m RSC CHROMATOGRAPHY MONOGRAPHS Chromatographie Integration Methods Second Edition Norman Dyson Dyson Instruments Ltd., UK THE ROYAL SOCIETY OF CHEMISTRY
Chapter 1 Measurements and Models The Basic Measurements Measurements and Their Use Quantitation Peak Area and Peak Height Peak 'Volume' Retention Time and Solute Identity Column Hold-up Time Diagnostics and System Suitability Tests Baseline Noise Baseline Signal Level Peak Boundaries Peak Width and Column Efficiency Peak Asymmetry Peak Resolution Retention Time Stability Results Assessment Correct Peak Measurements Total Peak Area Correct Number of Peaks Coefficient of Variation and Relative Standard Deviation Comparison Against Standards Trend Analysis Performance Measurement Chromatograph Utilization Analyst Workload Cost per Analysis Chromatographie Peak Models The Gaussian Function The Function Peak Height Ratio of Area/Height Calculation of Peak Width at Various Heights Gaussian Peak Shape Tests The Points of Inflection 1 1 1 1 3 4 4 4 5 6 6 6 7 9 10 10 10 10 12 12 12 13 13 14 14 15 16 16 IX
Fractional Peak Area Bounded by Various Widths 17 Loss of Area from the Base of a Gaussian Peak 18 Gaussian Peak Maximum as an Approximate Parabola 18 The Exponentially Modified Gaussian Function 20 The Function 20 Practical Application of the EMG Function 22 EMG Peak Shape Tests 23 Statistical Moments of a Chromatographie Peak 23 Zeroeth Moment, m 0 24 First Moment, m\ 24 Second Moment, w 2 25 Third Moment, m 3 25 Fourtli Moment, m 4 26 Higher Odd Moments 27 Higher Even Moments 27 Measurement of Peak Moments 27 Practical Disadvantages and Uses 27 Manual Peak Area Measurement 28 Height XWidthatHalfHeight 28 The Condal-Bosch Area 29 Peak Area by Triangulation 30 Manual Measurement of Asymmetrie (EMG) Peaks 31 References 33 Chapter 2 Errors in Peak Area Measurement 35 1 Accuracy and Precision 35 Accuracy 35 Precision 35 Inaccuracy and Uncertainty 35 Repeatability 36 Reproducibility 36 Random Errors 37 Systematic Errors 37 Spurious Errors 37 Causes of Imprecision 37 Causes of Inaccuracy 37 Precision of Integrator Measurements 37 2 Accurate Representation of the Solute Profile 39 Additivity of Signals 40 Negative Detector Signals 41 Electronic Peak Distortion 41 3 Peak Area and Solute Quantity 43 Mass and Flow Sensitive Detectors 43
Flow Sensitive Detectors Mass Sensitive Detectors Detector Overload Linearity Detector Non-linearity Column Non-linearity Electronic Noise and Drift Sources of Peak Measurement Error Hardware Errors Noise Noise and Frequency Short-term Noise Long-term Noise Drift Errors Created by Noise Signal-to-noise Ratio: The Smallest Measurable Peak Limits of Detection and Quantitation A 'Good Baseline' Errors Created by Baseline Drift Drifting Baseline and Peak Measurement Baseline Drift and Retention Time Reduced Detector Operating Range Some Preliminary Conclusions Errors of Incomplete Peak Resolution Height of a Fused Peak Perpendicular Separation Effect of Overlap on Area Measurement Accuracy Error Correction Strategies Error Propagation through Overlapping Groups Peak Overlap and Calibration Tangent Skim Errors Errors of Perpendicular/Tangent Transition Overlapping Peaks on Sloping Baselihes Multiple Fused Peaks Mathematical Deconvolution of Overlapping Peaks The Isomer Test Errors from Peak Asymmetry Asymmetry and Peak Tailing Asymmetry and Base Broadening Asymmetry and Manual Peak Measurement Unequal Asymmetry The Achievement of Accuracy in Chromatographie Analyses Peak Area vs. Peak Height User Surveys References 44 45 47 48 49 49 50 50 50 53 54 55 55 56 56 58 59 60 60 62 62 64 67 68 70 71 72 72 74 76 77 78 78 80 80 81 82 83 85 86
xii Contents Chapter 3 Manual Measurement of Peaks 89 Representation of the Detector Signal by Chart Recorder Slow Response Time Non-linear Signal Response Pen Head Damping Amplifier Noise Manual Measurement of Noise Dead Band Chart Motor Control Attenuator Accuracy Measurement Strategies Counting Squares Cutting and Weighing Planimeters Measurements based on a Peak Model Pencil and Rule Methods Measurement of Peak Height Height vs. Area Measurements Triangulation Peak Height X Width at Half Height Condal-Bosch Variation The Foley Variations Measurement of Overlapping Asymmetrie Peaks Peak Shape Tests Errors of Manual Measurement Optimum Peak Shape Advantages and Disadvantages of Manual Peak Measurement References 89 89 89 90 90 91 91 92 92 92 93 93 94 94 95 95 95 96 97 98 99 101 101 101 103 105 105 Chapter 4 Digital Integrators 107 1 ABrief History of Integrators 107 Strip Chart Recorder Techniques 107 Electromechanical Counters 107 Electronic Integrators 0 TTL Instruments - The First Electronic Integrators 0 Microprocessor-based Integrators 1 Integrators with Printer Plotters 1 The Impact of the Microcomputer 2 2 Current Integrator Status 2 Standard Integrator Specification 3 Integrator Files 4 Analysis Parameters for Peak Measurement 4 Peak Width 5
Slope Sensitivity or Detection Threshold Baseline Drift Tolerance Time to Double Minimum Area or Height Threshold Analysis Duration Integrate Inhibit Forcing Tangent or Perpendicular Separation Forcing Baseline Detection Horizontal Baseline Projection Inverting Negative Peaks Instrument Control and Communications Sample Management, Calculations and Calibrations Peak and Solute Identity Relative Retention Times Standard Calculations Area% or Normalization Internal Standard Extemal Standard Sample Scheduling Calibration Report Preparation and Output Trends Report Distribution Validation of Integrators The Integrator as a Diagnostic Tool Specification, Installation, Operational, Performance Qualification Integrator Specification and Selection (SQ) Installation Checks (IQ) Operational Qualincation (OQ) Validation and Calibration: The Difference Records Performance Qualification (PQ): Regulär Testing of the Integrator Logging Results Validation of Software Standard Chromatograms Creation of Standard Chromatograms Computer-based Standard Chromatograms Specification of Standard Chromatograms Creation of Synthetic Chromatograms Baselines Baseline Noise Drift Traceability of Synthetic Chromatograms References 5 7 7 8 8 8 8 120 120 122 123 123 123 124 124 124 125 125 126 126 127 128 128 129 129 130 130 131 132 132 132 133 134 134 135 136 136 137 137 137 137 138 138 138
xiv Contents Chapter 5 Digital Measurement of Peak Areas 140 1 Signal Sampling 140 Analogue to Digital Conversion 140 Voltage to Frequency Conversion 140 Dual Slope, Integrating A/D Conversion 141 Resolution of A/D Converters 143 Auto-ranging of A/D Converters 143 Data Sampling Frequency 144 Sampling Frequency and Integrator Manufacture 144 Sampling Frequency and Data Processing Algorithms 144 Data Bunching 144 Baseline Bunching 145 Estimating the A/D Sampling Frequency and Bunch Size 146 Data Bunching and the Peak Width Parameter 148 Peak Width Parameter and Analysis Reprocessing 148 Peak Sampling Synchronization 149 Rounding or Truncation Errors 149 Aperture Time Jitter 149 2 Filtering and Smoothing the Chromatographie Signal 150 Filtering 150 Smoothing 150 Electronic Filters 150 Sampling Frequency and Mains Coupling 150 Smoothing Techniques 1 Digitizing and Integrating 1 Bunching 1 Moving Windows and Polynomial Curve Fitting 153 Optimum Filtering 154 Signal Subtraction 155 Chromatogram Plotting 157 Matched Filtering 15 7 3 Location and Measurement ofpeaks 158 Finding the Peaks 159 Retention Time 160 Peak Shape Test 160 Properties of the Smoothed Data 160 Data Integrals 161 Baseline Fluctuations and Slope Sensitivity 162 Programming Slope Sensitivity 162 Slope Sensitivity and Representative Baseline 162 Updating Peak Width and Slope Sensitivity during Analyses 163 Location of the Limits of Integration 163 Small Peak Filtering 165 Location of Peak End 165
Measurement of Peak Area 166 Baseline Convention 168 Measurement of Peak Height 168 Measurement of Retention Time 168 Measurement of Two Unresolved Peaks 169 Measurement of Individual Peak Areas 170 Peak Measurement Diagnostics 170 Measurement of FusedGroups 170 Shoulders 171 Measurement oftangent Peaks 172 Tangent Skimmed Groups 173 Small Peaks between Larger Ones 174 Tangents on Tangents 175 4 Baselines, A More Detailed Discussion 175 Baselme Drift Limit 175 False Starts 177 Formulating a Baseline Definition 177 Mis-timing 'Start' and 'End' 178 End of Tntegrate Inhibit' 178 Forcing Baseline 179 Incorrect Programming of Baseline Drift Tolerance 180 Fused Tangent Measurement 182 Single Peaks on a Rising Baseline 183 Valleys Between Fully-resolved Peaks 184 Negative Dips and Constructed Baselines 184 Assigning Baseline Beneath the Whole Chromatogram 187 Valley-Valley Skim 190 5 Conclusions 190 6 References 191 xv AuthorIndex 193 Subject Index 196