Contents

1 Introduction, Definitions, Goal 1

1.1  History of Chromatography 3

1.2  Definitions 12

1.3  Goal of the Book 15

References 16

2 The Mass Balance Equation of Chromatography and Its General Proper
ties 19

2.1  Mass and Heat Balance Equations in Chromatography 21

2.2  Solution of the System of Mass Balance Equations 42

2.3  Important Definitions 57

References 63

3 Single­Component Equilibrium Isotherms 67

3.1  Fundamentals of Adsorption Equilibria 70

3.2  Models of Adsorption Isotherms in Liquid-Solid Equilibria .... 80

3.3  Adsorption and Affinity Energy Distribution 109

3.4  Influence of Experimental Conditions on Equilibrium Isotherms . . 117

3.5  Determination of Single­Component Isotherms 122

3.6  Data Processing and Assessment 135

References 144

4 Competitive Equilibrium Isotherms 151

4.1  Models of Multicomponent Competitive Adsorption Isotherms . . 153

4.2  Determination of Competitive Isotherms 191

References 216

5 Transfer Phenomena in Chromatography 221

5.1  Diffusion 222

5.2  Axial Dispersion and Mass Transfer Resistance in Porous Media . . 240

5.3  The Viscosity of Liquids 257

References 275

6 Linear Chromatography 281

6.1  The Plate Models 283

6.2  The Solution of the Mass Balance Equation 290

6.3  The General Rate Model of Chromatography 301

6.4  Moment Analysis and Plate Height Equations 310

6.5  The Statistic Approach 328

6.6  Sources of Band Asymmetry and Tailing in Linear Chromatography 335

6.7  Extension of Linear to Nonlinear Chromatography Models 341

References 342

vii

viii CONTENTS

7 Band Profiles of Single­Components with the Ideal Model 347

7.1  Retrospective of the Solution of the Ideal Model of Chromatogra-
phy 349

7.2  Migration and Evolution of the Band Profile 351

7.3  Analytical Solutions of the Ideal Model 363

7.4  The Ideal Model in Gas Chromatography 377

7.5  Practical Relevance of Results of the Ideal Model 379

8 Band Profiles of Two Components with the Ideal Model 387

8.1  General Principle of the Solution 390

8.2  Elution of a Wide Band With Competitive Langmuir Isotherms . . 395

8.3  Elution of a Narrow Band with Competitive Langmuir Isotherms . 401

8.4  Method of Calculation of the Ideal Model Solution in a Specific Case 407

8.5  Dimensionless Plot of a Two­component Band System 414

8.6  The Displacement Effect 416

8.7  The Tag­Along Effect 419

8.8  The Ideal Model in Gas Chromatography 421

8.9  Practical Relevance of the Ideal Model 423

References 435

9 Band Profiles in Displacement Chromatography with the Ideal Model 437

9.1  Steady State in the Displacement Mode. The Isotachic Train .... 439

9.2  The Theory of Characteristics 450

9.3  Coherence Theory 461

9.4  Practical Relevance of the Results of the Ideal Model 467

References 468

10 Single­Component Profiles with the Equilibrium Dispersive Model 471

10.1  Fundamental Basis of the Equilibrium Dispersive Model 473

10.2  Approximate Analytical Solutions 476

10.3  Numerical Solutions of the Equilibrium-Dispersive Model 492

10.4  Results Obtained with the Equilibrium Dispersive Model 509

References 527

11 Two­Component Band Profiles with the Equilibrium-Dispersive Model 531

11.1  Numerical Analysis of the Equilibrium-Dispersive Model 532

11.2  Applications of the Equilibrium-Dispersive Model 542

References 567

12 Frontal Analysis, Displacement and the Equilibrium-Dispersive Model 569

12.1  Displacement Chromatography with a Nonideal Column 570

12.2  Applications of Displacement Chromatography 587

12.3  Comparison of Calculated and Experimental Results 599

References 603

CONTENTS ix

13 System Peaks with the Equilibrium-Dispersive Model 605

13.1  System Peaks in Linear Chromatography 606

13.2  High­Concentration System Peaks 626

References 647

14 Kinetic Models and Single­Component Problems 651

14.1  Solution of the Breakthrough Curve under Constant Pattern Con
dition 653

14.2  Analytical and Numerical Solutions of the Kinetic Models 669

14.3  Comparison Between the Various Kinetic Models 680

14.4  Results of Computer Experiments 687

14.5  Numerical Solution of the Lumped Pore Diffusion Model 689

14.6 The Monte Carlo Model of Nonlinear Chromatography 693

References 695

15 Gradient Elution Chromatography under Nonlinear Conditions 699

15.1  Retention Times and Band Profiles in Linear Chromatography . . . 701

15.2  Retention of the Organic Modifier or Modulator 705

15.3  Numerical Solutions of Nonlinear Gradient Elution 711

15.4  Gradient Elution in Ion­Exchange Chromatography 726

References 731

16 Kinetic Models and Multicomponent Problems 735

16.1  Analytical Solution for Binary Mixture; Constant Pattern Behavior . 736

16.2  Linear Driving Force Model Approach 747

16.3  Numerical Solution of The General Rate Model of Chromatography 753
References 775

17 Simulated Moving Bed Chromatography 779

17.1  Introduction 780

17.2  Modeling of Simulated Moving Bed (SMB) Separations 783

17.3  Analytical Solution of the Linear, Ideal Model of SMB 785

17.4  Analytical Solution of the Linear, Nonideal Model of SMB 806

17.5  McCabe-Thiele Analysis 808

17.6  Optimization of the SMB Process 809

17.7  Nonlinear, Ideal Model of SMB 816

17.8  Recent Improvements in SMB Performance with New Operating
Modes 826

17.9 Numerical Solutions for Nonlinear, Nonideal SMB 836

References 845

18 Optimization of the Experimental Conditions 849

18.1  Definitions 851

18.2  The Economics of Chromatographic Separations 857

18.3  Optimization Based on Theoretical Considerations 867

18.4  Optimization Using Numerical Solutions 883

18.5  Recycling Procedures 915

x CONTENTS

18.6  Practical Rules 920

18.7  Optimization of the SMB Process 924

References 935

Glossary of Symbols 939

Glossary of Terms 949

Index 969