ternary- or Quaternary-Solvent Gradients 3659 Theory and Derivations 3709.1 The Linear Solvent Strength Model 3709.1.1 Retention 3729.1.1.1 Gradient and Isocratic Retention Compared 3749.1.1.2 Small Values of k 0 3769.1.2 Peak Width 3789.1.2.1 Gradient Compression 3809.1.3 Selectivity and Resolution 3839.1.4 Advantages of LSS Behavior 3859.2 Second-Order Effects 3869.2.1 Assumptions About Φ and k 3869.2.1.1 Incomplete Column Equilibration 3869.2.1.2 Solvent Demixing 3919.2.1.3 Nonlinear Plots of log k vs Φ 3939.2.1.4 Dependence of V m on Φ 3939.2.2 Nonideal Equipment 3939.3. Accuracy of Gradient Elution Predictions 3979.3.1 Gradient Retention Time 3979.3.1.1 Confirmation of Equation (9.2) 3979.3.1.2 Computer Simulation 3999.3.2 Peak Width Predictions 3999.3.3 Measurement of Values of S and log k 0 4009.4 Values of S 4019.4.1 Estimating Values of S from Solute Properties and Experimental Conditions 4029.5 Values of N in Gradient Elution 404Appendix I The Constant-S Approximation In Gradient Elution 414Appendix II Estimation of Conditions for Isocratic Elution, Based on An Initial Gradient Run 416Appendix III Characterization of Reversed-phase Columns for Selectivity and Peak Tailing 418Appendix IV Solvent Properties Relevant to the Use of Gradient Elution 434Appendix V Theory Of Preparative Separation 436Appendix Vi Further Information On Virus Chromatography 445Index 450

LLOYD R. SNYDER, PHD, is a Principal at LC Resources in Walnut Creek, California. He is the author or coauthor of several books including An Introduction to Separation Science, Introduction to Modern Liquid Chromatography, Second Edition, and the bestselling Practical HPLC Method Development, Second Edition, all published by Wiley. JOHN W. DOLAN, PHD, is a Principal at LC Resources. He is author of the popular " LC Troubleshooting" column in LCGC Magazine and coauthor with Lloyd Snyder of Troubleshooting LC Systems.

"This book is clear, well written, and easy to understand despite the complexity of the subject." (Journal of the American Chemical Society, July 2007)

• Preface xvGlossary of Symbols and Terms xxi1 Introduction 11.1 The “General Elution Problem” and the Need for Gradient Elution 11.2 Other Reasons for the Use of Gradient Elution 41.3 Gradient Shape 71.4 Similarity of Isocratic and Gradient Elution 101.4.1 Gradient and Isocratic Elution Compared 101.4.2 The Linear-Solvent-Strength Model 131.5 Computer Simulation 181.6 Sample Classification 191.6.1 Sample Compounds of Related Structure (“Regular Samples”) 191.6.2 Sample Compounds of Unrelated Structure (“Irregular” Samples) 192 Gradient Elution Fundamentals 232.1 Isocratic Separation 232.1.1 Retention 232.1.2 Peak Width and Plate Number 242.1.3 Resolution 252.1.4 Role of Separation Conditions 272.1.4.1 Optimizing Retention [Term a of Equation (2.7)] 272.1.4.2 Optimizing Selectivity a [Term b of Equation (2.7)] 282.1.4.3 Optimizing the Column Plate Number N [Term c of Equation (2.7)] 282.2 Gradient Separation 312.2.1 Retention 322.2.1.1 Gradient and Isocratic Separation Compared for “Corresponding” Conditions 342.2.2 Peak Width 382.2.3 Resolution 392.2.3.1 Resolution as a Function of Values of S for Two Adjacent Peaks (“Irregular” Samples) 422.2.3.2 Using Gradient Elution to Predict Isocratic Separation 452.2.4 Sample Complexity and Peak Capacity 472.3 Effect of Gradient Conditions on Separation 492.3.1 Gradient Steepness b: Change in Gradient Time 502.3.2 Gradient Steepness b: Change in Column Length or Diameter 512.3.3 Gradient Steepness b: Change in Flow Rate 552.3.4 Gradient Range ∆Φ: Change in Initial Percentage B (Φ0) 582.3.5 Gradient Range ∆Φ: Change in Final Percentage B (Φf) 602.3.6 Effect of a Gradient Delay 632.3.6.1 Equipment Dwell Volume 662.3.7 Effect of Gradient Shape (Nonlinear Gradients) 672.3.8 Overview of the Effect of Gradient Conditions on the Chromatogram 712.4 Related Topics 722.4.1 Nonideal Retention in Gradient Elution 722.4.2 Gradient Elution Misconceptions 723 Method Development 743.1 A Systematic Approach to Method Development 743.1.1 Separation Goals (Step 1 of Fig. 3.1) 753.1.2 Nature of the Sample (Step 2 of Fig. 3.1) 783.1.3 Initial Experimental Conditions 793.1.4 Repeatable Results 793.1.5 Computer Simulation: Yes or No? 803.1.6 Sample Preparation (Pretreatment) 813.2 Initial Experiments 813.2.1 Interpreting the Initial Chromatogram (Step 3 of Fig. 3.1) 853.2.1.1 “Trimming” a Gradient Chromatogram 873.2.1.2 Possible Problems 883.3 Developing a Gradient Separation: Resolution versus Conditions 903.3.1 Optimizing Gradient Retention k* (Step 4 of Fig. 3.1) 923.3.2 Optimizing Gradient Selectivity a* (Step 5 of Fig. 3.1) 923.3.3 Optimizing the Gradient Range (Step 6 of Fig. 3.1) 953.3.3.1 Changes in Selectivity as a Result of Change in k* 963.3.4 Segmented (Nonlinear) Gradients (Step 6 of Fig. 3.1 Continued) 1003.3.5 Optimizing the Column Plate Number N* (Step 7 of Fig. 3.1) 1023.3.6 Column Equilibration Between Successive Sample Injections 1063.3.7 Fast Separations 1063.4 Computer Simulation 1083.4.1 Quantitative Predictions and Resolution Maps 1093.4.2 Gradient Optimization 1113.4.3 Changes in Column Conditions 1123.4.4 Separation of “Regular” Samples 1143.4.5 Other Features 1153.4.5.1 Isocratic Prediction (5 in Table 3.5) 1153.4.5.2 Designated Peak Selection (6 in Table 3.5) 1173.4.5.3 Change in Other Conditions (7 in Table 3.5) 1173.4.5.4 Computer-Selection of the Best Multisegment Gradient (8 in Table 3.5) 1173.4.5.5 “Two-Run” Procedures for the Improvement of Sample Resolution 1193.4.6 Accuracy of Computer Simulation 1193.4.7 Peak Tracking 1193.5 Method Reproducibility and Related Topics 1203.5.1 Method Development 1213.5.2 Routine Analysis 1223.5.3 Change in Column Volume 1233.6 Additional Means for an Increase in Separation Selectivity 1243.7 Orthogonal Separations 1273.7.1 Two-Dimensional Separations 1284 Gradient Equipment 1334.1 Gradient System Design 1334.1.1 High-Pressure vs Low-Pressure Mixing 1334.1.2 Tradeoffs 1354.1.2.1 Dwell Volume 1354.1.2.2 Degassing 1364.1.2.3 Accuracy 1374.1.2.4 Solvent Volume Changes and Compressibility 1374.1.2.5 Flexibility 1394.1.2.6 Independent Module Use 1404.1.3 Other System Components 1404.1.3.1 Autosampler 1404.1.3.2 Column 1404.1.3.3 Detector 1414.1.3.4 Data System 1414.1.3.5 Extra-Column Volume 1424.2 General Considerations in System Selection 1424.2.1 Which Vendor? 1434.2.2 High-Pressure or Low-Pressure Mixing? 1444.2.3 Who Will Fix It? 1444.2.4 Special Applications 1444.3 Measuring Gradient System Performance 1454.3.1 Gradient Performance Test 1464.3.1.1 Gradient Linearity 1464.3.1.2 Dwell Volume Determination 1474.3.1.3 Gradient Step-Test 1474.3.1.4 Gradient Proportioning Valve Test 1484.3.2 Additional System Checks 1494.3.2.1 Flow Rate Check 1494.3.2.2 Pressure Bleed-Down 1504.3.2.3 Retention Reproducibility 1504.3.2.4 Peak Area Reproducibility 1514.4 Dwell Volume Considerations 1515 Separation Artifacts and Troubleshooting 1535.1 Avoiding Problems 1545.1.1 Equipment Checkout 1575.1.1.1 Installation Qualification, Operational Qualification, and Performance Qualification 1575.1.2 Dwell Volume 1585.1.3 Blank Gradient 1585.1.4 Suggestions for Routine Applications 1585.1.4.1 Reagent Quality 1595.1.4.2 System Cleanliness 1595.1.4.3 Degassing 1595.1.4.4 Dedicated Columns 1595.1.4.5 Equilibration 1595.1.4.6 Priming Injections 1595.1.4.7 Ignore the First Injection 1605.1.4.8 System Suitability 1605.1.4.9 Standards and Calibrators 1605.1.5 Method Development 1605.1.5.1 Use a Clean and Stable Column 1605.1.5.2 Use Reasonable Mobile Phase Conditions 1615.1.5.3 Clean Samples 1625.1.5.4 Reproducible Runs 1625.1.5.5 Sufficient Equilibration 1625.1.5.6 Reference Conditions 1625.1.5.7 Additional Tests 1625.2 Method Transfer 1635.2.1 Compensating for Dwell Volume Differences 1635.2.1.1 Injection Delay 1635.2.1.2 Adjustment of the Initial Isocratic Hold 1645.2.1.3 Use of Maximum-Dwell-Volume Methods 1655.2.1.4 Adjustment of Initial Percentage B 1655.2.2 Other Sources of Method Transfer Problems 1685.2.2.1 Gradient Shape 1695.2.2.2 Gradient Rounding 1695.2.2.3 Inter-Run Equilibration 1695.2.2.4 Column Size 1695.2.2.5 Column Temperature 1695.2.2.6 Interpretation of Method Instructions 1705.3 Column Equilibration 1705.3.1 Primary Effects 1715.3.2 Slow Equilibration of Column and Mobile Phase 1735.3.3 Practical Considerations and Recommendations 1745.4 Separation Artifacts 1755.4.1 Baseline Drift 1765.4.2 Baseline Noise 1795.4.2.1 Baseline Noise: A Case Study 1805.4.3 Peaks in a Blank Gradient 1825.4.3.1 Mobile Phase Water or Organic Solvent Impurities 1825.4.3.2 Other Sources of Background Peaks 1855.4.4 Extra Peaks for Injected Samples 1855.4.4.1 t0 Peaks 1855.4.4.2 Air Peaks 1865.4.4.3 Late Peaks 1875.4.5 Peak Shape Problems 1885.4.5.1 Tailing and Fronting 1885.4.5.2 Excess Peak Broadening 1885.4.5.3 Split Peaks 1905.4.5.4 Injection Conditions 1915.4.5.5 Sample Decomposition 1935.5 Troubleshooting 1955.5.1 Problem Isolation 1965.5.2 Troubleshooting and Maintenance Suggestions 1975.5.2.1 Removing Air from the Pump 1975.5.2.2 Solvent Siphon Test 1975.5.2.3 Premixing to Improve Retention Reproducibility in Shallow Gradients 1985.5.2.4 Cleaning and Handling Check-Valves 1995.5.2.5 Replacing Pump Seals and Pistons 2005.5.2.6 Leak Detection 2005.5.2.7 Repairing Fitting Leaks 2005.5.2.8 Cleaning Glassware 2015.5.2.9 For Best Results with TFA 2015.5.2.10 Improved Water Purity 2015.5.2.11 Isolating Carryover Problems 2035.5.2.12 Troubleshooting Rules of Thumb 2045.5.3 Gradient Performance Test Failures 2065.5.3.1 Linearity (4.3.1.1) 2065.5.3.2 Step Test (4.3.1.3) 2065.5.3.3 Gradient-Proportioning-Valve Test (4.3.1.4) 2095.5.3.4 Flow Rate (4.3.2.1) 2115.5.3.5 Pressure Bleed-Down (4.3.2.2) 2125.5.3.6 Retention Reproducibility (4.3.2.3) 2125.5.3.7 Peak Area Reproducibility (4.3.2.4) 2135.5.4 Troubleshooting Case Studies 2135.5.4.1 Retention Variation – Case Study 1 2135.5.4.2 Retention Variation – Case Study 2 2185.5.4.3 Contaminated Reagents – Case Study 3 2205.5.4.4 Baseline and Retention Problems – Case Study 4 2246 Separation of Large Molecules 2286.1 General Considerations 2286.1.1 Values of S for Large Molecules 2296.1.2 Values of N* for Large Molecules 2356.1.3 Conformational State 2366.1.4 Homo-Oligomeric Samples 2386.1.4.1 Separation of Large Homopolymers 2416.1.5 Proposed Models for the Gradient Separation of Large Molecules 2426.1.5.2 “Critical Elution Behavior”: Biopolymers 2466.1.5.3 Measurement of LSS Parameters for Large Molecules 2476.2 Biomolecules 2486.2.1 Peptides and Proteins 2486.2.1.1 Sample Characteristics 2496.2.1.2 Conditions for an Initial Gradient Run 2496.2.1.3 Method Development 2536.2.1.4 Segmented Gradients 2596.2.2 Other Separation Modes and Samples 2616.2.2.1 Hydrophobic Interaction Chromatography 2626.2.2.2 Ion Exchange Chromatography 2646.2.2.3 Hydrophilic Interaction Chromatography 2666.2.2.4 Separation of Viruses 2676.2.3 Separation Problems 2716.2.4 Fast Separations of Peptides and Proteins 2746.2.5 Two-Dimensional Separations of Peptides and Proteins 2746.3 Synthetic Polymers 2756.3.1 Determination of Molecular Weight Distribution 2776.3.2 Determination of Chemical Composition 2787 Preparative Separations 2837.1 Introduction 2837.1.1 Equipment for Preparative Separation 2857.2 Isocratic Separation 2867.2.1 Touching-Peak Separation 2877.2.1.1 Theory 2877.2.1.2 Column Saturation Capacity 2897.2.1.3 Sample-Volume Overload 2927.2.2 Method Development for Isocratic Touching-Peak Separation 2927.2.2.1 Optimizing Separation Conditions 2957.2.2.2 Selecting a Sample Weight for Touching-Peak Separation 2977.2.2.3 Scale-Up 2987.2.2.4 Sample Solubility 3007.2.3 Beyond Touching-Peak Separation 3017.3 Gradient Separation 3027.3.1 Touching-Peak Separation 3067.3.2 Method Development for Gradient Touching-Peak Separation 3067.3.2.1 Step Gradients 3117.3.3 Sample-Volume Overload 3127.3.4 Possible Complications of Simple Touching-Peak Theory and Their Practical Impact 3127.3.4.1 Crossing Isotherms 3137.3.4.2 Unequal Values of S 3147.4 Severely Overloaded Separation 3157.4.1 Is Gradient Elution Necessary? 3167.4.2 Displacement Effects 3177.4.3 Method Development 3177.4.4 Separations of Peptides and Small Proteins 3187.4.5 Column Efficiency 3207.4.6 Production-Scale Separation 3208 other Applications of Gradient Elution 3238.1 Gradient Elution for LC-MS 3248.1.1 Application Areas 3258.1.2 Requirements for LC-MS 3258.1.3 Basic LC-MS Concepts 3268.1.3.1 The Interface 3268.1.3.2 Column Configurations 3288.1.3.3 Quadrupoles and Ion Traps 3288.1.4 LC-UV vs LC-MS Gradient Conditions 3308.1.5 Method Development for LC-MS 3328.1.5.1 Define Separation Goals (Step 1, Table 8.2) 3328.1.5.2 Collect Information on Sample (Step 2, Table 8.2) 3348.1.5.3 Carry Out Initial Separation (Run 1, Step 3, Table 8.2) 3398.1.5.4 Optimize Gradient Retention k* (Step 4, Table 8.2) 3398.1.5.5 Optimize Selectivity a* (Step 5, Table 8.2) 3398.1.5.6 Adjust Gradient Range and Shape (Step 6, Table 8.2) 3408.1.5.7 Vary Column Conditions (Step 7, Table 8.2) 3418.1.5.8 Determine Inter-Run Column Equilibration (Step 8, Table 8.2) 3418.1.6 Special Challenges for LC-MS 3418.1.6.1 Dwell Volume 3428.1.6.2 Gradient Distortion 3428.1.6.3 Ion Suppression 3438.1.6.4 Co-Eluting Compounds 3458.1.6.5 Resolution Requirements 3468.1.6.6 Use of Computer Simulation Software 3478.1.6.7 Isocratic Methods 3478.1.6.8 Throughput Enhancement 3478.2 Ion-Exchange Chromatography 3498.2.1 Theory 3498.2.2 Dependence of Separation on Gradient Conditions 3568.2.3 Method Development for Gradient IEC 3568.2.3.1 Choice of Initial Conditions 3568.2.3.2 Improving the Separation 3578.3 Normal-Phase Chromatography 3598.3.1 Theory 3598.3.2 Method Development for Gradient NPC 3608.3.3 Hydrophilic Interaction Chromatography 3618.3.3.1 Method Development for Gradient HILIC 3618.4 Ternary- or Quaternary-Solvent Gradients 3659 Theory and Derivations 3709.1 The Linear Solvent Strength Model 3709.1.1 Retention 3729.1.1.1 Gradient and Isocratic Retention Compared 3749.1.1.2 Small Values of k 0 3769.1.2 Peak Width 3789.1.2.1 Gradient Compression 3809.1.3 Selectivity and Resolution 3839.1.4 Advantages of LSS Behavior 3859.2 Second-Order Effects 3869.2.1 Assumptions About Φ and k 3869.2.1.1 Incomplete Column Equilibration 3869.2.1.2 Solvent Demixing 3919.2.1.3 Nonlinear Plots of log k vs Φ 3939.2.1.4 Dependence of V m on Φ 3939.2.2 Nonideal Equipment 3939.3. Accuracy of Gradient Elution Predictions 3979.3.1 Gradient Retention Time 3979.3.1.1 Confirmation of Equation (9.2) 3979.3.1.2 Computer Simulation 3999.3.2 Peak Width Predictions 3999.3.3 Measurement of Values of S and log k 0 4009.4 Values of S 4019.4.1 Estimating Values of S from Solute Properties and Experimental Conditions 4029.5 Values of N in Gradient Elution 404Appendix I The Constant-S Approximation In Gradient Elution 414Appendix II Estimation of Conditions for Isocratic Elution, Based on An Initial Gradient Run 416Appendix III Characterization of Reversed-phase Columns for Selectivity and Peak Tailing 418Appendix IV Solvent Properties Relevant to the Use of Gradient Elution 434Appendix V Theory Of Preparative Separation 436Appendix Vi Further Information On Virus Chromatography 445Index 450

LLOYD R. SNYDER, PHD, is a Principal at LC Resources in Walnut Creek, California. He is the author or coauthor of several books including An Introduction to Separation Science, Introduction to Modern Liquid Chromatography, Second Edition, and the bestselling Practical HPLC Method Development, Second Edition, all published by Wiley. JOHN W. DOLAN, PHD, is a Principal at LC Resources. He is author of the popular " LC Troubleshooting" column in LCGC Magazine and coauthor with Lloyd Snyder of Troubleshooting LC Systems.

"This book is clear, well written, and easy to understand despite the complexity of the subject." (Journal of the American Chemical Society, July 2007)

• Preface xvGlossary of Symbols and Terms xxi1 Introduction 11.1 The “General Elution Problem” and the Need for Gradient Elution 11.2 Other Reasons for the Use of Gradient Elution 41.3 Gradient Shape 71.4 Similarity of Isocratic and Gradient Elution 101.4.1 Gradient and Isocratic Elution Compared 101.4.2 The Linear-Solvent-Strength Model 131.5 Computer Simulation 181.6 Sample Classification 191.6.1 Sample Compounds of Related Structure (“Regular Samples”) 191.6.2 Sample Compounds of Unrelated Structure (“Irregular” Samples) 192 Gradient Elution Fundamentals 232.1 Isocratic Separation 232.1.1 Retention 232.1.2 Peak Width and Plate Number 242.1.3 Resolution 252.1.4 Role of Separation Conditions 272.1.4.1 Optimizing Retention [Term a of Equation (2.7)] 272.1.4.2 Optimizing Selectivity a [Term b of Equation (2.7)] 282.1.4.3 Optimizing the Column Plate Number N [Term c of Equation (2.7)] 282.2 Gradient Separation 312.2.1 Retention 322.2.1.1 Gradient and Isocratic Separation Compared for “Corresponding” Conditions 342.2.2 Peak Width 382.2.3 Resolution 392.2.3.1 Resolution as a Function of Values of S for Two Adjacent Peaks (“Irregular” Samples) 422.2.3.2 Using Gradient Elution to Predict Isocratic Separation 452.2.4 Sample Complexity and Peak Capacity 472.3 Effect of Gradient Conditions on Separation 492.3.1 Gradient Steepness b: Change in Gradient Time 502.3.2 Gradient Steepness b: Change in Column Length or Diameter 512.3.3 Gradient Steepness b: Change in Flow Rate 552.3.4 Gradient Range ∆Φ: Change in Initial Percentage B (Φ0) 582.3.5 Gradient Range ∆Φ: Change in Final Percentage B (Φf) 602.3.6 Effect of a Gradient Delay 632.3.6.1 Equipment Dwell Volume 662.3.7 Effect of Gradient Shape (Nonlinear Gradients) 672.3.8 Overview of the Effect of Gradient Conditions on the Chromatogram 712.4 Related Topics 722.4.1 Nonideal Retention in Gradient Elution 722.4.2 Gradient Elution Misconceptions 723 Method Development 743.1 A Systematic Approach to Method Development 743.1.1 Separation Goals (Step 1 of Fig. 3.1) 753.1.2 Nature of the Sample (Step 2 of Fig. 3.1) 783.1.3 Initial Experimental Conditions 793.1.4 Repeatable Results 793.1.5 Computer Simulation: Yes or No? 803.1.6 Sample Preparation (Pretreatment) 813.2 Initial Experiments 813.2.1 Interpreting the Initial Chromatogram (Step 3 of Fig. 3.1) 853.2.1.1 “Trimming” a Gradient Chromatogram 873.2.1.2 Possible Problems 883.3 Developing a Gradient Separation: Resolution versus Conditions 903.3.1 Optimizing Gradient Retention k* (Step 4 of Fig. 3.1) 923.3.2 Optimizing Gradient Selectivity a* (Step 5 of Fig. 3.1) 923.3.3 Optimizing the Gradient Range (Step 6 of Fig. 3.1) 953.3.3.1 Changes in Selectivity as a Result of Change in k* 963.3.4 Segmented (Nonlinear) Gradients (Step 6 of Fig. 3.1 Continued) 1003.3.5 Optimizing the Column Plate Number N* (Step 7 of Fig. 3.1) 1023.3.6 Column Equilibration Between Successive Sample Injections 1063.3.7 Fast Separations 1063.4 Computer Simulation 1083.4.1 Quantitative Predictions and Resolution Maps 1093.4.2 Gradient Optimization 1113.4.3 Changes in Column Conditions 1123.4.4 Separation of “Regular” Samples 1143.4.5 Other Features 1153.4.5.1 Isocratic Prediction (5 in Table 3.5) 1153.4.5.2 Designated Peak Selection (6 in Table 3.5) 1173.4.5.3 Change in Other Conditions (7 in Table 3.5) 1173.4.5.4 Computer-Selection of the Best Multisegment Gradient (8 in Table 3.5) 1173.4.5.5 “Two-Run” Procedures for the Improvement of Sample Resolution 1193.4.6 Accuracy of Computer Simulation 1193.4.7 Peak Tracking 1193.5 Method Reproducibility and Related Topics 1203.5.1 Method Development 1213.5.2 Routine Analysis 1223.5.3 Change in Column Volume 1233.6 Additional Means for an Increase in Separation Selectivity 1243.7 Orthogonal Separations 1273.7.1 Two-Dimensional Separations 1284 Gradient Equipment 1334.1 Gradient System Design 1334.1.1 High-Pressure vs Low-Pressure Mixing 1334.1.2 Tradeoffs 1354.1.2.1 Dwell Volume 1354.1.2.2 Degassing 1364.1.2.3 Accuracy 1374.1.2.4 Solvent Volume Changes and Compressibility 1374.1.2.5 Flexibility 1394.1.2.6 Independent Module Use 1404.1.3 Other System Components 1404.1.3.1 Autosampler 1404.1.3.2 Column 1404.1.3.3 Detector 1414.1.3.4 Data System 1414.1.3.5 Extra-Column Volume 1424.2 General Considerations in System Selection 1424.2.1 Which Vendor? 1434.2.2 High-Pressure or Low-Pressure Mixing? 1444.2.3 Who Will Fix It? 1444.2.4 Special Applications 1444.3 Measuring Gradient System Performance 1454.3.1 Gradient Performance Test 1464.3.1.1 Gradient Linearity 1464.3.1.2 Dwell Volume Determination 1474.3.1.3 Gradient Step-Test 1474.3.1.4 Gradient Proportioning Valve Test 1484.3.2 Additional System Checks 1494.3.2.1 Flow Rate Check 1494.3.2.2 Pressure Bleed-Down 1504.3.2.3 Retention Reproducibility 1504.3.2.4 Peak Area Reproducibility 1514.4 Dwell Volume Considerations 1515 Separation Artifacts and Troubleshooting 1535.1 Avoiding Problems 1545.1.1 Equipment Checkout 1575.1.1.1 Installation Qualification, Operational Qualification, and Performance Qualification 1575.1.2 Dwell Volume 1585.1.3 Blank Gradient 1585.1.4 Suggestions for Routine Applications 1585.1.4.1 Reagent Quality 1595.1.4.2 System Cleanliness 1595.1.4.3 Degassing 1595.1.4.4 Dedicated Columns 1595.1.4.5 Equilibration 1595.1.4.6 Priming Injections 1595.1.4.7 Ignore the First Injection 1605.1.4.8 System Suitability 1605.1.4.9 Standards and Calibrators 1605.1.5 Method Development 1605.1.5.1 Use a Clean and Stable Column 1605.1.5.2 Use Reasonable Mobile Phase Conditions 1615.1.5.3 Clean Samples 1625.1.5.4 Reproducible Runs 1625.1.5.5 Sufficient Equilibration 1625.1.5.6 Reference Conditions 1625.1.5.7 Additional Tests 1625.2 Method Transfer 1635.2.1 Compensating for Dwell Volume Differences 1635.2.1.1 Injection Delay 1635.2.1.2 Adjustment of the Initial Isocratic Hold 1645.2.1.3 Use of Maximum-Dwell-Volume Methods 1655.2.1.4 Adjustment of Initial Percentage B 1655.2.2 Other Sources of Method Transfer Problems 1685.2.2.1 Gradient Shape 1695.2.2.2 Gradient Rounding 1695.2.2.3 Inter-Run Equilibration 1695.2.2.4 Column Size 1695.2.2.5 Column Temperature 1695.2.2.6 Interpretation of Method Instructions 1705.3 Column Equilibration 1705.3.1 Primary Effects 1715.3.2 Slow Equilibration of Column and Mobile Phase 1735.3.3 Practical Considerations and Recommendations 1745.4 Separation Artifacts 1755.4.1 Baseline Drift 1765.4.2 Baseline Noise 1795.4.2.1 Baseline Noise: A Case Study 1805.4.3 Peaks in a Blank Gradient 1825.4.3.1 Mobile Phase Water or Organic Solvent Impurities 1825.4.3.2 Other Sources of Background Peaks 1855.4.4 Extra Peaks for Injected Samples 1855.4.4.1 t0 Peaks 1855.4.4.2 Air Peaks 1865.4.4.3 Late Peaks 1875.4.5 Peak Shape Problems 1885.4.5.1 Tailing and Fronting 1885.4.5.2 Excess Peak Broadening 1885.4.5.3 Split Peaks 1905.4.5.4 Injection Conditions 1915.4.5.5 Sample Decomposition 1935.5 Troubleshooting 1955.5.1 Problem Isolation 1965.5.2 Troubleshooting and Maintenance Suggestions 1975.5.2.1 Removing Air from the Pump 1975.5.2.2 Solvent Siphon Test 1975.5.2.3 Premixing to Improve Retention Reproducibility in Shallow Gradients 1985.5.2.4 Cleaning and Handling Check-Valves 1995.5.2.5 Replacing Pump Seals and Pistons 2005.5.2.6 Leak Detection 2005.5.2.7 Repairing Fitting Leaks 2005.5.2.8 Cleaning Glassware 2015.5.2.9 For Best Results with TFA 2015.5.2.10 Improved Water Purity 2015.5.2.11 Isolating Carryover Problems 2035.5.2.12 Troubleshooting Rules of Thumb 2045.5.3 Gradient Performance Test Failures 2065.5.3.1 Linearity (4.3.1.1) 2065.5.3.2 Step Test (4.3.1.3) 2065.5.3.3 Gradient-Proportioning-Valve Test (4.3.1.4) 2095.5.3.4 Flow Rate (4.3.2.1) 2115.5.3.5 Pressure Bleed-Down (4.3.2.2) 2125.5.3.6 Retention Reproducibility (4.3.2.3) 2125.5.3.7 Peak Area Reproducibility (4.3.2.4) 2135.5.4 Troubleshooting Case Studies 2135.5.4.1 Retention Variation – Case Study 1 2135.5.4.2 Retention Variation – Case Study 2 2185.5.4.3 Contaminated Reagents – Case Study 3 2205.5.4.4 Baseline and Retention Problems – Case Study 4 2246 Separation of Large Molecules 2286.1 General Considerations 2286.1.1 Values of S for Large Molecules 2296.1.2 Values of N* for Large Molecules 2356.1.3 Conformational State 2366.1.4 Homo-Oligomeric Samples 2386.1.4.1 Separation of Large Homopolymers 2416.1.5 Proposed Models for the Gradient Separation of Large Molecules 2426.1.5.2 “Critical Elution Behavior”: Biopolymers 2466.1.5.3 Measurement of LSS Parameters for Large Molecules 2476.2 Biomolecules 2486.2.1 Peptides and Proteins 2486.2.1.1 Sample Characteristics 2496.2.1.2 Conditions for an Initial Gradient Run 2496.2.1.3 Method Development 2536.2.1.4 Segmented Gradients 2596.2.2 Other Separation Modes and Samples 2616.2.2.1 Hydrophobic Interaction Chromatography 2626.2.2.2 Ion Exchange Chromatography 2646.2.2.3 Hydrophilic Interaction Chromatography 2666.2.2.4 Separation of Viruses 2676.2.3 Separation Problems 2716.2.4 Fast Separations of Peptides and Proteins 2746.2.5 Two-Dimensional Separations of Peptides and Proteins 2746.3 Synthetic Polymers 2756.3.1 Determination of Molecular Weight Distribution 2776.3.2 Determination of Chemical Composition 2787 Preparative Separations 2837.1 Introduction 2837.1.1 Equipment for Preparative Separation 2857.2 Isocratic Separation 2867.2.1 Touching-Peak Separation 2877.2.1.1 Theory 2877.2.1.2 Column Saturation Capacity 2897.2.1.3 Sample-Volume Overload 2927.2.2 Method Development for Isocratic Touching-Peak Separation 2927.2.2.1 Optimizing Separation Conditions 2957.2.2.2 Selecting a Sample Weight for Touching-Peak Separation 2977.2.2.3 Scale-Up 2987.2.2.4 Sample Solubility 3007.2.3 Beyond Touching-Peak Separation 3017.3 Gradient Separation 3027.3.1 Touching-Peak Separation 3067.3.2 Method Development for Gradient Touching-Peak Separation 3067.3.2.1 Step Gradients 3117.3.3 Sample-Volume Overload 3127.3.4 Possible Complications of Simple Touching-Peak Theory and Their Practical Impact 3127.3.4.1 Crossing Isotherms 3137.3.4.2 Unequal Values of S 3147.4 Severely Overloaded Separation 3157.4.1 Is Gradient Elution Necessary? 3167.4.2 Displacement Effects 3177.4.3 Method Development 3177.4.4 Separations of Peptides and Small Proteins 3187.4.5 Column Efficiency 3207.4.6 Production-Scale Separation 3208 other Applications of Gradient Elution 3238.1 Gradient Elution for LC-MS 3248.1.1 Application Areas 3258.1.2 Requirements for LC-MS 3258.1.3 Basic LC-MS Concepts 3268.1.3.1 The Interface 3268.1.3.2 Column Configurations 3288.1.3.3 Quadrupoles and Ion Traps 3288.1.4 LC-UV vs LC-MS Gradient Conditions 3308.1.5 Method Development for LC-MS 3328.1.5.1 Define Separation Goals (Step 1, Table 8.2) 3328.1.5.2 Collect Information on Sample (Step 2, Table 8.2) 3348.1.5.3 Carry Out Initial Separation (Run 1, Step 3, Table 8.2) 3398.1.5.4 Optimize Gradient Retention k* (Step 4, Table 8.2) 3398.1.5.5 Optimize Selectivity a* (Step 5, Table 8.2) 3398.1.5.6 Adjust Gradient Range and Shape (Step 6, Table 8.2) 3408.1.5.7 Vary Column Conditions (Step 7, Table 8.2) 3418.1.5.8 Determine Inter-Run Column Equilibration (Step 8, Table 8.2) 3418.1.6 Special Challenges for LC-MS 3418.1.6.1 Dwell Volume 3428.1.6.2 Gradient Distortion 3428.1.6.3 Ion Suppression 3438.1.6.4 Co-Eluting Compounds 3458.1.6.5 Resolution Requirements 3468.1.6.6 Use of Computer Simulation Software 3478.1.6.7 Isocratic Methods 3478.1.6.8 Throughput Enhancement 3478.2 Ion-Exchange Chromatography 3498.2.1 Theory 3498.2.2 Dependence of Separation on Gradient Conditions 3568.2.3 Method Development for Gradient IEC 3568.2.3.1 Choice of Initial Conditions 3568.2.3.2 Improving the Separation 3578.3 Normal-Phase Chromatography 3598.3.1 Theory 3598.3.2 Method Development for Gradient NPC 3608.3.3 Hydrophilic Interaction Chromatography 3618.3.3.1 Method Development for Gradient HILIC 3618.4 Ternary- or Quaternary-Solvent Gradients 3659 Theory and Derivations 3709.1 The Linear Solvent Strength Model 3709.1.1 Retention 3729.1.1.1 Gradient and Isocratic Retention Compared 3749.1.1.2 Small Values of k 0 3769.1.2 Peak Width 3789.1.2.1 Gradient Compression 3809.1.3 Selectivity and Resolution 3839.1.4 Advantages of LSS Behavior 3859.2 Second-Order Effects 3869.2.1 Assumptions About Φ and k 3869.2.1.1 Incomplete Column Equilibration 3869.2.1.2 Solvent Demixing 3919.2.1.3 Nonlinear Plots of log k vs Φ 3939.2.1.4 Dependence of V m on Φ 3939.2.2 Nonideal Equipment 3939.3. Accuracy of Gradient Elution Predictions 3979.3.1 Gradient Retention Time 3979.3.1.1 Confirmation of Equation (9.2) 3979.3.1.2 Computer Simulation 3999.3.2 Peak Width Predictions 3999.3.3 Measurement of Values of S and log k 0 4009.4 Values of S 4019.4.1 Estimating Values of S from Solute Properties and Experimental Conditions 4029.5 Values of N in Gradient Elution 404Appendix I The Constant-S Approximation In Gradient Elution 414Appendix II Estimation of Conditions for Isocratic Elution, Based on An Initial Gradient Run 416Appendix III Characterization of Reversed-phase Columns for Selectivity and Peak Tailing 418Appendix IV Solvent Properties Relevant to the Use of Gradient Elution 434Appendix V Theory Of Preparative Separation 436Appendix Vi Further Information On Virus Chromatography 445Index 450