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