High-Performance Gradient Elution: The Practical Application of the Linear-Solvent-Strength Model »

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.

Gradient elution demystified

Of the various ways in which chromatography is applied today, few have been as misunderstood as the technique of gradient elution, which presents many challenges compared to isocratic separation. When properly explained, however, gradient elution can be less difficult to understand and much easier to use than often assumed.

Written by two well-known authorities in liquid chromatography, High-Performance Gradient Elution: The Practical Application of the Linear-Solvent-Strength Model takes the mystery out of the practice of gradient elution and helps remove barriers to the practical application of this important separation technique. The book presents a systematic approach to the current understanding of gradient elution, describing theory, methodology, and applications across many of the fields that use liquid chromatography as a primary analytical tool.

This up-to-date, practical, and comprehensive treatment of gradient elution:

• Provides specific, step-by-step recommendations for developing a gradient separation for any sample
• Describes the best approach for troubleshooting problems with gradient methods
• Guides the reader on the equipment used for gradient elution
• Lists which conditions should be varied first during method development, and explains how to interpret scouting gradients
• Explains how to avoid problems in transferring gradient methods

With a focus on the use of linear solvent strength (LSS) theory for predicting gradient LC behavior and separations by reversed-phase HPLC, High-Performance Gradient Elution gives every chromatographer access to this useful tool.

Preface     xv
Glossary of Symbols and Terms     xxi
Introduction     1
The "General Elution Problem" and the Need for Gradient Elution     1
Other Reasons for the Use of Gradient Elution     4
Gradient Shape     7
Similarity of Isocratic and Gradient Elution     10
Gradient and Isocratic Elution Compared     10
The Linear-Solvent-Strength Model     13
Computer Simulation     18
Sample Classification     19
Sample Compounds of Related Structure ("Regular Samples")     19
Sample Compounds of Unrelated Structure ("Irregular" Samples)     19
Gradient Elution Fundamentals     23
Isocratic Separation     23
Retention     23
Peak Width and Plate Number     24
Resolution     25
Role of Separation Conditions     27
Optimizing Retention [Term a of Equation (2.7)]     27
Optimizing Selectivity [alpha] [Term b of Equation (2.7)]     28
Optimizing the Column Plate Number N [Term c of Equation (2.7)]     28
Gradient Separation     31
Retention     32
Gradient and Isocratic Separation Compared for "Corresponding" Conditions     34
Peak Width     38
Resolution     39
Resolution as a Function of Values of S for Two Adjacent Peaks ("Irregular" Samples)     42
Using Gradient Elution to Predict Isocratic Separation     45
Sample Complexity and Peak Capacity     47
Effect of Gradient Conditions on Separation     49
Gradient Steepness b: Change in Gradient Time     50
Gradient Steepness b: Change in Column Length or Diameter     51
Gradient Steepness b: Change in Flow Rate     55
Gradient Range [delta phi]: Change in Initial Percentage B ([phi subscript 0])     58
Gradient Range [delta phi]: Change in Final Percentage B ([delta subscript f])     60
Effect of a Gradient Delay     63
Equipment Dwell Volume     66
Effect of Gradient Shape (Nonlinear Gradients)     67
Overview of the Effect of Gradient Conditions on the Chromatogram     71
Related Topics     72
Nonideal Retention in Gradient Elution     72
Gradient Elution Misconceptions     72
Method Development     74
A Systematic Approach to Method Development     74
Separation Goals (Step 1 of Fig. 3.1)     75
Nature of the Sample (Step 2 of Fig. 3.1)      78
Initial Experimental Conditions     79
Repeatable Results     79
Computer Simulation: Yes or No?     80
Sample Preparation (Pretreatment)     81
Initial Experiments     81
Interpreting the Initial Chromatogram (Step 3 of Fig. 3.1)     85
"Trimming" a Gradient Chromatogram     87
Possible Problems     88
Developing a Gradient Separation: Resolution versus Conditions     90
Optimizing Gradient Retention k* (Step 4 of Fig. 3.1)     92
Optimizing Gradient Selectivity [alpha]* (Step 5 of Fig. 3.1)     92
Optimizing the Gradient Range (Step 6 of Fig. 3.1)     95
Changes in Selectivity as a Result of Change in k*     96
Segmented (Nonlinear) Gradients (Step 6 of Fig. 3.1 Continued)     100
Optimizing the Column Plate Number N* (Step 7 of Fig. 3.1)     102
Column Equilibration Between Successive Sample Injections     106
Fast Separations     106
Computer Simulation     108
Quantitative Predictions and Resolution Maps     109
Gradient Optimization     111
Changes in Column Conditions     112
Separation of "Regular" Samples     114
Other Features     115
Isocratic Prediction (5 in Table 3.5)     115
Designated Peak Selection (6 in Table 3.5)     117
Change in Other Conditions (7 in Table 3.5)     117
Computer-Selection of the Best Multisegment Gradient (8 in Table 3.5)     117
"Two-Run" Procedures for the Improvement of Sample Resolution     119
Accuracy of Computer Simulation     119
Peak Tracking     119
Method Reproducibility and Related Topics     120
Method Development     121
Routine Analysis     122
Change in Column Volume     123
Additional Means for an Increase in Separation Selectivity     124
Orthogonal Separations     127
Two-Dimensional Separations     128
Gradient Equipment     133
Gradient System Design     133
High-Pressure vs Low-Pressure Mixing     133
Tradeoffs     135
Dwell Volume     135
Degassing     136
Accuracy     137
Solvent Volume Changes and Compressibility     137
Flexibility     139
Independent Module Use     140
Other System Components     140
Autosampler     140
Column      140
Detector     141
Data System     141
Extra-Column Volume     142
General Considerations in System Selection     142
Which Vendor?     143
High-Pressure or Low-Pressure Mixing?     144
Who Will Fix It?     144
Special Applications     144
Measuring Gradient System Performance     145
Gradient Performance Test     146
Gradient Linearity     146
Dwell Volume Determination     147
Gradient Step-Test     147
Gradient Proportioning Valve Test     148
Additional System Checks     149
Flow Rate Check     149
Pressure Bleed-Down     150
Retention Reproducibility     150
Peak Area Reproducibility     151
Dwell Volume Considerations     151
Separation Artifacts and Troubleshooting     153
Avoiding Problems     154
Equipment Checkout     157
Installation Qualification, Operational Qualification, and Performance Qualification     157
Dwell Volume     158
Blank Gradient     158
Suggestions for Routine Applications     158
Reagent Quality      159
System Cleanliness     159
Degassing     159
Dedicated Columns     159
Equilibration     159
Priming Injections     159
Ignore the First Injection     160
System Suitability     160
Standards and Calibrators     160
Method Development     160
Use a Clean and Stable Column     160
Use Reasonable Mobile Phase Conditions     161
Clean Samples     162
Reproducible Runs     162
Sufficient Equilibration     162
Reference Conditions     162
Additional Tests     162
Method Transfer     163
Compensating for Dwell Volume Differences     163
Injection Delay     163
Adjustment of the Initial Isocratic Hold     164
Use of Maximum-Dwell-Volume Methods     165
Adjustment of Initial Percentage B     165
Other Sources of Method Transfer Problems     168
Gradient Shape     169
Gradient Rounding     169
Inter-Run Equilibration     169
Column Size     169
Column Temperature     169
Interpretation of Method Instructions      170
Column Equilibration     170
Primary Effects     171
Slow Equilibration of Column and Mobile Phase     173
Practical Considerations and Recommendations     174
Separation Artifacts     175
Baseline Drift     176
Baseline Noise     179
Baseline Noise: A Case Study     180
Peaks in a Blank Gradient     182
Mobile Phase Water or Organic Solvent Impurities     182
Other Sources of Background Peaks     185
Extra Peaks for Injected Samples     185
t[subscript 0] Peaks     185
Air Peaks     186
Late Peaks     187
Peak Shape Problems     188
Tailing and Fronting     188
Excess Peak Broadening     188
Split Peaks     190
Injection Conditions     191
Sample Decomposition     193
Troubleshooting     195
Problem Isolation     196
Troubleshooting and Maintenance Suggestions     197
Removing Air from the Pump     197
Solvent Siphon Test     197
Premixing to Improve Retention Reproducibility in Shallow Gradients     198
Cleaning and Handling Check-Valves     199
Replacing Pump Seals and Pistons     200
Leak Detection     200
Repairing Fitting Leaks     200
Cleaning Glassware     201
For Best Results with TFA     201
Improved Water Purity     201
Isolating Carryover Problems     203
Troubleshooting Rules of Thumb     204
Gradient Performance Test Failures     206
Linearity (4.3.1.1)     206
Step Test (4.3.1.3)     206
Gradient-Proportioning-Valve Test (4.3.1.4)     209
Flow Rate (4.3.2.1)     211
Pressure Bleed-Down (4.3.2.2)     212
Retention Reproducibility (4.3.2.3)     212
Peak Area Reproducibility (4.3.2.4)     213
Troubleshooting Case Studies     213
Retention Variation - Case Study 1     213
Retention Variation - Case Study 2     218
Contaminated Reagents - Case Study 3     220
Baseline and Retention Problems - Case Study 4     224
Separation of Large Molecules     228
General Considerations     228
Values of S for Large Molecules     229
Values of N* for Large Molecules     235
Conformational State      236
Homo-Oligomeric Samples     238
Separation of Large Homopolymers     241
Proposed Models for the Gradient Separation of Large Molecules     242
"Critical Elution Behavior": Biopolymers     246
Measurement of LSS Parameters for Large Molecules     247
Biomolecules     248
Peptides and Proteins     248
Sample Characteristics     249
Conditions for an Initial Gradient Run     249
Method Development     253
Segmented Gradients     259
Other Separation Modes and Samples     261
Hydrophobic Interaction Chromatography     262
Ion Exchange Chromatography     264
Hydrophilic Interaction Chromatography     266
Separation of Viruses     267
Separation Problems     271
Fast Separations of Peptides and Proteins     274
Two-Dimensional Separations of Peptides and Proteins     274
Synthetic Polymers     275
Determination of Molecular Weight Distribution     277
Determination of Chemical Composition     278
Preparative Separations     283
Introduction     283
Equipment for Preparative Separation      285
Isocratic Separation     286
Touching-Peak Separation     287
Theory     287
Column Saturation Capacity     289
Sample-Volume Overload     292
Method Development for Isocratic Touching-Peak Separation     292
Optimizing Separation Conditions     295
Selecting a Sample Weight for Touching-Peak Separation     297
Scale-Up     298
Sample Solubility     300
Beyond Touching-Peak Separation     301
Gradient Separation     302
Touching-Peak Separation     306
Method Development for Gradient Touching-Peak Separation     306
Step Gradients     311
Sample-Volume Overload     312
Possible Complications of Simple Touching-Peak Theory and Their Practical Impact     312
Crossing Isotherms     313
Unequal Values of S     314
Severely Overloaded Separation     315
Is Gradient Elution Necessary?     316
Displacement Effects     317
Method Development     317
Separations of Peptides and Small Proteins     318
Column Efficiency     320
Production-Scale Separation     320
Other Applications of Gradient Elution     323
Gradient Elution for LC-MS     324
Application Areas     325
Requirements for LC-MS     325
Basic LC-MS Concepts     326
The Interface     326
Column Configurations     328
Quadrupoles and Ion Traps     328
LC-UV vs LC-MS Gradient Conditions     330
Method Development for LC-MS     332
Define Separation Goals (Step 1, Table 8.2)     332
Collect Information on Sample (Step 2, Table 8.2)     334
Carry Out Initial Separation (Run 1, Step 3, Table 8.2)     339
Optimize Gradient Retention k* (Step 4, Table 8.2)     339
Optimize Selectivity [alpha]* (Step 5, Table 8.2)     339
Adjust Gradient Range and Shape (Step 6, Table 8.2)     340
Vary Column Conditions (Step 7, Table 8.2)     341
Determine Inter-Run Column Equilibration (Step 8, Table 8.2)     341
Special Challenges for LC-MS     341
Dwell Volume     342
Gradient Distortion     342
Ion Suppression     343
Co-Eluting Compounds     345
Resolution Requirements     346
Use of Computer Simulation Software     347
Isocratic Methods      347
Throughput Enhancement     347
Ion-Exchange Chromatography     349
Theory     349
Dependence of Separation on Gradient Conditions     356
Method Development for Gradient IEC     356
Choice of Initial Conditions     356
Improving the Separation     357
Normal-Phase Chromatography     359
Theory     359
Method Development for Gradient NPC     360
Hydrophilic Interaction Chromatography     361
Method Development for Gradient HILIC     361
Ternary- or Quaternary-Solvent Gradients     365
Theory and Derivations     370
The Linear Solvent Strength Model     370
Retention     372
Gradient and Isocratic Retention Compared     374
Small Values of k[subscript 0]     376
Peak Width     378
Gradient Compression     380
Selectivity and Resolution     383
Advantages of LSS Behavior     385
Second-Order Effects     386
Assumptions About [phi] and k     386
Incomplete Column Equilibration     386
Solvent Demixing     391
Nonlinear Plots of log k vs [phi]      393
Dependence of V[subscript m] on [phi]     393
Nonideal Equipment     393
Accuracy of Gradient Elution Predictions     397
Gradient Retention Time     397
Confirmation of Equation (9.2)     397
Computer Simulation     399
Peak Width Predictions     399
Measurement of Values of S and log k[subscript 0]     400
Values of S     401
Estimating Values of S from Solute Properties and Experimental Conditions     402
Values of N in Gradient Elution     404
The Constants Approximation in Gradient Elution     414
Estimation of Conditions for Isocratic Elution, Based on an Initial Gradient Run     416
Characterization of Reversed-Phase Columns for Selectivity and Peak Tailing     418
Solvent Properties Relevant to the Use of Gradient Elution     434
Theory of Preparative Separation     436
Further Information on Virus Chromatography     445
Index     450