Fundamentals of Preparatiue and Nonlinear Chromatography

Transcription

1 Fundamentals of Preparatiue and Nonlinear Chromatography Georges Guiochon University of Tennessee and Oak Ridge National Laboratory Distinguished Scientist Knoxville, Tennessee Sadroddin Golshan Shirazi Senior Scientist Applied Analytical Industries Wilmington, North Carolina Anita M. Katti Senior Development Engineer Mallinckrodt Chemical Inc. St. Louis, Academic Press Boston San Diego New York London Sydney Tokyo Toronto

2 TABLE OF CONTENTS Preface Acknowledgments xiii xv Chapter I. Introduction, Deflnitions, Goal 1 Introduction 1 I. History of Chromatography 3 1. Discovery by Tswett and Early Works 3 2. The Manhattan Project and the Purification of Rare Earth Elements 4 3. The API Project and the Extraction of Purified Hydrocarbons from Crude Oils 6 4- Preparative Chromatography as a Separation Process 6 IL Deflnitions Linear and Nonlinear Chromatography Ideal and Nonideal Chromatography Separation, Extraction, and Purification The Various Scales of Preparative Chromatography 16 III. Goal of the Book 17 References 18 Chapter II. The Mass Balance Equation of Chromatography and Its Properties..21 Introduction 21 I. The Mass and Heat Balance Equations of Chromatography Derivation of the Differential Mass Balance of a Compound Discussion of the Fundamental Assumptions Relationship between the Concentrations in the Stationary and Mobile Phases Near-Isothermal and Nonisothermal Systems Initial and Boundary Conditions 30 II. Solution of the System of Mass Balance Equations The Ideal Model The Equilibrium-Dispersive Model The Lumped Kinetic Models Eguivalence between Equilibrium-Dispersive and Kinetic Models of Chromatography 43 References 47 Chapter III. Single-Component Equilibrium Isotherms 49 Introduction 49 I. Fundamentals of Adsorption Equilibria Basic Thermodynamics of Adsorption and the Gibbs Isotherm The Linear Isotherm The Langmuir Isotherm in Gas-Solid Eguilibria The Virial Isotherm Statistical Thermodynamics of Adsorption Liquid-Solid Equilibria Surface Excess and Excess Isotherms 60 II. Models of Adsorption Isotherms The Langmuir Isotherm in Liquid-Solid Equilibria 61 vii

3 viii Fundamentals of Preparative and Nonlinear Chromatography 2. The Bi-Langmuir Isotherm The Fowler Isotherm The Freundlich Isotherm S-Shaped Isotherms and the Quadratic Isotherm Model Other Useful Isotherm Equations 78 III. Determination of Single-Component Isotherms Frontal Analysis (FA) Frontal Analysis by Characteristic Point (FACP) Elution by Characteristic Points (ECP) Pulse Methods The Retention Time Method Computation of Elution Profiles (CEP) Method Static Method 89 IV. Data Processing and Assessment Processing Experimental Data into an Isotherm Equation Accuracy and Precision Comparison of the Main Chromatographie Methods 93 References 96 Chapter IV. Competitive Equilibrium Isotherms 99 Introduction 99 I. Multicomponent Adsorption and Competitive Isotherm Models Competition for Adsorption The Competitive Langmuir Isotherm Model and Its Properties The Competitive Bi-Langmuir Isotherm The Ideal Adsorbed Solution The Statistical Isotherm The Competitive Fowler Isotherm The Competitive Freundlich-Langmuir Isotherm Competitive Isotherm Models for Chromatography Modes Other than Adsorption The Competitive Martire Isotherm 121 II. Determination of Competitive Isotherms Competitive Frontal Analysis Pulse Methods The Simple Wave Method 132 References 134 Chapter V. Fundamentals of Transport Phenomena in Chromatography 137 Introduction 137 I. Diffusion Diffusivity or Diffusion Coefficients Influence of the Concentration on the Bulk Diffusion Coefficients Influence of the Pressure on the Bulk Diffusion Coefficients Influence of the Temperature on the Bulk Diffusion Coefficients Measurement of the Diffusion Coefficients 146 II. Axial Dispersion and Mass Transfer Resistance in Packed Beds Axial Dispersion in Packed Beds Kinetics of Adsorption in Porous Adsorbents 148 III. The Viscosity of Liquids The Viscosity of the Mobile Phase Importance of the Mobile Phase Viscosity in Preparative Chromatography Calculation of the Inlet Pressure in the Case of a Variable Viscosity Feed Concentration, Mobile Phase Viscosity, and Inlet Pressure Flow Instability and Viscous Fingering 163 References 167 Chapter VI. Linear Chromatography 169 Introduction 169 I. The Plate Models Overview of the Approach 171

4 Table of Contents ix 2. The Martin and Synge Plate Model 3. The Craig Plate Model Comparison of the Two Plate Models 176 II. The Solution of the Mass Balance Equation The Equilibrium-Dispersive Model Solution of the Lumped Kinetic Model From the Lumped Kinetic Model back to the Equilibrium-Dispersive Model 189 III. The General Rate Model of Chromatography Analytical Solution in a Particular Case Inverse Laplace Transform of the Solution Moment Analysis and Plate Height Equations The Golay Plate Height Equation Dispersion and Partitioning in Short Coated Tubes 204 IV. The Statistical Approach Transport Equation in Chromatography with a Finite Speed of Signal Propagation. 206 V. Sources of Band Asymmetry and Tailing in Linear Chromatography VI. Extension of Linear Chromatography Models to Nonlinear Chromatography References 215 Chapter VII. The Ideal Model of Chromatography I. Elution of Single-Component Bands 217 Introduction 217 I. Retrospective of the Solution of the Ideal Model 218 IL Migration and Evolution of the Band Profile Continuous Part or Diffuse Boundary of the Profile Origin of the Concentration Shock Propagation of Concentration Shocks 226 III. Analytical Solution of the Ideal Model General Closed-Form Solution Case of the Langmuir Isotherm Concentration Profile along the Column Case of the Bi-Langmuir Isotherm Case of the Freundlich Isotherm Asymptotic Solution 240 IV. Practical Relevance of the Results of the Ideal Model 241 References 243 Chapter VIII. The Ideal Model of Chromatography II. Elution of Two-Component Bands 245 Introduction: Retrospective 245 I. General Principle of the Solution Statement of the Problem and Its Constraints Properties of the System of Mass Balance Equations 250 IL Analytical Solution for a Wide Band with Competitive Langmuir Isotherms Position of the Two Concentration Shocks Rear Diffuse Profiles of the Two Components The Intermediate Plateau on the Rear Diffuse Profile of the Second Component III. Analytical Solution for a Narrow Band with Competitive Langmuir Isotherms Retention Time of the Second Concentration Shock Maximum Concentration of the Two Components in the Mixed Zone Elution Profile of the First Component between the Two Shocks Retention Time of the First Shock 265 IV. Method of Calculation of the Solution of the Ideal Model in a Specific Case Case 1: Wide Injection Case 2: Injection Plateau Eroded, Pure First Component Plateau Present Case 3: Narrow Injection and Mixed Zone Case 4'- Touching Bands, Second Component Plateau Present Case 5: Resolved Bands Influence of the Width of the Injection Pulse 273 V. Dimensionless Plot of a Two-Component Band System 276 VI. The Displacement Effect 276

5 x Fundamentals of Preparative and Nonlinear Chromatography 1. Origin of the Displacement Effect Intensity of the Displacement Effect 278 VII. The Tag-Along Effect Origin of the Tag-Along Effect Intensity of the Tag-Along Effect 281 VIII. Practica! Relevance of the Results of the Ideal Model 281 References 284 Appendix 286 Chapter IX. The Ideal Model of Chromatography III. Displacement Chromatography 299 Introduction I. Steady State in the Displacement Mode. The Isotachic Train The Operating Line 2. Influence of the Displacer Concentration The Watershed Point 4- Case of a Trace Component II. The Theory of Characteristics Determination of the Characteristic Parameters 2. Application to Displacement Chromatography Wave Interactions Critical Value of the Displacer Concentration Plateau Concentrations and Bandwidth Critical Column Length for Isotachic Train Formation III. Practical Relevance of the Results of the Ideal Model References 322 Chapter X. The Equilibrium Dispersive Model I. Elution of Single-Component Bands 325 Introduction 325 I. Fundamental Basis of the Model and Apparent Dispersion Coefficient 327 II. Approximate Analytical Solutions The Houghton Solution The Haarhoff- Van der Linde Solution 3. Range of Validity of the Haarhoff-Van der Linde and Houghton Equations Influence of the Sample Size on the Bandwidth Comparison of the Experimental Band Profiles and the Prediction of These Equations 341 III. Numerical Solutions of the Equilibrium-Dispersive Model Principle of the Finite Difference Methods 2. Estimation of the Numerical Errors Made during the Calculation First Method: Calculation of Numerical Solutions of the Mass Balance Equation 4- Second Method: Replacement of Axial Dispersion by Numerical Dispersion Application of the Second Method Finite Element Method 357 IV. Results Obtained with the Equilibrium-Dispersive Model Comparison of Solutions of the Ideal and the Equilibrium-Dispersive Models Comparison of the Results of Different Calculation Methods Results of Computer Experiments Comparison with Experimental Results 371 References 378 Chapter XI. The Equilibrium-Dispersive Model II. Isocratic Separations of Two-Component Bands and Gradient Elution 381 Introduction 381 I. Numerical Analysis of the Equilibrium-Dispersive Model Finite Difference Methods. Principle Finite Difference Methods. Errors in the Case of Two Components Finite Element Method 390 IL Gradient Elution Solution of the Ideal Model in Gradient Elution Representation of the Isotherm in Gradient Elution 395

6 Table of Contents xi 3. Retention of the Modifier Calculation of Elution Band Profiles 398 III. Applications of the Equilibrium-Dispersive Model Comparison of Solutions of the Ideal and the Equilibrium-Dispersive Models The Hodograph Transform and Its Application Results of Computer Experiments Calculation of Multicomponent Chromatograms Comparison of Calculated Band Profiles and Experimental Results 6. Experimental and Calculated Band Profiles in Gradient Elution References 432 Chapter XII. The Equilibrium-Dispersive Model III. Frontal Analysis and Displacement 435 Introduction 435 I. Displacement Chromatography with a Nonideal Column Influence of the HETP Influence of the Sample Size and the Displacer Concentration Influence of the Column Length Influence of the Separation Factor Case of Trace Components Influence of the Impurities in the Displacer Solution Case of Selectivity Reversal 452 II. Applications of Displacement Chromatography Separation of Rare Earths and Other Cations Separation of Organic Compounds Separation of Peptides and Proteins Separation of Nucleic Acid Constituents 464 III. Comparison of Calculated and Experimental Results 467 References 471 Chapter XIII. The Equilibrium-Dispersive Model IV. System Peaks in Chromatography Introduction I. System Peaks in Linear Chromatography General Experimental Results on System Peaks Theory of System Peaks Indirect Detection Using System Peaks Application of System Peaks to Analyte Peak Compression Vacancy Chromatography 492 II. High-Concentration System Peaks High-Concentration System Peaks for a Single-Component Sample High-Concentration System Peaks for a Two-Component Sample 507 References 515 Chapter XIV. The Kinetic Models I. Frontal Analysis and Elution of Single-Component Bands 519 Introduction 519 I. Solution of the Breakthrough Curve under Constant Pattern Condition Analytical Solution for the Constant Pattern Profile Numerical Solution of the Breakthrough Curve under Constant Pattern Behavior Effect of Axial Dispersion The Shock Layer Theory Shock Layer in the Case of the Langmuir Isotherm Properties of the Shock Layer Thickness in Frontal Analysis Range of Validity of the Equilibrium-Dispersive Model 537 II. Analytical Solution of the Reaction-Kinetic Model Solution of the Reaction-Kinetic Model in the Case of a Step Injection Numerical Solutions of the Kinetic Model for a Breakthrough Curve Analytical Solution of the Reaction-Kinetic Model in the Case of a Pulse Injection Numerical Solution of the Reaction-Dispersive Model for a Pulse Injection 543

7 xii Fundamentals of Preparative and Nonlinear Chromatography III. Comparison of the Various Kinetic Models of Nonlinear Chromatography 545 IV. Results of Computer Experiments 552 V. Comparison between Theoretical and Experimental Results 554 References 558 Chapter XV. The Kinetic Models II. Frontal Analysis, Flution, and Displacement of Multicomponent Bands 561 Introduction I. Analytical Solution under Constant Pattern Behavior The Shock Layer Theory for a Binary Mixture Shock Layer in the Case of Competitive Langmuir Isotherms Shock Layer Thickness in Binary Frontal Analysis Shock Layer Thickness in Displacement Chromatography 568 II. Linear Driving Force Model Approach 574 III. Numerical Solution of the General Rate Model of Chromatography Formulation of the General Rate Model Solutions of the General Rate Model The VERSE Model IV. Comparison of Solutions of Rate Models and Experimental Results V. Effect of the Particle Size Distribution References Chapter XVI. Optimization of the Experimental Conditions in Preparative Chromatography 595 Introduction 595 I. Definitions Throughput Sample Size and Loading Factor Cycle Time Production Rate Cut Points Recovery Yield Purity of a Component 8. Specific Production II. The Economics of Chromatographie Separations The Components of the Production Cost The Different Objective Functions 3. Identification of the Experimental Parameters III. Optimization Based on Theoretical Considerations The Knox and Pyper Approach Optimization for Touching Band Using the Ideal Model Optimization for Overlapping Bands with No Yield Constraint 4- Optimization for Overlapping Bands with Yield Constraint IV. Optimization Using Numerical Solutions Maximum Production Rate in Elution Minimum Solvent Consumption in Elution Compromise between Maximum Production Rate and Minimum Solvent Consumption Maximum Production Rate in Displacement Chromatography Comparison between Elution and Displacement Chromatography 641 V. Recycling Procedures 648 VI. Comparison between Experimental and Calculated Results 649 VII. Practical Rules 651 References 656 Glossary of Symbols 659 Glossary of Terms 669 Subject Index 693