Advances In Chromatography: Volume 43 (Advances in Chromatography)

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Advances In Chromatography: Volume 43 (Advances in Chromatography)

DK1147-title 9/13/04 11:09 AM VOLUME 43 Advances in CHROMATOGRAPHY EDITORS: PHYLLIS R. BROWN University of Rhode Isl

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DK1147-title 9/13/04

11:09 AM



PHYLLIS R. BROWN University of Rhode Island Kingston, Rhode Island, U.S.A.

ELI GRUSHK A Hebrew University of Jerusalem Jerusalem, Israel

SUSAN LUNTE University of Kansas Lawrence, Kansas, U.S.A.

Marcel Dekker

New York

Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-5341-0 This book is printed on acid-free paper. Headquarters Marcel Dekker, 270 Madison Avenue, New York, NY 10016, U.S.A. tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Cimarron Road, Monticello, New York 12701, U.S.A. tel: 800-228-1160; fax: 845-796-1772 World Wide Web Copyright n 2005 by Marcel Dekker. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10

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Contributors Contents of Other Volumes 1. Gradient Elution in Liquid Column Chromatography—Prediction of Retention and Optimization of Separation Pavel Jandera

vii ix


I. Introduction II. Theory of Retention in Analytical Gradient-Elution Chromatography III. Reversed-Phase Chromatography with Binary Gradients IV. Normal-Phase Chromatography with Binary Gradients V. Ion-Exchange Gradient Elution Chromatography VI. Effects of the Instrumentation and of the Nonideal Retention Behavior on the Retention in Gradient Elution iii




VII. Gradient Elution Method Development VIII. Chromatography with Ternary Gradients IX. Peculiarities of Gradient Elution Separation of High-Molecular Compounds X. Conclusion Acknowledgments Symbols References Appendix A Appendix B 2. Supercritical Fluids for Off-Line Sample Preparation in Food Analysis Prior to Chromatography Jerry W. King



Supercritical Fluids for Sample Preparation Supercritical Fluid Extraction (SFE) Integration of Cleanup Step with SFE Coupling Reaction Chemistry (Derivatization) with SFE V. Applications of Critical Fluids for Sample Preparation VI. Status of the Technique—Conclusions References Appendix A

3. Correspondence Between Chromatography, Single-Molecule Dynamics, and Equilibrium: A Stochastic Approach Francesco Dondi, Alberto Cavazzini, and Michel Martin I. II. III. IV.

Summary Introduction The Stochastic Approach of Chromatography Peak Shape Features and Experimental Errors in the Determination of the Retention Factor V. Equilibrium Conditions in Chromatography VI. Discussion





VII. Conclusion Acknowledgments Glossary References Appendix A Appendix B Appendix C Appendix D Appendix E 4. Solid-Phase Microextraction: A New Tool in Contemporary Bioanalysis Georgios Theodoridis and Gerhardus J. de Jong I. II. III. IV. V. VI. VII.


Introduction Extraction Mode and Coupling Sorption Principles and Parameters Coatings Derivatization Bioanalytical Applications Possibilities and Limitations of SPME References

5. Polyelectrolytes as Stationary Phases in Liquid Chromatography Lilach Yishai-Aviram and Eli Grushka



Introduction The Principle of Dynamic Coating Column Characterization Positively Charged Polyelectrolytes as Stationary Phases V. Negatively Charged Polyelectrolytes as Stationary Phases VI. Complex Polyelectrolyte Layering References




Alberto Cavazzini University of Ferrara, Ferrara, Italy Francesco Dondi University of Ferrara, Ferrara, Italy Eli Grushka Department of Inorganic and Analytical Chemistry, The Hebrew University, Jerusalem, Israel Pavel Jandera University of Pardubice, Na´m. Cˇs. legiı´ , Pardubice, Czech Republic Gerhardus J. de Jong University Utrecht, Utrecht, The Netherlands Jerry W. King Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A. Michel Martin Ecole Supe´rieure de Physique et de Chimie Industrielles, Paris Cedex, France Georgios Theodoridis Aristotle University Thessaloniki, Thessaloniki, Greece Lilach Yishai-Aviram Department of Inorganic and Analytical Chemistry, The Hebrew University, Jerusalem, Israel vii

Contents of Other Volumes

Volumes 1–6

out of print

Volume 7 Theory and Mechanics of Gel Permeation Chromatography K. H. Altgelt Thin-Layer Chromatography of Nucleic Acid Bases, Nucleosides, Nucleotides, and Related Compounds Gyo¨rgy Pataki Review of Current and Future Trends in Paper Chromatography V. C. Weaver Chromatography of Inorganic Ions G. Nickless Process Control by Gas Chromatography I. G. McWilliam Pyrolysis Gas Chromatography of Involatile Substances S. G. Perry Labeling by Exchange on Chromatographic Columns Horst Elias Volume 8 Principles of Gel Chromatography Helmut Determann Thermodynamics of Liquid–Liquid Partition Chromatography David C. Locke ix



Contents of Other Volumes

Determination of Optimum Solvent Systems for Countercurrent Distribution and Column Partition Chromatography from Paper Chromatographic Data Edward Soczewin´ski Some Procedures for the Chromatography of the Fat-Soluble Chloroplast Pigments Harold H. Strain and Walter A. Svec Comparison of the Performance of the Various Column Types Used in Gas Chromatography Georges Guiochon Pressure (Flow) Programming in Gas Chromatography Leslie S. Ettre, La´szlo´ Ma´zor, and Jo´sef Taka´cs Gas Chromatographic Analysis of Vehicular Exhaust Emissions Basil Dimitriades, C. G. Ellis, and D. E. Seizinger The Study of Reaction Kinetics by the Distortion of Chromatographic Elution Peaks Maarten van Swaay Volume 9 Reversed-Phase Extraction Chomatography in Inorganic Chemistry E. Cerrai and G. Ghersini Determination of the Optimum Conditions to Effect a Separation by Gas Chromatography R. P. W. Scott Advances in the Technology of Lightly Loaded Glass Bead Columns Charles Hista, Joseph Bomstein, and W. D. Cooke Radiochemical Separations and Analyses by Gas Chromatography Stuart P. Cram Analysis of Volatile Flavor Components of Foods Phillip Issenberg and Irwin Hornstein Volume 10

out of print

Volume 11 Quantitative Analysis by Gas Chromatography Josef Nova´k Polyamide Layer Chromatography Kung-Tsung Wang, Yau-Tang Lin, and Iris S. Y. Wang Specifically Adsorbing Silica Gels H. Bartels and P. Prijs Nondestructive Detection Methods in Paper and Thin-Layer Chromatography G. C. Barrett

Contents of Other Volumes



Volume 12 The Use of High-Pressure Liquid Chromatography in Pharmacology and Toxicology Phyllis R. Brown Chromatographic Separation and Molecular-Weight Distributions in Cellulose and Its Derivatives Leon Segal Practical Methods of High-Speed Liquid Chromatography Gary J. Fallick Measurement of Diffusion Coefficients by Gas-Chromatography Broadening Techniques: A Review Virgil R. Maynard and Eli Grushka Gas-Chromatography Analysis of Polychlorinated Diphenyls and Other Nonpesticide Organic Pollutants Joseph Sherma High-Performance Electrometer Systems for Gas Chromatography Douglas H. Smith Steam Carrier Gas–Solid Chromatography Akira Nonaka

Volume 13

out of print

Volume 14 Nutrition: An Inviting Field to High-Pressure Liquid Chromatography Andrew J. Clifford Polyelectrolyte Effects in Gel Chromatography Bengt Stenlund Chemically Bonded Phases in Chromatography Imrich Sebestian and Istva´n Hala´sz Physicochemical Measurement Using Chromatography David C. Locke Gas–Liquid Chromatography in Drug Analysis W. J. A. VandenHeuvel and A. G. Zacchei The Investigation of Complex Association by Gas Chromatography and Related Chromatographic and Electrophoretic Methods C. L. de Ligny Gas–Liquid–Solid Chromatography Antonio De Corcia and Arnaldo Liberti Retention Indices in Gas Chromatography J. K. Haken



Contents of Other Volumes

Volume 15 Detection of Bacterial Metabolites in Spent Culture Media and Body Fluids by Electron Capture Gas–Liquid Chromatography John B. Brooks Signal and Resolution Enhancement Techniques in Chromatography Raymond Annino The Analysis of Organic Water Pollutants by Gas Chromatography and Gas Chromatography–Mass Spectrometry Ronald A. Hites Hydrodynamic Chromatography and Flow-Induced Separations Hamish Small The Determination of Anticonvulsants in Biological Samples by Use of High-Pressure Liquid Chromatography Reginald F. Adams The Use of Microparticulate Reversed-Phase Packing in High-Pressure Liquid Chromatography of Compounds of Biological Interest John A. Montgomery, Thomas P. Johnson, H. Jeanette Thomas, James R. Piper, and Caroll Temple Jr. Gas–Chromatographic Analysis of the Soil Atmosphere K. A. Smith Kinematics of Gel Permeation Chromatography A. C. Ouano Some Clinical and Pharmacological Applications of High-Speed Liquid Chromatography J. Arly Nelson Volume 16

out of print

Volume 17 Progress in Photometric Methods of Quantitative Evaluation in TLO V. Pollak Ion-Exchange Packings for HPLC Separations: Care and Use Fredric M. Rabel Micropacked Columns in Gas Chromatography: An Evaluation C. A. Cramers and J. A. Rijks Reversed-Phase Gas Chromatography and Emulsifier Characterization J. K. Haken Template Chromatography Herbert Schott and Ernst Bayer Recent Usage of Liquid Crystal Stationary Phases in Gas Chromatography George M. Janini Current State of the Art in the Analysis of Catecholamines Ante´ M. Krstulovic

Contents of Other Volumes



Volume 18 The Characterization of Long-Chain Fatty Acids and Their Derivatives by Chromatography Marcel S. F. Lie Ken Jie Ion-Pair Chromatography on Normal- and Reversed-Phase Systems Milton T. W. Hearn Current State of the Art in HPLC Analyses of Free Nucleotides, Nucleosides, and Bases in Biological Fluids Phyllis R. Brown, Ante´ M. Krstulovic, and Richard A. Hartwick Resolution of Racemates by Ligand-Exchange Chromatography Vadim A. Danakov The Analysis of Marijuana Cannabinoids and Their Metabolites in Biological Media by GC and/or GC-MS Techniques Benjamin J. Gudzinowicz, Michael J. Gudzinowicz, Joanne Hologgitas, and James L. Driscoll

Volume 19 Roles of High-Performance Liquid Chromatography in Nuclear Medicine Steven How-Yan Wong Calibration of Separation Systems in Gel Permeation Chromatography for Polymer Characterization Josef Janc˘a Isomer-Specific Assay of 2,4-D Herbicide Products by HPLC: Regulaboratory Methodology Timothy S. Stevens Hydrophobic Interaction Chromatography Stellan Hjerte´n Liquid Chromatography with Programmed Composition of the Mobile Phase Pavel Jandera and Jaroslav Chura´cˇek Chromatographic Separation of Aldosterone and Its Metabolites David J. Morris and Ritsuko Tsai

Volume 20 High-Performance Liquid Chromatography and Its Application to Protein Chemistry Milton T. W. Hearn Chromatography of Vitamin D3 and Metabolites K. Thomas Koshy High-Performance Liquid Chromatography: Applications in a Children’s Hospital Steven J. Soldin



Contents of Other Volumes

The Silica Gel Surface and Its Interactions with Solvent and Solute in Liquid Chromatography R. P. W. Scott New Developments in Capillary Columns for Gas Chromatography Walter Jennings Analysis of Fundamental Obstacles to the Size Exclusion Chromatography of Polymers of Ultrahigh Molecular Weight J. Calvin Giddings

Volume 21 High-Performance Liquid Chromatography/ Mass Spectrometry (HPLC/MS) David E. Grimes High-Performance Liquid Affinity Chromatography Per-Olof Larsson, Magnus Glad, Lennart Hansson, Mats-Olle Ma˚nsson, Sten Ohlson, and Klaus Mosbach Dynamic Anion-Exchange Chromatography Roger H. A. Sorel and Abram Holshoff Capillary Columns in Liquid Chromatography Daido Ishii and Toyohide Takeuchi Droplet Counter-Current Chromatography Kurt Hostettmann Chromatographic Determination of Copolymer Composition Sadao Mori High-Performance Liquid Chromatography of K Vitamins and Their Antagonists Martin J. Shearer Problems of Quantitation in Trace Analysis by Gas Chromatograhpy Josef Nova´k

Volume 22 High-Performance Liquid Chromatography and Mass Spectrometry of Neuropeptides in Biologic Tissue Dominic M. Desiderio High-Performance Liquid Chromatography of Amino Acids: Ion-Exchange and Reversed-Phase Strategies Robert F. Pfeifer and Dennis W. Hill Resolution of Racemates by High-Performance Liquid Chromatography Vadium A. Davankov, Alexander A. Kurganov, and Alexander S. Bochkov

Contents of Other Volumes



High-Performance Liquid Chromatography of Metal Complexes Hans Veening and Bennett R. Willeford Chromatography of Carotenoids and Retinoids Richard F. Taylor High-Performance Liquid Chromatography Zybslaw J. Petryka Small-Bore Columns in Liquid Chromatography Raymond P. W. Scott

Volume 23 Laser Spectroscopic Methods for Detection in Liquid Chromatography Edward S. Yeung Low-Temperature High-Performance Liquid Chromatography for Separation of Thermally Labile Species David E. Henderson and Daniel J. O’Connor Kinetic Analyis of Enzymatic Reactions Using High-Performance Liquid Chromatography Donald L. Sloan Heparin-Sepharose Affinity Chromatography Akhlaq A. Farooqui and Lloyd A. Horrocks New Developments in Capillary Columns for Gas Chomatography Walter Jennings

Volume 24 Some Basic Statistical Methods for Chromatographic Data Karen Kafadar and Keith R. Eberhardt Multifactor Optimization of HPLC Conditions Stanley N. Deming, Julie G. Bower, and Keith D. Bower Statistical and Graphical Methods of Isocratic Solvent Selection for Optimal Separation in Liquid Chromatography Haleem J. Issaq Electrochemical Detectors for Liquid Chromatography Ante M. Krstolovic´, Henri Colin, and Georges A. Guichon Reversed-Flow Gas Chromatography Applied to Physicochemical Measurements Nicholas A. Katsanos and George Karaiskakis Development of High-Speed Countercurrent Chromatography Yochiro Ito Determination of the Solubility of Gases in Liquids by Gas–Liquid Chromatography John F. Parcher, Monica L. Bell, and Ping L. Jin



Contents of Other Volumes

Multiple Detection in Gas Chromatography Ira S. Krull, Michael E. Swartz, and John N. Driscoll

Volume 25 Estimation of Physicochemical Properties of Organic Solutes Using HPLC Retention Parameters Theo L. Hafkenscheid and Eric Tomlinson Mobile Phase Optimization in RPLC by an Iterative Regression Design Leo de Galan and Hugo A. H. Billiet Solvent Elimination Techniques for HPLC/FT-IR of Polycyclic Aromatic Hydrocarbons Lane C. Sander and Stephen A. Wise Liquid Chromatographic Analysis of the Oxo Acids of Phosphorus Roswitha S. Ramsey Liquid Chromatography of Carbohydrates Toshihiko Hanai HPLC Analysis of Oxypurines and Related Compounds Katsuyuki Nakano HPLC of Glycosphingolipids and Phospholipids Robert H. McCluer, M. David Ullman, and Firoze B. Jungalwala

Volume 26 RPLC Retention of Sulfur and Compounds Containing Divalent Sulfur Hermann J. Mo¨ckel The Application of Fleuric Devices to Gas Chromatographic Instrumentation Raymond Annino High Performance Hydrophobic Interaction Chromatography Yoshio Kato HPLC for Therapeutic Drug Monitoring and Determination of Toxicity Ian D. Watson Element Selective Plasma Emission Detectors for Gas Chromatography A. H. Mohamad and J. A. Caruso The Use of Retention Data from Capillary GC for Qualitative Analysis: Current Aspects Lars G. Blomberg Retention Indices in Reversed-Phase HPLC Roger M. Smith HPLC of Neurotransmitters and Their Metabolites Emilio Gelpi

Contents of Other Volumes



Volume 27 Physicochemical and Analytical Aspects of the Adsorption Phenomena Involved in GLC Victor G. Berezkin HPLC in Endocrinology Richard L. Patience and Elizabeth S. Penny Chiral Stationary Phases for the Direct LC Separation of Enantiomers William H. Pirkle and Thomas C. Pochapsky The Use of Modified Silica Gels in TLC and HPTLC Willi Jost and Heinz E. Hauck Micellar Liquid Chromatography John G. Dorsey Derivation in Liquid Chromatography Kazuhiro Imai Analytical High-Performance Affinity Chromatography Georgio Fassina and Irwin M. Chaiken Characterization of Unsaturated Aliphatic Compounds by GC/Mass Spectrometry Lawrence R. Hogge and Jocelyn G. Millar Volume 28 Theoretical Aspects of Quantitative Affinity Chromatography: An Overview Alain Jaulmes and Claire Vidal-Madjar Column Switching in Gas Chromatography Donald E. Willis The Use and Properties of Mixed Stationary Phases in Gas Chromatography Gareth J. Price On-line Small-Bore-Chromatography for Neurochemical Analysis in the Brain William H. Church and Joseph B. Justice, Jr. The Use of Dynamically Modified Silica in HPLC as an Alternative to Chemically Bonded Materials Per Helboe, Steen Honore´ Hansen, and Mogens Thomsen Gas Chromatographic Analysis of Plasma Lipids Arnis Kuksis and John J. Myher HPLC of Penicillin Antibiotics Michel Margosis Volume 29 Capillary Electrophoresis Ross A. Willingford and Andrew G. Ewing Multidimensional Chromatography in Biotechnology Daniel F. Samain



Contents of Other Volumes

High-Performance Immunoaffinity Chromatography Terry M. Phillips Protein Purification by Multidimensional Chromatography Stephen A. Berkowitz Fluorescence Derivitization in High-Performance Liquid Chromatography Yosuke Ohkura and Hitoshi Nohta

Volume 30 Mobile and Stationary Phases for Supercritical Fluid Chromatography Peter J. Schoenmakers and Luis G. M. Uunk Polymer-Based Packing Materials for Reversed-Phase Liquid Chromatography Nobuo Tanaka and Mikio Araki Retention Behavior of Large Polycyclic Aromatic Hydrocarbons in Reversed-Phase Liquid Chromatography Kiyokatsu Jinno Miniaturization in High-Performance Liquid Chromatography Masashi Goto, Toyohide Takeuchi, and Daido Ishii Sources of Errors in the Densitometric Evaluation of Thin-Layer Separations with Special Regard to Nonlinear Problems Victor A. Pollak Electronic Scanning for the Densitometric Analysis of Flat-Bed Separations Viktor A. Pollak

Volume 31 Fundamentals of Nonlinear Chromatography: Prediction of Experimental Profiles and Band Separation Anita M. Katti and Georges A. Guiochon Problems in Aqueous Size Exclusion Chromatography Paul L. Dubin Chromatography on Thin Layers Impregnated with Organic Stationary Phases Jiri Gasparic Countercurrent Chromatography for the Purification of Peptides Martha Knight Boronate Affinity Chromatography Ram P. Singhal and S. Shymali M. DeSilva Chromatographic Methods for Determining Carcinogenic Benz(c)-acridine Noboru Motohashi, Kunihiro Kamata, and Roger Meyer

Contents of Other Volumes



Volume 32 Porous Graphitic Carbon in Biomedical Applications Chang-Kee Lim Tryptic Mapping by Reversed Phase Liquid Chromatography Michael W. Dong Determination of Dissolved Gases in Water by Gas Chromatography Kevin Robards, Vincent R. Kelly, and Emilios Patsalides Separation of Polar Lipid Classes into Their Molecular Species Components by Planar and Column Liquid Chromatography V. P. Pchelkin and A. G. Vereshchagin The Use of Chromatography in Forensic Science Jack Hubball HPLC of Explosives Materials John B. F. Lloyd Volume 33 Planar Chips Technology of Separation Systems: A Developing Perspective in Chemical Monitoring Andreas Manz, D. Jed Harrison, Elizabeth Verpoorte, and H. Michael Widmer Molecular Biochromatography: An Approach to the Liquid Chromatographic Determination of Ligand-Biopolymer Interactions Irving W. Wainer and Terence A. G. Noctor Expert Systems in Chromatography Thierry Hamoir and D. Luc Massart Information Potential of Chromatographic Data for Pharmacological Classification and Drug Design Roman Kaliszan Fusion Reaction Chromatography: A Powerful Analytical Technique for Condensation Polymers John K. Haken The Role of Enatioselective Liquid Chromatographic Separations Using Chiral Stationary Phases in Pharmaceutical Analysis Shulamit Levin and Saleh Abu-Lafi Volume 34 High-Performance Capillary Electrophoresis of Human Serum and Plasma Proteins Oscar W. Reif, Ralf Lausch, and Ruth Freitag Analysis of Natural Products by Gas Chromatography/Matrix Isolation/Infrared Spectrometry W. M. Coleman III and Bert M. Gordon



Contents of Other Volumes

Statistical Theories of Peak Overlap in Chromatography Joe M. Davis Capillary Electrophoresis of Carbohydrates Ziad El Rassi Environmental Applications of Supercritical Fluid Chromatography Leah J. Mulcahey, Christine L. Rankin, and Mary Ellen P. McNally HPLC of Homologous Series of Simple Organic Anions and Cations Norman E. Hoffman Uncertainty Structure, Information Theory, and Optimization of Quantitative Analysis in Separation Science Yuzuru Hayashi and Rieko Matsuda

Volume 35 Optical Detectors for Capillary Electrophoresis Edward S. Yeung Capillary Electrophoresis Coupled with Mass Spectrometry Kenneth B. Tomer, Leesa J. Deterding, and Carol E. Parker Approaches for the Optimization of Experimental Parameters in Capillary Zone Electrophoresis Haleem J. Issaq, George M. Janini, King C. Chan, and Ziad El Rassi Crawling Out of the Chiral Pool: The Evolution of Pirkle-Type Chiral Stationary Phases Christopher J. Welch Pharmaceutical Analysis by Capillary Electrophoresis Sam F. Y. Li, Choon Lan Ng, and Chye Pend Ong Chromatographic Characterization of Gasolines Richard E. Pauls Reversed-Phase Ion-Pair and Ion-Interaction Chromatography M. C. Gennaro Error Sources in the Determination of Chromatographic Peak Size Ratios Veronika R. Meyer

Volume 36 Use of Multivariate Mathematical Methods for the Evaluation of Retention Data Matrices Tibor Cserha´ti and Esther Forga´cs Separation of Fullerenes by Liquid Chromatography: Molecular Recognition Mechanism in Liquid Chromatographic Separation Kiyokatsu Jinno and Yoshihiro Saito

Contents of Other Volumes



Emerging Technologies for Sequencing Antisense Oligonucleotides: Capillary Electrophoresis and Mass Spectrometry Aharon S. Cohen, David L. Smisek, and Bing H. Wang Capillary Electrophoretic Analysis of Glycoproteins and Glycoprotein-Derived Oligosaccharides Robert P. Oda, Benjamin J. Madden, and James P. Landers Analysis of Drugs of Abuse in Biological Fluids by Liquid Chromatography Steven R. Binder Electrochemical Detection of Biomolecules in Liquid Chromatography and Capillary Electrophoresis Jian-Ge Chen, Steven J. Woltman, and Steven G. Weber The Development and Application of Coupled HPLC-NMR Spectroscopy John C. Lindon, Jeremy K. Nicholson, and Ian D. Wilson Microdialysis Sampling for Pharmacological Studies: HPLC and CE Analysis Susan M. Lunte and Craig E. Lunte Volume 37 Assessment of Chromatographic Peak Purity Muhammad A. Sharaf Fluorescence Detectors in HPLC Maria Brak Smalley and Linda B. McGown Carbon-Based Packing Materials for Liquid Chromatography: Structure, Perfomance, and Retention Mechanisms John H. Knox and Paul Ross Carbon-Based Packing Materials for Liquid Chromatography: Applications Paul Ross and John H. Knox Directly Coupled (On-Line) SFE-GC: Instrumentation and Applications Mark D. Burford, Steven B. Hawthorne, and Keith D. Bartle Sample Preparation for Gas Chromatography with Solid-Phase Extraction and Solid-Phase Microextraction Zelda E. Penton Capillary Electrophoresis of Proteins Tim Wehr, Robert RodriguezDiaz, and Cheng-Ming Liu Chiral Micelle Polymers for Chiral Separations in Capillary Electrophoresis Crystal C. Williams, Shahab A. Shamsi, and Isiah M. Warner Analysis of Derivatized Peptides Using High-Performance Liquid Chromatography and Capillary Electrophoresis Kathryn M. De Antonis and Phyllis R. Brown



Contents of Other Volumes

Volume 38 Band Spreading in Chromatography: A Personal View John H. Knox The Stochastic Theory of Chromatography Francesco Dondi, Alberto Cavazzini, and Maurizio Remelli Solvating Gas Chromatography Using Packed Capillary Columns Yufeng Shen and Milton L. Lee The Linear-Solvent-Strength Model of Gradient Elution L. R. Snyder and J. W. Dolan High-Performance Liquid Chromatography-Pulsed Electrochemical Detection for the Analysis of Antibiotics William R. LaCourse and Catherine O. Dasenbrock Theory of Capillary Zone Electrophoresis H. Poppe Separation of DNA by Capillary Electrophoresis Andra´s Guttman and Kathi J. Ulfelder Volume 39 Theory of Field Flow Fractionation Michel Martin Particle Simulation Methods in Separation Science Mark R. Schure Mathematical Analysis of Multicomponent Chromatograms Attila Felinger Determination of Association Constants by Chromatography and Electrophoresis Daniel W. Armstrong Method Development and Selectivity Optimization in High-Performance Liquid Chromatography H. A. H. Billet and G. Rippel Chemical Equilibria in Ion Chromatography: Theory and Applications Pe´ter Hajo´s, Otto´ Horva´th, and Gabriella Re´ve´sz Fundamentals and Simulated Moving Bed Chromatography Under Linear Conditions Guoming Zhong and Georeges Guiochon Volume 40 Fundamental Interpretation of the Peak Profiles in Linear ReversedPhase Liquid Chromatography Kanji Miyabe and Georges Guiochon Dispersion in Micellar Electrokinetic Chromatography Joe M. Davis

Contents of Other Volumes



In Search of a Chromatographic Model for Biopartitioning Colin F. Poole, Salwa K. Poole, and Ajith D. Gunatilleka Advances in Physico-chemical Measurements Using Inverse Gas Chromatography Nicholas A. Katsanos and Fani Roubani-Kalantzopoulou Fundamental Aspects of Aerosol-Based Light-Scattering Detectors for Separations John A. Koropchak, Salma Sadain, Xiaohui Yang, Lars-Erik Magnusson, Mari Heybroek, and Michael P. Anisimov New Developments in Liquid-Chromatographic Stationary Phases Toshiko Hanai Non-Silica-Based Supports in Liquid Chromatography of Bioactive Compounds Esther Forga´cs and Tibor Cserha´ti Overview of the Surface Modification Techniques for the Capillary Electrophoresis of Proteins Marie-Claude Millot and Claire Vidal-Madjar Continuous Bed for Conventional Column and Capillary Column Chromatography Jia-li Liao Countercurrent Chromatography: Fundamentally a Preparative Tool Alain Berthod and Beatrice Billardello Analysis of Oligonucleotides by ESI-MS Dieter L. Deforce and Elfriede G. Van den Eeckhout Determination of Herbicides in Water Using HPLC-MS Techniques G. D’Ascenzo, F. Bruno, A. Gentili, S. Marchese, and D. Perret Effect of Adsorption Phenomena on Retention Values in Capillary Gas–Liquid Chromatography Victor G. Berezkin Volume 41 Fundamentals of Capillary Electrochromatography Ute Pyell Membrane Extraction Techniques for Sample Preparation Jan A˚ke Jo¨nsson and Lennart Mathiasson Design of Rapid Gradient Methods for the Analysis of Combinatorial Chemistry Libraries and the Preparation of Pure Compounds Uwe D. Neue, Judy L. Carmody, Yung-Fong Cheng, Ziling Lu, Charles H. Phoebe, and Thomas E. Wheat Molecularly Imprinted Extraction Materials of Highly Selective Sample Clean-Up and Analyte Enrichment Francesca Lanza and Bo¨rje Sellergren



Contents of Other Volumes

Biomembrane Chromatography: Application to Purification and Biomolecule-Membrane Interactions Tzong-Hsien Lee and Marie-Isabel Aguilar Transformation of Analytes for Electrochemical Detection: A Review of Chemical and Physical Approaches Mark J. Rose, Susan M. Lunte, Robert G. Carlson, and John F. Stobaugh High-Performance Liquid Chromatography: Trace Metal Determination and Speciation Corrado Sarzanini Temperature-Responsive Chromatography Hideko Kanazawa, Yoshikazu Matsushima, and Teruo Okano Carrier Gas in Capillary Gas–Liquid Chromatography V. G. Berezkin Cathechins in Tea: Chemistry and Analysis Christina S. Robb and Phyllis R. Brown Volume 42 Chemometric Analysis of Comprehensive Two-Dimensional Separations Robert E. Synovec, Bryan J. Prazen, Kevin J. Johnson, Carlos G. Fraga, and Carsten A. Bruckner Column Technology for Capillary Electrochromatography Luis A. Colo´n, Todd D. Maloney, Jason Anspach, and He´ctor Colo´n Gas Chromatography with Inductively Coupled Plasma Mass Spectrometric Detection (GP-ICP MS) Brice Bouyssiere, Joanna Szpunar, Gae¨tne Lespes, and Ryszard Lobinski GC-MS Analysis of Halocarbons in the Environment Filippo Mangani, Michela Maione, and Pierangela Palma Microfluidics for Ultrasmall-Volume Biological Analysis Todd O. Windman, Barb J. Wyatt, and Mark A. Hayes Recent Trends in Proteome Analysis Pier Giorgio Righetti, Annalisa Castagna, and Mahmoud Hamdan Improving Our Understanding of Reversed-Phase Separations for the 21st Century Patrick D. McDonald Clinical Applications of High-Performance Affinity Chromatography David S. Hage

1 Gradient Elution in Liquid Column Chromatography—Prediction of Retention and Optimization of Separation ˇ legii,´ Pardubice, Pavel Jandera University of Pardubice, Na´m. Cs. Czech Republic


3 9 9 17 19 25 34


2 / Jandera VI. EFFECTS OF THE INSTRUMENTATION AND OF THE NONIDEAL RETENTION BEHAVIOR ON THE RETENTION IN GRADIENT ELUTION A. Effects of the dwell volume on retention in gradient elution LC. Retention data in gradient elution with an initial hold-up period. Gradient preelution and postelution B. Effects of the adsorption of strong solvents on retention VII. GRADIENT ELUTION METHOD DEVELOPMENT A. Transfer of gradient methods and effects of changing operating conditions on separation 1. Changing flow rate of the mobile phase in gradient elution chromatography 2. Changing column diameter in gradient elution chromatography 3. Changing column length in gradient elution chromatography 4. Rapid prediction of the effects of changing gradient steepness (gradient range) and initial mobile phase composition on the separation B. Optimization of gradient elution separations 1. Peak capacity and fast gradients 2. Optimization of gradients for specific separation problems VIII. CHROMATOGRAPHY WITH TERNARY GRADIENTS IX. PECULIARITIES OF GRADIENT ELUTION SEPARATION OF HIGH-MOLECULAR COMPOUNDS X. CONCLUSION ACKNOWLEDGMENTS SYMBOLS REFERENCES APPENDIX A. Correction of the retention volume in normal-phase HPLC for the column uptake of polar solvents


37 48 55 56 58 59 61

62 69 69 71 78

81 90 90 92 96

Gradient Elution in LC Chromatography during gradient elution (solventdemixing effect) APPENDIX B. Schematics of a spreadsheet program for optimization of gradient elution



104 107

I. INTRODUCTION Many complex samples contain compounds that differ widely in retention, so that HPLC in isocratic elution mode with a mobile phase of fixed composition often does not yield successful separation of the individual solutes. To keep the time of analysis within acceptable limits, the retention factors of the most strongly retained sample components, k, usually should be lower than 10. Once the appropriate chromatographic column is selected, the retention can be controlled by setting appropriate flow rate, column temperature and—most efficiently—the composition of the mobile phase. In the isocratic elution mode, the working conditions are kept constant during the separation run and in many cases satisfactory results are obtained. However, for some complex samples weakly retained compounds elute as poorly—if at all—separated bands close to the column holdup time under the conditions adjusted for adequate retention of strongly retained solutes (Fig. 1A). On the other hand, with the mobile phase adjusted to achieve desired resolution of weakly retained compounds, the elution of strongly retained sample components can be slow, their peaks are broad and their concentration in the eluate may even fall down below the detection limits (Fig. 1B). To obtain satisfactory separation of both weakly and strongly retained sample compounds, the operating conditions controlling the retention should be varied during the chromatographic run [1–5]. This can be achieved by gradually increasing the temperature, the flow rate or the elution strength of the mobile phase (as in Fig. 1C). Flow programming in HPLC is limited by maximum operation pressure, usually 30–40 MPa, and has little advantage when smallparticle packed columns are used. Although recently introduced monolithic columns are more suitable for the programmed flow rate operation because of their lower flow resistance [6], the retention factors are independent of the flow rate, hence the improvement of separation is only marginal in comparison with techniques relying on gradual decreasing of the retention factors during the analysis. The

4 / Jandera

Fig. 1 Reversed-phase separation of 1,2-naphthoylenebenzimidazole alkylsulphonamides. Column: Lichrosorb RP-18, 10 Am (300  4 mm i.d.). Mobile phase: (A) 80% methanol in water, (B) 95 methanol in water, (C) linear gradient, 70–100% methanol in 20 min, 1 mL/min. Numbers of the peaks agree with the numbers of carbon atoms in the alkyls.

resolution can be improved by using simultaneous gradient elution and flow programming [7]. The retention in HPLC usually decreases with increasing temperature, but temperature programming is rarely used in conventional HPLC, in contrast to gas chromatography. One reason is a relatively slow response of the temperature inside the conventional

Gradient Elution in LC Chromatography



columns to a change in the temperature setting in an air-heated thermostated compartment, which might cause poor retention data reproducibility in short analyses requiring a steep temperature ramp. This limitation does not concern packed capillary HPLC columns with rapid radial heat transfer [8,9]. Further, some HPLC packing materials are not stable enough at elevated temperatures. A large rise in temperature during the run is usually needed to reduce significantly the retention of strongly retained small molecules. Hence, the temperature programming can offer results comparable to gradient elution over a relatively narrow range of the elution strength [10]. Only moderate change in the elution strength in the course of separation is usually sufficient for the separation or fractionation of large molecules such as synthetic polymer samples, where temperature programming offers promising alternative to gradient elution technique [11]. Anyway, potential merits of temperature programming in HPLC are still to be proven. On the other hand, simultaneous optimization of the temperature and of the gradient time in gradient-elution HPLC offers interesting possibilities for the separation of complex samples [12–16]. Gradient elution still remains the most widely used programming technique in liquid chromatography, since its introduction in 1952 [17–19]. Gradual increase in the elution strength of the mobile phase allows decreasing the retention factors of small molecules by two to three orders of magnitude in a single gradient run, which results in shorter separation time, increased peak capacity and more regular band spacing of compounds with large differences in affinities to the stationary phase with respect to isocratic separation. The instrumentation for gradient elution is more sophisticated and more expensive than in isocratic liquid chromatography, as two or more components of the mobile phase should be accurately mixed according to a preset time program. Binary gradients are formed by mixing two mobile phase components: the concentration of a strong solvent B with a higher elution strength in a weak solvent A with a lower elution strength increases during the gradient run. Binary gradients are used more frequently than ternary gradients prepared from three mobile phase components, whereas quaternary or more complex gradients are rarely necessary for optimum separation performance. The gradient program can be composed of a few subsequent isocratic steps, or the composition of the mobile phase can be changed continuously during the gradient run. It is also possible to employ gradients composed of several continuous steps with different slopes,

6 / Jandera if necessary combined with isocratic hold-up steps. The profile of a continuous gradient is characterized by three adjustable parameters: 1) the gradient range (i.e., the initial and the final concentrations of the solvent B); 2) the steepness (i.e., the gradient time); and 3) the shape (curvature), which all affect the elution time and the spacing of the peaks in the chromatogram and should be taken into account in the development of gradient separations. According to the shape, gradients can be classified as linear (the most common), convex, or concave. A few examples of various linear, concave, and convex gradient profiles are shown in Fig. 2. Because of a higher number of experimental variables that should be taken into account, the development of gradient elution methods is more complicated than the development of isocratic methods and the retention behavior is more difficult to describe in quantitative terms. Column dimensions and the flow rate of the mobile phase affect the retention in gradient elution in a more complex way than the isocratic retention. The effective use of gradient elution technique is easier if the theoretical principles of gradient elution are well understood.

Fig. 2 Examples of linear, concave, and convex gradients from 0% to 100% stronger eluent, B. c—concentration of B, V—volume of the eluate from the start of the gradient with various values of the gradient shape parameter j (Eq. (7)). j = 1 for linear, j > 1 for concave, and j < 1 for convex gradients.

Gradient Elution in LC Chromatography



The actual impact of the gradient program on the separation of the sample depends on the effect of the mobile phase composition on the retention in the HPLC mode used (conveniently characterized by isocratic retention factors, k). To describe the retention in gradientelution chromatography, the dependence of the instantaneous retention factors on the gradient program should be known. For this purpose, either an equation based on more or less exact retention model or merely an empirical equation can be used, as far as it describes accurately enough the experimental data. Snyder [20,21] developed a widely used theory of linear solvent strength (LSS) binary gradients assuming linear change in the logarithms of retention factors, k, with the time, t, elapsed from the start of the gradient run: log k ¼ log ka  bs

t tm


Here, ka is the value of k at the start of the gradient, t = 0, tm is the column hold-up time, and bs is a measure of the gradient steepness. The LSS theory facilitates the comparison of the retention behavior in isocratic chromatography and in gradient elution chromatography, but it is not always straightforward to preset an exact LSS gradient program in real chromatographic systems. Most easy to employ are linear concentration gradients, which correspond to LSS gradients in the chromatographic systems where the isocratic retention can be described by a simple retention equation—Eq. (2). The LSS gradients are often (but not always) reasonably well approximated in reversedphase (RP) chromatography where the gradient elution is applied most frequently [22–25]: log k ¼ a  Su


Here, the constant a is the extrapolated (not necessarily the real) value of the logarithm of the retention factor in pure weak solvent A (water in RP systems) and the constant S is a measure of the solvent strength of the strong solvent B contained in concentration u in a binary mobile phase. The gradient steepness in LSS gradients is defined as: bs ¼

t0 SDu Vm SDu ¼ tG tG F m


where tG is the gradient time corresponding to the change Du from the start to the end of gradient elution, Vm is the column hold-up

8 / Jandera volume, and Fm is the flow rate of the mobile phase. In other HPLC modes, i.e., in ion-exchange and in normal-phase liquid chromatography, Eq. (2) can be used only over a narrow range of mobile phase concentrations and the utility of the LSS model is limited [26]. Stout et al. [27] and other workers [28] advocated applicability of the empirically corrected LSS model for gradient-elution separations of multiply charged proteins. Recently, Snyder and Dolan published an excellent review of the LSS gradient approach [4], hence the LSS approach will not be discussed here in more detail. Gradient elution is often used in ion-exchange chromatography of ionic compounds such as charged biopolymers. Despite being described most early, the applications of gradient elution in normalphase LC (liquid–solid adsorption chromatography) have been so far less frequent than in other LC modes, but they are becoming increasingly popular, especially for the separation of noncharged industrial polymer samples. Whereas reversed-phase gradient elution with aqueous–organic mobile phases provides excellent results for the separation of peptides, proteins, and other biopolymers [29–34], gradient-elution chromatography on nonpolar chemically bonded phases or on polar adsorbents with increasing concentration of a polar organic solvent in a nonpolar one [35–37] often shows better selectivity than RP separations of synthetic nonionic oligomers and polymers containing polar monomer units such as surfactants [38], homopolymers [11,39,40], and copolymers [41–46]. As the range of HPLC phase systems in which gradient elution is applied becomes increasingly broader, accurate approaches are more urgently needed for the prediction and optimization of gradientelution separations in various HPLC modes. Earlier, we reviewed the possibilities of using a general non-LSS approach for various liquid chromatography modes with binary gradients [2,3]. The present review is focused on some more recent developments of the non-LSS gradient elution approach for binary and ternary gradients in various HPLC modes, including reversed-phase, normal-phase, and ion-exchange systems. Prediction and optimization of the retention in gradient elution are discussed together with problems arising from various sources of nonideal behavior and possible ways to suppression or compensation of their impact on the accuracy of the predicted gradient-elution data. Finally, peculiarities of the applications of gradient elution theory to the separation of high-molecular compounds are addressed.

Gradient Elution in LC Chromatography



II. THEORY OF RETENTION IN ANALYTICAL GRADIENT-ELUTION CHROMATOGRAPHY A. Calculation of Retention Times and of Retention Volumes The theory of gradient-elution chromatography is now elaborated to the degree that it allows to predict the gradient-elution behavior of sample compounds from their isocratic retention data (or from two initial gradient experiments) and to optimize the profile of the gradient in various reversed-phase, normal-phase, and ion-exchange systems [2–4]. Two or more initial gradient runs can also be used to estimate the optimum composition of the mobile phase for isocratic separations [26,47–51]. Calculation of the retention in gradientelution chromatography is possible using adequate equations describing the dependence of the retention on the parameters characterizing the profile of the gradient. In isocratic liquid chromatography, the elution times, tR, or volumes, VR, are simply related to the retention factors, k, that remain constant during the separation run, tRtm = tRV = ktm; VRVm = VRV = kVm. This simple relationship cannot be used in gradient elution chromatography, where the retention factors decrease during the run. The band migration velocities change during the separation run and the final elution times depend on the solute and the HPLC phase system which control the relationship between the k and the actual mobile phase composition. Figure 3 shows decreasing instantaneous k of neburon during its migration along the column in 20-min gradients starting at the initial k = 50, both in reversed-phase chromatography (RPC) on a C18 column (a gradient from 57.5% to 100% methanol in water) and in normal-phase chromatography on a silica gel (a gradient from 0.84% to 17% 2-propanol in hexane). The retention data in gradient elution can be described assuming that the gradient elution is represented by the sum of consequent elementary migration steps in which the solute migrates a differential distance along the column corresponding to a differential increment of the column hold-up time d(tm) or column hold-up volume d(Vm). Unlike the isocratic LC, the relationship between the retention factor and the retention volume is defined only for a differential step by differential Eqs. (4a,b). Only during such a differential step can the change in concentration of the strong eluent B in the mobile phase,

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Fig. 3 Examples of changing instantaneous retention factors, ki, of neburon at the fraction distance X from the top of the column migrated by the sample zone during reversed-phase (full line) and normal-phase (dashed line) gradient elution. Gradient volume VG = 20 Vm. RPC: Silasorb C18, 57.5–100% methanol in water, a = 4, m = 4 in Eq. (11), NPC Silasorb silica gel, 0.84– 17% 2-propanol in hexane, k0 = 0.076, m = 1.3 in Eq. (15). l = column length, li = fractional distance from the top of the column at the retention factor ki.

u(V ), be neglected and the retention factors, k, of all sample solutes remain constant. Each elementary step contributes to the final retention time, tR, and retention volume, VR, by the increments d(t) and d(V ), respectively: dðtÞ ¼ kdðtm Þ;

dðV Þ ¼ kdðVmÞ

ð4a; bÞ

Equation (4a,b) can be integrated after introducing the actual dependence of k on the time, t (or on the volume of the eluate, V, passed through the column) from the start of the gradient until the

Gradient Elution in LC Chromatography



elution to yield the expressions for the net gradient-elution retention times, tRV, or volumes, VRV, respectively: ð tR V 0

1 tm

dðtÞ ¼ 1; k

ðV RV 0

1 Vm

dðV Þ ¼1 k

ð5a; bÞ

The approach for the calculation of the gradient-elution retention volumes or times based on the solution of Eq. (5a,b) was first suggested almost 50 years ago [52,53] and since that time this approach has been applied to calculate the retention data in various specific gradient elution separation applications, see the survey in Refs. [2] and [3]. The solution of Eq. (5a,b) is simple for linear solvent strength gradients where log k is a linear function of V and was presented by Snyder et al. [4,26,27]. Theoretically, it should be possible to compensate for any nonlinear dependence of log k on u by designing an appropriate complementary gradient profile, but setting a suitable program for an exactly linear change in log k during the gradient elution can be impractically tedious and often is not feasible with many commercial instruments. An easier approach, which can be used for a great variety of combinations of gradient programs and chromatographic phase systems, divides the function characterizing changes in k with increasing V (or t) into two partial contributions [2,3,54] 1. The retention function describes the dependence of k on the concentration of the strong eluent B in the mobile phase, u, controlled by the thermodynamics of the distribution process of a sample solute, which differs in various reversed-phase, normal-phase, and ionexchange chromatographic systems [the retention equation k = f V(u)]. 2. The gradient function u = f(V ) controls the gradient profile (the change in u with time t or with the volume V of the eluate) and is adjusted by the operator. To avoid confusion, it is important to fix the time (place), which corresponds to the actual mobile phase composition described by the gradient function—at the time the mobile phase components are mixed in a low-pressure or high-pressure part of gradient chromatograph, or at the time the peaks leave the column and are detected. The first option is more practical as it corresponds directly to the gradient program set by the operator and is therefore consequently used in this work. On the other hand, the second possibility corresponds better to the effect of the gradient on the

12 / Jandera retention behavior of the individual compounds, and it should be kept in mind that the actual gradient composition at the detector corresponds to the composition at the outlet from the gradient mixer before the time elapsed necessary for the mobile phase to migrate to the top of the column (the gradient dwell volume) and through the column (the column hold-up volume). This gradient delay can be respected in the calculation of the retention data, as shown in Sections III–VI. Linear concentration gradients are employed most frequently because they are most simple to understand and can be generated in all modern gradient-elution instruments. However, in some cases curved gradients may yield better separation and more regular band spacing by increasing the resolution in the shallower parts of the gradient and speeding up the elution of the bands in the steeper parts of the gradient program, as illustrated by the examples of a convex and a concave gradient in Fig. 4. By more regular band spacing, nonlinear gradients can increase the peak capacity, especially for the separation of polymers and oligomers, as it is schematically shown in Fig. 5 for normal-phase gradient elution of lower oligostyrenes on a silica gel column.

Fig. 4 Effect of the gradient shape on the band spacing in the chromatograms. Convex (A) and concave (B) gradients of acetonitrile in water. Sample and other separation conditions as in Fig. 1.

Gradient Elution in LC Chromatography



Fig. 5 Normal-phase gradient-elution separation of lower oligostyrenes on two Separon SGX, 7 Am, silica gel columns in series (150  3.3 mm i.d. each), using the optimized linear and convex gradients of dioxane in heptane. Flow rate = 1 mL/min. Normalized response relates to the original concentrations of the oligomers in the sample, c0.

14 / Jandera In the early stage of liquid column chromatography, 30–40 years ago, the most frequently used instruments for gradient elution employed the exponential dilution in a chamber of a fixed volume containing originally solvent A. Solvent B was delivered by a pump at a constant flow rate into the chamber, the contents of which was continuously mixed. Such devices, generating nonlinear (convex) gradients, are neither accurate nor flexible and hence are no more employed in contemporary practice of HPLC on conventional columns, but are still useful in microbore or packed capillary HPLC [55–57] or in electrochromatography [58], because of technical problems connected with the design of precise low-volume gradient instruments operating with flow rates in the range of microliters per minute or even lower. The linear gradients are described by the gradient function: u ¼ A þ B Vt ¼ A þ

Dut B VV DuV ¼Aþ ¼ A þ BV ¼ A þ tG Fm VG


Here, A is the initial concentration u of the strong eluent B in the mobile phase at the start of the gradient, and B = Du/VG or B V = Du/tG is the steepness (slope) of the gradient, i.e., the increase in u per the time unit or per the volume unit of the eluate, respectively. VG and tG are the gradient volume and the gradient time during which the concentration u is changed from the initial value A = u0 to the concentration uG = A+Du at the end of the gradient; Du = (uGA) is the gradient concentration range. It has been found earlier [54] that a convenient curved gradient function for characterization of various convex and concave gradient profiles can be conveniently described by Eq. (7):  1 j u ¼ Að j Þ þ BV ð7Þ where A = u0 is the initial concentration of the strong eluent B at the start of the gradient, B = [uG(1/j)  A(1/j)]/VG is the steepness (slope) of the gradient and uG is the concentration of B at the end of the gradient. j is the gradient shape parameter characterizing the curvature of the gradient: j = 1 for linear gradients, whereas j < 1 for convex and j > 1 for concave nonlinear gradients (as illustrated by several examples in Fig. 2). The gradient function described by Eq. (7) is especially useful for prediction and optimization of retention in normal-phase and ion- exchange chromatography. Many gradient

Gradient Elution in LC Chromatography



instruments do not allow direct setting of a continuous nonlinear gradient, and curved gradients should be substituted by linear segmented gradients consisting in a series of subsequent linear gradient steps with gradually increasing or decreasing slopes, B. After introducing the appropriate retention equation and gradient function, Eq. (5a,b) can be solved to enable calculations of elution volumes in various HPLC separation modes. A survey of the equations describing a variety of possible solutions can be found elsewhere [2,3]. Even in cases where the integration of Eq. (5a,b) results in an equation that does not allow the separation of the variables, the retention data can be easily calculated using numerical iteration approach; a plethora of suitable software packages are now available for such purposes. The equations for gradient times (volumes) most useful in reversed-phase, normal-phase, and ionexchange gradient modes are discussed in Sections III–V. The calculation of the elution times or of the elution volumes by integration of Eq. (5a,b) in ‘‘ideal gradient elution’’ is based on several simplified assumptions concerning both the phase equilibrium in the column and the function of the instrumentation used. 1. The interactions between various compounds in the separation column should not change the column properties and the gradient profile should not change as it moves along the column, so that its profile does not change from the start of the gradient till the elution of the last sample solute. This may not always be the case, as any part of the column is at any time in equilibrium with a multicomponent mobile phase of changing composition, from which one or more components may be preferentially adsorbed on to the surface of the stationary phase in the column. In some systems this effect can become significant, so that not only the composition of the adsorbed layer, but also the profile of the gradient may change in the course of gradient elution in dependence on time elapsed and on the distance along the column. This problem is discussed in Section VI.B. 2. The kinetics of the chromatographic process is fast enough to allow instantaneous establishment of the distribution equilibrium between the mobile and the stationary phases. This can be expected during a gradient on columns packed with fine particle materials used in modern practice of HPLC. However, the reequilibration of the column to the initial mobile phase with a lower elution strength after the end of the gradient can be rather slow if one or more mobile phase components are strongly adsorbed on the column. Generally, approx-

16 / Jandera imately 15 column hold-up volumes are necessary to reestablish the initial equilibrium after the end of the gradient, but the exact volume necessary for reequilibration depends on the chromatographic system and on the initial mobile phase at the start of the gradient. Further, the establishment of the equilibrium can be less than perfect with fast generic gradients used for high sample throughput in the laboratory. 3. It is assumed that the solute concentration is low enough for its distribution isotherm between the mobile and stationary phases to be linear, so that the retention factor is independent of the concentration of the solute. This problem is essentially the same as in isocratic-elution chromatography, and the application of Eqs. (4a,b) and (5a,b) is limited to the linear range of the sample distribution isotherms, common in analytical HPLC. On the other hand, preparative chromatography on overloaded separation columns usually employs nonlinear range of adsorption isotherms and requires different approach to the description of the retention behavior and of the band profiles. 4. The solution of Eq. (5) assumes a constant value of the column hold-up volume during the gradient elution. This is not always straightforward as the hold-up volume can change to a certain extent with changing mobile phase [59–61]. Several different methods were suggested for the determination of the Vm (see, e.g., Ref. [34]). The determination of the mobile phase volume in the column by weighing method using two solvents of different densities gives the Vm independent of the mobile phase composition [35]. However, this method may be not accurate enough and it is more practical for routine practice to define the hold-up volume in gradient elution LC by convention. A useful definition of Vm is the isocratic elution volume of a nonretained compound in pure strong eluent B as the mobile phase. 5. In gradient elution, the trailing edge of the solute zone moves along the column in the mobile phase with a higher elution strength, i.e., faster than the leading edge. This leads to additional sharpening of chromatographic bands with respect to isocratic elution [4,25,26], but usually little affects the migration of the centers of gravity of the solute zones and can be neglected in calculations of the elution volumes. The more efficient the column is, the narrower are the zones and the less significant is the band sharpening effect. 6. Correct function of the gradient instrument is essential for successful theoretical description of the experimental data. Differ-

Gradient Elution in LC Chromatography



ences of the actual gradient profile from the preset gradient program are an inevitable consequence of any error in flow rate caused by pump failure or of possible errors in the mixing of the gradient components caused either by device malfunction or by improper construction design (for example, poor flow rate matching in the pumps delivering the components of the gradient). Such errors can occur both with high-pressure and low-pressure gradient instruments [62,63]. Other deviations from the preset gradient profile which can occur even with properly functioning devices are the rounding of the gradient at the beginning and at the end of the gradient and the gradient delay. These effects depend on the construction design of the instrument and are discussed in more detail in Section VI.A. 7. It is important to set properly the integration limits when solving Eq. (5a,b) by considering either the volume of the mobile phase that has flown through the column since the sample introduction or the volume that has passed through the solute zone maximum. Both ways of derivation give correct solutions and have been reported in the earlier literature, but they should not be confused with one another [70], as the first approach yields the equation for the uncorrected elution volume, VR = VRV+Vm, whereas the second one results in the equation for the corrected elution volume, VRV. The solution of Eq. (5a,b) considering the volume of the mobile phase which has passed through the peak maximum is more simple and therefore is used in this work. 8. Another problem can arise when calculating the retention data for large molecules which are partially excluded from the pores of the packing material by size-exclusion. This effect can be corrected by using the size-exclusion volume, VSEC, instead of the hold-up volume, Vm, in the calculations of the elution times or elution volumes in gradient elution [26]; it is assumed that size exclusion does not affect the phase ratio in the column.

B. Bandwidths and Resolution in Gradient Elution LC Once the elution volume of a solute is calculated, bandwidths wg and resolution Rs in gradient elution can be determined. Exact determination of bandwidths in gradient elution chromatography necessitates calculation of the complete profile of the elution curve using numerical methods [71]. However, this approach is not practical for routine application and a simplified procedure is often used for this

18 / Jandera purpose. To first approximation, the bandwidths in gradient elution can be set equal to the isocratic bandwidths in the mobile phase of the same composition as the instantaneous composition at the column outlet at the time of elution of the band maximum. Using this assumption, the gradient bandwidths can be predicted from Eq. (8) and the resolution from Eq. (9), introducing the value of the instantaneous retention factor kf in the mobile phase with the concentration of the strong eluent (solvent B), uf, at the elution time of the band maximum. kf can be calculated from the elution volume introducing the gradient function uf = f(VR) into the appropriate equation kf = f V(uf) describing the dependence of the retention on the concentration of B in the chromatographic system [2–4,54,72]: wg ¼

4Vm ð1 þ kf Þ pffiffiffiffiffi N


Rs ¼

VRð2Þ  VRð1Þ wg


VR(1), VR(2) are the elution volumes of sample compounds with adjacent peaks, N is the number of theoretical plates determined under isocratic conditions, and Vm is the column hold-up volume. It should be kept in mind that the correct plate number value cannot be determined directly from a gradient-elution chromatogram, unlike the isocratic elution where the retention factors are constant. The instantaneous retention factor kf at the peak maximum decreases as the steepness of the gradient increases and is not very different for various sample solutes eluted during a gradient run. Often, the values of kf are in between 1 and 2 [4,54]. Consequently, all sample components have approximately equal bandwidths in gradient elution, which are considerably narrower than in isocratic elution, especially for late eluting compounds [1–4,21,49,73,74], and hence the sensitivity in gradient elution is higher than under isocratic conditions [4], even at increased baseline noise usual in gradient elution. This also means that the sample structure effects on the separation efficiency are generally less important in gradient than in isocratic runs, at least for small molecules. Equation (8) neglects an additional band compression in gradient elution resulting from a faster migration of the trailing edge of the band in a mobile phase with a higher elution strength, whereas the leading edge moves along the column more slowly. In exact calcu-

Gradient Elution in LC Chromatography



lations, the bandwidths calculated using Eq. (8) can be corrected by a band compression factor, G [73,75,76]. The effect of the additional band compression in most cases results in approximately 10% reduction of the experimental wg [4,23,77]. However, other—yet not well understood—effects often contribute to additional band broadening in gradient elution and largely compensate for the gradient band compression [23,26,77–79], so that the errors caused by neglecting these effects usually are not very significant, except for very steep gradients, where the experimental bandwidths can be broader than the calculated values by as much as 20–50% [78].

III. REVERSED-PHASE CHROMATOGRAPHY WITH BINARY GRADIENTS Reversed-phase chromatography is nowadays by far the most widely used liquid chromatography mode, because it is likely to result in satisfactory separation of a great variety of samples, containing nonpolar, polar, and even ionic compounds. Gradient elution RPC is the technique of choice for separations of complex mixtures according to the hydrophobicity and (or) size of sample compounds [80,81]. Figure 6 shows an example of reversed-phase gradient elution separa-

Fig. 6 Separation of a polyethylene glycol sample PEG 1000 with 4–27 oxyethylene monomer units on an Alltima C18, 5 Am, column, 250  4.6 mm i.d., by linear gradient elution, 30–50% methanol in water in 40 min at 0.75 mL/min and 40jC. Evaporative-light scattering detector SEDEX 75 (Sedere, France), 60jC nebulizer temperature, nitrogen pressure 3.4 bar.

20 / Jandera tion of a polyethylene glycol sample (PEG 1000) according to the number of ethylene oxide units. The stationary phase in RPC— usually a nonpolar hydrocarbon chemically bonded on an inorganic support—is less polar than the mobile phase, normally an aqueous solution of one or more organic solvents. The most useful solvents for RPC are—in order of decreasing polarities—acetonitrile, methanol, dioxane, tetrahydrofuran, and propanol. The sample retention increases as its polarity decreases and as the polarity of the mobile phase increases. For successful separation of ionic, acidic, or basic substances, it is necessary to use additives to the mobile phasebuffers, neutral salts, weak acids, or compounds forming molecular associates with ionized sample solutes. By appropriate choice of the type of the organic solvent, selective polar dipole–dipole, proton– donor, or proton–acceptor interactions with analytes can be either enhanced or suppressed and the selectivity of separation adjusted. The retention is most efficiently controlled by setting the concentration(s) of the organic solvent(s) in the mobile phase. Despite widespread applications, the exact mechanism of retention in RPC is still controversial. Various theoretical models of retention for RPC were suggested such as the model using the Hildebrand solubility parameter theory [22,24,82,83], or the model supported by the concept of molecular connectivity [84], models based on the solvophobic theory [85,86] or on the molecular statistical theory [87]. Unfortunately, sophisticated theoretical RPC retention models introduce a number of physicochemical constants which are often not known or are difficult and time-consuming to determine, so that such models are not very suitable for rapid prediction of retention data. To first approximation, the interactions in the nonpolar stationary phase are less significant than the polar interactions in the mobile phase, which are the main factor controlling the retention. Hence the transition of a nonpolar or of a moderately polar solute molecule from the bulk mobile phase to the surface of the stationary phase is attributed primarily to a decrease in the contact area of the solute molecules with the strongly polar mobile phase, which results in a decrease of the energy in the chromatographic system. This solvophobic effect is the principal driving force of the retention in the absence of strong (polar) interactions of the solute with the stationary phase. In the real world, attractive interactions with the stationary phase contribute more or less to the retention. The nonpolar bonded stationary phases have properties similar to liquid alkanes, but the

Gradient Elution in LC Chromatography



alkyl chains bonded to a solid support cannot move freely like alkane molecules in a bulk liquid phase. Further, specific polar interactions of residual silanol groups in silica-based bonded phases can contribute to the retention of polar, especially basic, solutes. Finally, organic solvents used as the mobile phase components in reversed-phase systems can be preferentially sorbed by the nonpolar bonded stationary phase and modify its properties [88,89]. The elution times in RPC are controlled by the concentration(s) of the organic solvent(s) in the mobile phase. If a relatively small entropic contribution to the retention and secondary interaction effects are neglected, various retention models such as semi-empirical model of interaction indices [90], the regular solution theory [20,24,82,83,91], or the molecular statistical theory [87] yield, with some simplification, a quadratic equation describing the effect of the concentration of organic solvent, u, in a binary aqueous–organic mobile phase on the logarithm of the retention factor of a solute, log k: log k ¼ a  mu þ du2


The constants a, m, d depend on the type of the organic solvent in the mobile phase and of the solute. The quadratic term du2 in Eq. (10) explains the occasionally observed nonlinearity of log k vs. u plots, which increases with decreasing polarity of the organic solvent and with increasing size of the solute molecules, as illustrated in the experimental plots of k of alkyl-3,5-dinitrobenzoates in methanol– water and in tetrahydrofuran–water mobile phases in Figs. (7) and (8) [92]. The quadratic term in Eq. (10) usually is not very significant over a limited concentration range of methanol–water and acetonitrile– water mobile phases, where Eq. (10) reduces to the well-known and widely used semi-empirical Eq. (11), formally identical to Eq. (2) [1–5,22–25,49]: log k ¼ a  mu


Equation (11) was first introduced in thin-layer chromatography by Soczewin´ski and Wachtmeister [93] to describe the dependence between RM (equivalent of log k) on the concentration of water in mixed aqueous–organic solvents for thin-layer chromatography. The constant a in Eqs. (11) and (12) increases as the polarity of the solute decreases and as its size increases and theoretically should be equal to the logarithm of the solute retention factor in pure water, kw.

22 / Jandera

Fig. 7 Dependence of the retention factors, k, of homologous n-alkyl-3,5dinitrobenzoates on the concentration, u (vol% 102), of methanol in water on a Silasorb SPH C8 (7.5 Am) column (300  4.0 mm i.d.). Sample compounds: methyl-(1)-n-hexyl (6) esters. Points—experimental data, lines— best fit linear regression plots of Eq. (11).

Fig. 8 Dependence of the retention factors, k, of homologous n-alkyl-3,5dinitrobenzoates on the concentration, u (vol% 102), of tetrahydrofuran in water on a Silasorb SPH C8 (7.5 Am) column (300  4.0 mm i.d.). Sample compounds: methyl-(1)-n-hexyl (6) esters. Points—experimental data, lines— best fit non-linear regression plots of Eq. (10).

Gradient Elution in LC Chromatography



However, the values of log k extrapolated to u = 0 from various experimental plots do not describe accurately the real solute retention in water [94,95], probably because of the preferential adsorption of the organic solvent on the surface of the nonpolar stationary phase [96]. The constant m increases with decreasing polarity of the organic solvent B and is a measure of its elution strength (corresponding to the parameter S in the Snyder model of linear solvent strength gradients [4]). m also increases with increasing size of the molecule of the analyte [26,97]. Other models based on the combination of adsorption and partition mechanism in RPC result in more complex equations for the retention factors [98–100], which are, however, less suitable for prediction of retention and optimization of separation. In RPC systems described by Eq. (11), the approach outlined in Section II was employed for the derivation of the equations for elution volumes VR and bandwidths wg using linear gradients of organic solvents in water [2–4,23,24,54,77]. The equations were published in various forms, which can all be formally rearranged to Eqs. (12) and (13): h i 1 log 2:31 mBVm 10ðamAÞ þ 1 þ Vm mB   4Vm 1 wg ¼ pffiffiffiffiffi 1 þ 2:31 mBVm þ 10ðmAaÞ N

VR ¼

ð12Þ ð13Þ

with the constants a and m of Eq. (11). A is the initial concentration and B is the steepness of the gradient, N is the column plate number (under isocratic conditions) and Vm is the column hold-up volume. Equation (12) describes adequately the retention in a variety of reversed-phase gradient-elution separations (see, e.g., Refs. [3–5,19– 27,38–41,46–57]). However, using Eq. (12) with the parameters a and m determined experimentally in a range of binary mobile phase composition narrower than the actually used gradient concentration range may cause significant errors in the calculated elution volumes of late eluted compounds. This should be taken into account when planning the experiments for the determination of the constants of Eq. (11). Equation (11) can often describe the effect of the concentration of organic solvents on the retention in micellar LC [101] and in ion-pair or salting-out RPC occasionally employed for the separation of

24 / Jandera organic acids or bases [102–104] such as isomeric naphthalene monoto tetrasulphonic acids (Fig. 9). Hence Eqs. (12) and (13) can also be used principally for the calculation of the retention data in the elution with organic solvent gradients in these techniques. Changing concentration of the organic solvent during such a gradient affects the distribution equilibrium of the ion-pairing reagent between the stationary and the mobile phase [105], which impairs the accuracy of the calculated elution data in gradient-elution ion-pair chromatography. However, for carefully designed gradients, short column reequilibration times in between gradient runs and, consequently, predictable and reproducible retention data can be obtained [106]. Reversedphase behavior is also observed in HPLC on silica gel dynamically modified by adsorption of a long-alkyl surfactant, where the increasing concentration of the organic solvent during gradient elution speeds up the elution not only by increasing the elution strength of

Fig. 9 Separation of 12 naphthalene sulfonic acids by gradient-elution RPC on a Separon SGX RPS column, 7 Am (250  4 mm i.d.). Solvent program: 5 min isocratic, 0.4 mol/L Na2SO4 at 0.5 mL/min, followed by linear gradient from 0.4 mol/L Na2SO4 to 40% (v/v) methanol in water in 15 min at 1 mL/ min. Detection: UV, 230 nm; column temperature 40jC. naphthalene sulfonic acids: 1,3,5,7-tetra (1), 1,3,6-tri (2), 1,3,5-tri (3), 1,3,7-tri (4), 1,5-di (5), 2,6-di (6), 1,6-di (7), 2,7-di (8), 1,3-di (9), 1,7-di (10), 1-(11), 2-(12), unidentified less polar impurities (X).

Gradient Elution in LC Chromatography



the mobile phase, but also by simultaneously decreasing the amount of the adsorbed surfactant stationary phase [107]. From Eqs. (12) and (13) it follows that a lower parameter B (a less steep gradient) is required to compensate for a higher parameter m to obtain comparable retention volumes. This is important especially for compounds with higher molecular weights, as m usually increases with increasing size of the molecules [26,97,108] and has the following practical consequences: 1) Shallow gradients are frequently required for separations of oligomers or polymers, so that appropriate selection of a suitable combination of the gradient parameters A and B is more critical here than for the separation of small molecules; 2) for the separation of samples with a broad range of molecular masses a flatter gradient at the end of the chromatogram than at its start provides more regular band spacing than linear gradients and a convex gradient can be more useful than a linear gradient [109], see, e.g., the example in Fig. 4A. For very large molecules m can be so great that a very small change in the concentration of the organic solvent, u, may increase the retention even by several orders of magnitude, causing an abrupt change from ‘‘full retention’’ to ‘‘complete elution’’ [34]. Hence, isocratic fractionation of large molecules is more difficult than their separation using gradient elution (if possible at all). This is why gradient elution with acetonitrile in aqueous buffers at a low pH is normally required for separating peptide and protein samples in RPC [1]. For reversed-phase systems where the retention is controlled by the quadratic Eq. (10), the equation for the elution volume (time) is not obtained in the analytical form with separated variables and should be solved by numerical methods to calculate the retention data [2,3,83]. However, linear approximation of the experimental retention data using Eq. (11) usually does not affect significantly the agreement between the calculated and the experimental gradientelution retention data [110].

IV. NORMAL-PHASE CHROMATOGRAPHY WITH BINARY GRADIENTS Normal-phase chromatography (NPC) is the oldest liquid chromatographic mode. The column packings are either inorganic adsorbents (silica or, less often, alumina) or moderately polar bonded phases,

26 / Jandera most often cyanopropyl –(CH2)3–CN, diol –(CH2)3–O–CH2–CHOH– CH2–OH, or aminopropyl –(CH2)3–NH2, chemically bonded on a silica gel support. Many new chemically bonded polar phases, which can be used either in RP or in NP systems, have been introduced recently [111]. As the retention on inorganic adsorbents originates in the interactions of the polar adsorption centers on the solid surface with polar functional groups of the analytes, this mode was previously called also as adsorption or liquid–solid chromatography (LSC). The mobile phase is usually a mixture of two or more organic solvents of different polarities, such as hexane and propanol or hexane and dichloromethane. The first model of retention in adsorption chromatography developed by Snyder [112,113] is based on the assumption offlat adsorption in a monomolecular layer on a homogeneous adsorption surface. The retention in NPC results from the competition between the molecules of the solute and of the solvent for the adsorption sites on the adsorbent surface. The interactions in the mobile phase are less significant and can be neglected to first approximation. Later, corrections were introduced for preferential adsorption on localized adsorption centers [114–116]. Soczewinski [117,118] developed a similar displacement model of retention assuming the formation of association complexes of the sample solutes and of the solvents on the adsorption centers. This model was further elaborated by Jaroniec et al. [119]. Another adsorption model considering the retention as the result of probability and strength of interactions between the solutes and the adsorbent was suggested by Scott and Kucera [120,121]. The displacement and the interaction adsorption models were compared by Snyder and Poppe [122]. Martire and Boehm [123] introduced another adsorption model based on molecular statistical– mechanical theory of adsorption chromatography. Regardless of the exact retention mechanism, the stationary phase in normal-phase chromatography is more polar than the mobile phase. The sample retention is enhanced as the polarity of the stationary phase increases and as the polarity of the mobile phase decreases, opposite to the behavior observed in RPC. The retention also increases with increasing polarity and number of adsorption sites in the column. This means that the retention is stronger on the adsorbents with a larger specific surface area and that the strength of interactions with analytes generally increases in the order: cyanopropyl < diol < aminopropyl b silica gel c alumina stationary

Gradient Elution in LC Chromatography



phases. However, strong selective interactions may change this order. Basic solutes are strongly retained by the acidic silanol groups of silica gel whereas acidic compounds show increased affinities to chemically bonded aminopropyl stationary phases. Aminopropyl and diol bonded phases prefer compounds with proton–acceptor or proton–donor functional groups (alcohols, esters, ethers, ketones, etc.), whereas other polar compounds are usually more strongly retained on cyanopropyl silica than on aminopropyl silica. Alumina favors interactions with k electrons and often yields better selectivity for the separation of compounds with different numbers or spacing of unsaturated (double) bonds than silica. The polarity and the elution strength, i.e., the ability to enhance the elution, generally increase in the following order of the most common NPC solvents: hexanecheptanecoctane0

From Eq. (A-8), one can see that the average time spent in the stationary phase obtained by neglecting the peak splitting is biased and greater than the true value. Finally, from Eq. (A-8), one can write: Dt s;1 t s;app;1  t s Pðns ¼ 0Þ cPðns ¼ 0Þ ¼ ¼ 1  Pðns ¼ 0Þ ts ts


The last approximation holds true if the peak splitting effect is small, i.e., when P(ns = 0)b1. This equation is quite general. When ns is distributed according to a Poisson law [Eq. (6) in the main text], one can write: Pðns ¼ 0Þ ¼ expðns Þ


When, in addition, ss is exponentially distributed, one gets the Giddings–Eyring model for which [37,40]: NVs ¼

ns 2


where  2 ts NVs ¼ rt


is the effective number of theoretical plates. rt is the peak standard deviation, which, for constant mobile phase velocity models, is equal to the standard deviation of ts. Then, the subscript s for NVs empha-



Dondi et al.

sizes the fact that such models refer to a hypothetical column where only the mobile-stationary phase exchange process contributes to the peak dispersion. In this case, the absolute error is: Dt s;1 cexpð2NVs Þ ts


It decreases exponentially on increasing column efficiency. A.1.2. Peak Tailing The second type of error arises in assuming the peak maximum as the first moment. This problem can be handled in a general way, in the case of the basic stochastic model, i.e., in general, in linear chromatography. In fact, as discussed in Ref. 35, this model has the important mathematical property of being a stochastic process with independent and stationary increments, and, because of this, the peak profile can be represented by the Edgeworth–Crame´r series expansion [25,28]. This series expansion is an asymptotic approximation of the peak profile, where the asymptotic quantity is the average number of sorption steps [35,36,47]. This series expansion is related to the central limit theorem of probability theory which establishes that the sum of an increasing number of equally distributed random variables converges to a Gaussian law [25–27]. More specifically, the Edgeworth–Crame´r series expansion describes the rate of convergence of the actual profile toward the Gaussian law and provides a better approximation of this profile than the Gaussian law when the limiting condition of a very large number of added variables is not satisfied and, more concretely, when the peak shape exhibits a significant tailing. When this number is large enough, the distribution function can be approximated by the Gaussian law, which is the first term of the Edgeworth–Crame´r expansion. Then, the maximum of the frequency function, tmax, becomes indistinguishable from the first moment, tR. Thanks to these properties and provided that tailing is moderate, one has [25]: Xmax u

tmax  tR Dt R;2 S ¼ c 2 rt rt


where S is the peak skewness: S¼

l3 r3t


Chromatography: A Stochastic Approach



l3 is the third central moment of the peak. In a constant mobile phase velocity model, one has Dt R;2 ¼ Dt s;2 . Hence combining Eqs. (A-13), (A-15), and (A-16), it becomes: Dt s;2 S c  pffiffiffiffiffiffiffiffi ts 2 NVs


If the duration of the individual steps in the mobile and in the stationary phases are both exponentially distributed, i.e., in the case of Giddings–Eyring model, one can prove that [37,40]: 3 S ¼ pffiffiffiffiffiffi 2 NVs


By combining Eqs. (A-17) and (A-18), one has: Dt s;2 3 c 4NVs ts


The major problem of Eq. (A-17)—which applies to the basic stochastic model—is that it contains the quantity S, which is difficult to estimate with accuracy, whereas Eq. (A-19) only contains the effective number of theoretical plates, which can more easily be measured. The hypothesis under which Eq. (A-19) is derived is, however, strict: it assumes a first-order kinetics of exchange between mobile and stationary phase. In general, for modern high-efficiency chromatographic systems, this approximation is acceptable. However, in a significant number of applications, the hypothesis of a column having identical sorption sites with a single first-order kinetics of phase exchange is only a rough approximation [19,21]. The matter is obviously general and many cases are possible. Situations in which a much complex kinetics is involved are numerous. One particular, but important, case is that of a heterogeneous chromatographic column containing sorption sites with different firstorder kinetics or having sites on which several first-order sorption processes are simultaneously involved. In this instance, it was proved that: S¼

3  const pffiffiffiffiffiffi 2 NVs




Dondi et al.

const is a numerical quantity greater than 1 and, depending on the relative strength and abundance of the sites [40], is equal to:  X pi s3s;i const ¼





pi s2s;i


where pi is the abundance of sites of mean sorption time equal to ss;i . By combining Eq. (A-20) with Eq. (A-17), one has the expression for the multiple site case: Dt s;2 3  const c 4NVs ts


It appears thus that the stochastic treatment allows us to evaluate the bias made in evaluating the peak first moment from the peak maximum in a sufficient number of cases of practical interest. A most significant error source is the column heterogeneity and the site sorption kinetics. The relative error in k V will be simply equal to the relative error over t s because of the proportionality between the two quantities. Thus one has:   ykV 3 c ðA-23Þ kV 2 4NVs for the case of homogeneous first-order kinetics of both the mobile phase and stationary phase times, while, for the multiple-site adsorption kinetics, one has:   ykV 3  const c ðA-24Þ kV 2 4NVs One must observe that, according to Eqs. (A-23) and (A-24), the difference between peak maximum and peak first moment are inversely proportional to N Vs and thus to the number of sorption–desorption steps [see Eq. (A-12)]. However, it is well known that the central limit theorem states that the convergence to the Gaussian law is inversely proportional to the square root number of added random variables [27]. This apparent contradiction is simply explained by the fact that

Chromatography: A Stochastic Approach



the central limit theorem refers to the normalized random variable quantity X [see Eq. (A-15)], but by combining it with Eq. (A-18) or (A-20), this contradiction disappears. Note that the above developed handling only applies to conditions of linear chromatography. This type of tailing is referred to as kinetic tailing.

APPENDIX B B.1. Stochastic Bias Effect One considers, in the following, that the analyte retention factor, k V, is obtained from the measurements of the analyte retention time, tR, and of the elution time, t m;u , of an unretained solute (also called tracer) as: kV ¼

tR  t m;u tR ¼ 1 t m;u t m;u


B.1.1. Relative Random Errors on k V and on tR/ t m,u Accordingly, the random error on k V, r(k V), is due to the random error on tR =t m;u , rðtR =t m;u Þ. Hence: r2 ðkVÞ ¼ r2 ðtR =t m;u Þ


Hence from Eq. (B-2), the square of the relative error on k V is related to that on tR =t m;u by:   r2 ðkVÞ r2 ðtR =t m;u Þ 1 þ kV 2 ¼ kV kV2 ðtR =t m;u Þ2


The random error on tR =t m;u arises itself on separated random errors on tR, r(tR), and on t m;u , rðt m;u Þ. Since tR and t m;u are independent variables, one gets, according to Ref. 54 (p. 33, Example 1-6-12): r2 ðtR =t m;u Þ ðtR =t m;u Þ2

" # r2 ðtR Þ r2 ðt m;u Þ r2 ðt m;u Þ ¼ 1 þ þ t2R t 2m;u t 2m;u




Dondi et al.

B.1.2. Relative Errors on tR and on t m,u The analyte retention time is the mean value of the residence time in the column of the injected solute molecules, i.e. mol 1 X tc; j Nmol j¼1


tR ¼


where tc, j is the column residence time of the jth molecule of analyte and Nmol is the number of analyte molecules in the injected sample. Because of the stochastic character of the column residence process, the values of tc for the individual molecules are randomly distributed according to some frequency function f(tc) having a mean value, t c, and a variance, r2(tc), defined as usual as: ðl tc ¼ tc f ðtc Þdtc ðB-6Þ 0

and r2 ðtc Þ ¼


ðtc  t c Þ2 f ðtc Þdtc



From Ref. 54 [Eqs. (25) and (26)], it is easy to show that as long as the individual variables tc, j in Eq. (B-5) are independent, i.e., for a linear chromatographic process (no overloading effect), one has: tR ¼ t c


and N mol X 1 r ðtR Þ ¼ 2 r2 tc; j Nmol j¼1 2


mol 1 X 1 r2 ðtc; j Þ ¼ r2 ðtc Þ 2 Nmol Nmol j¼1



ðB-9Þ from which one gets the square of the relative error on tR: r2 ðtR Þ 1 r2 ðtc Þ ¼ Nmol t 2c t2R


Chromatography: A Stochastic Approach



The chromatographic literature makes a frequent use of the concept of plate number to characterize the relative width a peak. Let N be the analyte plate number, defined as: Nu

t2R t 2c ¼ r2 ðtc Þ r2 ðtc Þ


One gets from Eqs. (B-10) and (B-11): r2 ðtR Þ 1 1 ¼ Nmol N t2R


This equation provides the relative error on the retention time of the solute of interest, arising from the fact that the sample contains a limited number of analyte molecules. Because this number is limited, the distribution of their residence time is not exactly equal to the probability density distribution of the individual molecules, f(tc). Equation (B-12) shows that the relative error on tR becomes vanishingly small as the number of analyte molecules increases. Repeating the above derivation for the unretained tracer used to measure t m;u , one gets: r2 ðt m;u Þ t 2m;u


1 1 Nmol;u Nu


where Nmol,u is the number of molecules of the unretained tracer in the injected tracer sample and Nu is the plate number for the unretained tracer, defined as: Nu u

t 2m;u r2 ðtc;u Þ


Here r2(tc,u) is the variance of the frequency distribution of the residence time of the tracer molecules. B.1.3. Relative Error on k V Combining Eqs. (B-3), (B-4), (B-12), and (B-13), one gets the expression of the square of the relative error on k V as: 

   r2 ðkVÞ 1 1 1 1 1 1 1 þ kV 2 1 þ ¼ þ Nmol N Nmol;u Nu Nmol;u Nu kV kV2 ðB-15Þ



Dondi et al.

The residence time of an analyte molecule in the column is the sum of the time, tm, that the molecule spent in the mobile phase and of the time, ts, spent in the stationary phase: tc ¼ tm þ ts


These two times are distributed according to some frequency functions with mean values, t m and t s , and variances, r2(tm) and r2(ts), respectively. It was shown previously [37,46] that: tR ¼ t c ¼ t m þ t s


r2 ðtc Þ ¼ ð1 þ kVÞ2 r2 ðtm Þ þ r2 ðts Þ



Combining Eqs. (B-11) and (B-18), one can write: 1 r2 ðtm Þ r2 ðts Þ r2 ðtm Þ r2 ðts Þ ¼ ð1 þ kVÞ þ 2 ¼ þ 2 N t2R tR tR t 2m


Let us define Nm in a way similar to Eq. (B-14) for the unretained tracer as: 1 r2 ðtm Þ u Nm t 2m


If the analyte and the unretained tracer have similar diffusivities, Nu and Nm should also have similar values (note that the subscript m, for mobile phase contribution, does not appear in Nu because the whole residence of the unretained tracer in the column occurs in this phase). In addition, it is customary to define the effective plate number, NV, by relating the time variance to the square of the mean time spent in the stationary phase, instead of that of the retention time. Then: 1 r2 ðtc Þ 1 u 2 ¼ NV N ts

 1 þ kV 2 r2 ðtm Þ r2 ðts Þ r2 ðtm Þ 1 ¼ þ ¼ þ 2 2 2 kV NV s ts ts ts ðB-21Þ

where NsV can be regarded as the effective plate number arising from the stationary phase.

Chromatography: A Stochastic Approach



Furthermore, according to the stochastic theory of chromatography, one has:   1 r2 ðts Þ ns r2 ðss Þ þ s2s r2 ðns Þ 1 r2 ðss Þ r2 ðns Þ u u 2 ¼ ¼ þ ¼ s 2 2 NVs n n ns s s s ts ðns ss Þ s ðB-22Þ In this equation, the mean values and variances of the number of visits of a molecule to the stationary phase during its stay in the column, ns, and of the duration of one visit, ss, appear. us, equal to the term in brackets in Eq. (B-22), is a number, the value of which depends on the particular forms of the probability distribution functions of ns and ss. In the case of a Poisson distribution of ns and of an exponential distribution of ss, us is equal to 2 [35]. Combining Eqs. (B-15) and (B-20–B-22), one obtains the square of the relative error on k V as: " #    r2 ðkVÞ 1 1 1 þ kV 2 us 1 1 ¼ þ 1 þ Nmol Nm kV Nmol;u Nu ns kV2 ðB-23Þ  2 1 1 1 þ kV þ Nmol;u Nu kV This equation, like Eq. (B-15), is quite general. It can take a simpler form in some particular cases. For instance, when the dispersion process in the mobile phase is negligible, Nm and Nu vanish and one gets: r2 ðkVÞ 1 us ¼ ¼ 2 Nmol NVs Nmol ns kV The relative error on k V, r(kV)/kV, is then equal to: sffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 ðkVÞ r2 ðkVÞ us u ¼ 2 kV N kV mol n s or, with Eq. (B-22): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rðkVÞ 1 ¼ kV Nmol NVs






Dondi et al.

Equation (B-25) reveals that Nmol and ns play a very similar role as concerns the error on k V. The larger they are, the more the analyte molecules ‘‘sample’’ the stationary phase. It is then equivalent to have a small mean number of visits to the stationary phase (short columns or fast carrier velocities) and a large number of molecules as to have a few molecules visiting, in average, a large number of times the stationary phase. In the case of the Giddings–Eyring model, as mentioned above, us is equal to 2. Then, one gets, together with Eq. (A-12): rðkVÞ ¼ kV

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Nmol ns


APPENDIX C C.1. Expression of the Maximum Number of Analyte Molecules The number, Nmol, of molecules of a given analyte injected in a chromatographic column is given by: Nmol ¼ NAv cM Vinj


where NAv is the Avogadro number, cM is the molar concentration of the analyte in the injected sample, and Vinj is the injected volume. The number of analyte molecules injected in the chromatographic column is obviously proportional to the injected sample volume. It can thus be increased by increasing this volume. However, the finite volume of the injection band contributes to the overall width of the peak and must be limited in order to limit the degradation of the chromatographic resolution. In fact, one has to tolerate some loss of efficiency due to the sample volume contribution to peak broadening. This can be expressed by stating that the contribution to the peak variance arising from the injection process, r2V;inj , must not exceed a fraction h2 of that, r2V;c , arising from the column migration process [41]. Then, its maximum value becomes: r2V;inj ¼ h2 r2V;c


Chromatography: A Stochastic Approach



where the variances are expressed in terms of square of volume units. Obviously, r2V;inj is related to the injected volume, which can be written as: r2V;inj ¼

2 Vinj



where a2 is a parameter which depends on the shape of the injection profile. For a plug injection, which corresponds to the least dispersive injection profile, a2 is equal to 12. In practice, a2 is smaller and has been found to lie between 3.5 and 7 in liquid chromatography and to have quite lower values in gas chromatography [42]. The column variance can be related to the column plate number, N, or to the effective plate number, NV, as: r2V;c

V2 V2 ¼ R ¼ R N NV

kV 1 þ kV

2 ðC-4Þ

where VR is the retention volume of the analyte, which is related to the volume Vm of mobile phase in the column through: VR ¼ Vm ð1 þ kVÞ


By combining Eqs. (C-1–5), one gets the expression of the maximum number of analyte molecules which can be introduced in the chromatographic column under the accepted tolerance criterion: kV Nmol ¼ ahNAv pffiffiffiffiffiffi Vm cM NV


This number of analyte molecules is seen to depend on a characteristic of the injection device (a), on the tolerance factor, and on the column effective plate number and to be proportional to the retention factor, to the volume of mobile phase in the column, and to the analyte molar concentration in the sample. Equation (C-6) gives the maximum number of analyte molecules which are injected in the column under the tolerance criterion. However, the number of molecules which are detected may be only a fraction, U, of this number. U is called the molecular detection efficiency. Obviously, only the detected molecules contribute to the



Dondi et al.

determination of the retention factor. Then, the relevant number of molecules becomes: kV Nmol ¼ ahUNAv pffiffiffiffiffiffi Vm cM NV


APPENDIX D D.1. Error Resulting from the Effect of the Injection Process on the First Moment of the Peak Because all analyte molecules do not enter simultaneously the chromatographic column, there is a systematic bias in the mean elution time of the analyte peak. In fact, the distribution of the elution times of the analyte results from the convolution of the distribution of the injection times by the distribution of the residence times in the column. Let t inj be the mean injection time. The mean elution time of the analyte peak, t el , is then: t el ¼ tR þ t inj


If t el is used instead of tR in Eq. (B-1) to compute kV, an error in k V results. However, the mean column residence time of an unretained solute is frequently taken as a measure of the time spent by the analyte in the mobile phase, tm (or, more precisely, of the mean time spent by the analyte in the mobile phase, t m , when there is a distribution of tm due to mobile phase dispersion). If, because of the finite duration of the injection process, the mean elution time of the unretained solute, t el;u, differs from t m, by the amount t inj, an apparent value of k V, k aV , is obtained: kVa ¼

t el  t el;u tR  t m ¼ t el;u t m þ t inj


If t m can be independently determined, supposedly without error, one gets then an apparent k V value, kVb, given by: t el  t m tR  t m þ t inj kVb ¼ ¼ ðD-3Þ tm tm The relative error resulting on k V becomes in the first case:   t inj =t m ykV kVa  kV ¼ u kV a kV 1 þ t inj =t m


Chromatography: A Stochastic Approach and in the second case:   ykV kVb  kV t inj =t m ¼ u kV b kV kV




In the first case (determination of t m by means of an unretained solute injected present in the analyte sample), it appears that the difference between the first moments of the elution peaks of the analyte and of the unretained solute is not affected by the injection process so that the error on k V arises solely from the deviation of the first moment of the unretained solute. When t m is independently known, the error on k V generally decreases with increasing k V and is generally lower than in the first case. The value of t inj can be related to the injected volume, Vinj, as: t inj ¼ c

Vinj F


where c is a proportionality factor, the value of which depends on the injection device. Then, the smaller is the value of Vinj, the smaller is the error on k V resulting from the injection effect. When the maximum volume compatible with a tolerated deterioration of the column efficiency, given by Eq. (C-3), is injected, t inj becomes using Eqs. (C-2–5) together with (D-6): kV t inj ¼ ach pffiffiffiffiffiffi t m NV


Then, the relative errors on k V become, combining Eqs. (D-4), (D-5), and (D-7):

kV ach pffiffiffiffiffiffi ykV NV ¼ kV kV a 1 þ ach pffiffiffiffiffiffi NV


 ykV ach ¼ pffiffiffiffiffiffi kV b NV





Dondi et al.

APPENDIX E E.1. Error on k V Resulting from an Improper Selection of the Unretained Tracer The experimental determination of the retention factor, k V, of the solute of interest requires the measurement of the retention time, tR, of this solute and of the mean elution time, t m;u , of a supposedly unretained compound which is visiting only the mobile phase, according to Eq. (B-1). If the supposedly unretained tracer is not really unretained, but has itself a retention factor, kVu, such that:

kVu ¼

t m;u 1 tm


where t m is the mean elution time of a truly unretained compound, there is a systematic error made on kV when using Eq. (B-1). If kVo is the true retention factor of the analyte, defined as:

kVo u

tR 1 tm


the relative systematic error on k V is equal to: 

ykV kV


kVo  kV kVu 1 þ kVo ¼ kVo 1 þ kVu kVo


which, for small k Vu, becomes: 

 ykV 1 þ kVo ckVu kV kVo


4 Solid-Phase Microextraction: A New Tool in Contemporary Bioanalysis Georgios Theodoridis Aristotle University Thessaloniki, Thessaloniki, Greece Gerhardus J. de Jong University Utrecht, Utrecht, The Netherlands


232 234 238 242 246 247 249 250 255 258 264 268 231



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I. INTRODUCTION Solid-phase microextraction (SPME) has been introduced recently as a useful method in sample preparation. This technique integrates sampling, extraction, preconcentration, and sample introduction in a simple single-step procedure. Additionally, it facilitates automation and direct coupling to chromatographic analysis: gas chromatography (GC) and high-performance liquid chromatography (HPLC). When performed in the most known fiber format, SPME is based on the sorption of the analyte on an extraction phase coated on a small fused silica fiber. The fiber is mounted in a syringe-like protective holder (Fig. 1). During extraction, the fiber is exposed to the sample, either immersed in a liquid sample or exposed to the headspace above the sample. After equilibrium or a defined time, the fiber is withdrawn in the septum-piercing needle and introduced into the analytical instru-

Fig. 1 Schematic of the SPME device commercially available from Supelco.

SPME: A New Tool in Contemporary Bioanalysis



ment. There the analytes are either thermally desorbed (GC) or redissolved in a proper solvent for HPLC or capillary electrophoresis (CE). The technique has been commercialized in 1993 by Supelco. Initial work was exclusively aimed at SPME-GC combinations since SPME was originally introduced as a method aiming at the sample pretreatment of environmental samples. Furthermore, coupling to GC is straightforward and convenient because the fiber is introduced into the GC injector. In the few years of its practice, SPME has developed to a mature technique and a useful alternative to contemporary techniques in various scientific and research fields. Not surprisingly, SPME was one of the six ‘‘great ideas of the decade’’ as illustrated in a recent survey of Analytical Chemistry [1]. Solid-phase microextraction offers unique advantages: solventless extraction, low cost, simplicity, on-site sampling, high efficiency and reproducibility, and compatibility with numerous analytical techniques. Furthermore, due to its distinctive features (e.g., geometry, portability), the technique provides the ground for innovative approaches and designs. As a result, SPME has more specific advantages to cover niches in analytical sciences as will be exemplified in the following chapter. A clear example of the profound evolution is the continuous annual increase in the number of research papers published in peer-reviewed journals (Fig. 2). In

Fig. 2 Annual plot of the number of publications reporting on SPME.



Theodoridis and de Jong

less than a decade of existence as a commercially available technique, SPME has risen above the landmark of 1000 publications. In this chapter, the practice and application of SPME are described with special emphasis to bioanalytical applications. Solidphase microextraction modes are illustrated with emphasis on novel technological approaches. Theoretical discussion is limited to fundamental terms and features, whereas technological aspects as coating materials and special devices are stressed. Finally, specific advantages and limitations of SPME are discussed.

II. EXTRACTION MODE AND COUPLING There are, as a rule, two extraction modes: direct immersion (DI) in liquid samples and headspace (HS) extraction. The major criteria for mode selection are the nature of the sample matrix, the volatility of the analyte, and the affinity of the analyte for the matrix. Medium volatile or nonvolatile analytes such as macromolecules and polar analytes are extracted by direct immersion of the fiber into the sample. The mass transfer rate is determined mainly by diffusion of the analyte in the coating, provided that the convection in the liquid sample is ideal and the sample is a single homogeneous phase. In practice, however, a thin boundary layer of static liquid sample is formed around the fiber, hindering the access of the analytes to the coating. This boundary cannot be removed without vigorous agitation methods. Analytes exhibiting low vapor pressure remain trapped on the fiber allowing field sampling and analysis by GC or HPLC in a second stage. For dirtier samples, the fiber can be protected by a membrane [2,3]. Employment of a membrane can enhance the overall efficiency due to the added membrane selectivity. However, mass transfer is reduced; thus increased temperatures or thin membranes are necessary for relatively short extraction times. HS-SPME is preferred for volatile compounds because it may provide cleaner extracts, greater selectivity, and longer fiber lifetime. In this case, there are three phases (coating, headspace, and sample matrix) involved in the extraction process. As a rule, equilibrium is faster in HS-SPME than in DI-SPME since diffusion in gaseous phases is typically much faster than in liquid phases. The timelimiting step is the transfer of the analytes from the sample to the

SPME: A New Tool in Contemporary Bioanalysis



headspace. Hence gentle heating or stirring of the sample will improve extraction. However, higher temperatures will result in reduction of the partition coefficients. Although often regarded as the less critical step in SPME, desorption is also important for a successful method. For the SPME-GC combination, analyte desorption from the fiber is straightforward. The septum-piercing needle of the SPME device is introduced into the GC injector, where the fiber is exposed to the heated chamber and the analytes are thermally desorbed. For faster desorption, elevated temperatures and a narrow bore insert are required. To eliminate carryover effects, split/splitless injection is used: desorption occurs in splitless mode, so that the main part of the desorbed amount of analyte is introduced in the GC column, where it can be cryofocused. During analysis, the fiber remains exposed in the injector (operating now in split mode); thus possible carryover is thermally desorbed without entering the column. Coupling to LC requires an appropriate interface, and one such is commercialized by Supelco. The fiber is placed into a low-volume desorption chamber with 3 ports in T-configuration. The chamber is mounted in a typical 6-port injection valve in the place of the injection loop. Desorption occurs either statically or dynamically. In static mode, the desorption chamber is filled with an appropriate solvent, and then, the fiber is introduced to the interface for a determined time. Static desorption depends on time and the composition of the desorption liquid. Switching the valve introduces the plug of the backextracted analytes to the analytical column. In dynamic desorption, the mobile phase flows within the desorption chamber, desorbing the analytes and driving them to the analytical column. Dynamic desorption is governed by the selection of the mobile phase and the flow rate and often suffers from substantial peak broadening [4]. Heating the interface was shown to enhance mass transfer rates and thus to affect desorption and separation, reducing peak broadening and carryover [5]. One possibility that seems to be overlooked so far is the off-line combination of fiber SPME with liquid chromatography with no interface. In this approach, desorption may occur in a small volume tube, (e.g., an autosampler insert) in static mode. Subsequently, an aliquot of the resulting solution is injected in HPLC. In general, however, SPME-LC offers no profound advantages to displace SPE-LC; thus it is not surprising that SPME-LC applications are limited to almost 10% of the total of SPME reports.



Theodoridis and de Jong

In-tube SPME is an attractive alternative for the automation of SPME-LC. In this case, extraction takes place in the inside of a fused silica capillary, which is coated with the extractive phase. For sorption, an aliquot (some microliters) of the sample is aspirated and dispensed into the capillary. Desorption of the analytes is achieved by aspiring a proper organic solvent and dispensing the eluate into the injection loop (Fig. 3). In-tube SPME exhibits different geometry than fiber SPME. This method enhances full automation and can be performed with typical LC autosamplers after minor modifications. Moreover, in-tube desorption was reported to be quantitative, eliminating carryover effects. In general, sample introduction of relatively large sample volumes in capillary electrophoresis is a challenge. Although both SPME

Fig. 3 Various designs for the in-tube coupling of SPME to HPLC. Extraction capillary in place of transfer line (a). Extraction capillary in place of standard loop (b). Extraction capillary in place of flush injection loop (c). (From Ref. 2.)

SPME: A New Tool in Contemporary Bioanalysis



and CE are capillary techniques, it is rather difficult to couple them on line. So far, only experimental ‘‘house-built’’ interfaces have been developed. In one approach, an SPME-CE device was developed in house by gluing two CE capillaries in a Teflon sleeve containing a small amount of C18 material. Another alternative is to introduce the fiber via guides to the end of the capillary (Fig. 4) [6]. Recently, SPME has been coupled with confocal Raman spectroscopic analysis for airborne sampling of contaminated air. Raman spectroscopy is a powerful method for chemical fingerprinting of analyte molecules. Combination with SPME provided a novel procedure for identification and possible numeration of airborne particulate matter. Mass loading in SPME fibers was changed by altering the sampling time. The polydimethylsiloxane (PDMS) fiber was next subjected to confocal Raman microspectroscopic analysis. Raman spectroscopic analysis resulted in the identification of several characteristic bands enabling single particle analysis of less than 1 Am in diameter [7].

Fig. 4 Coupling of SPME to CE. (From Ref. 6.)



Theodoridis and de Jong

A. Novel Devices Solid-phase microextraction is a new and unique extraction technique. Therefore researchers from diversifying fields have shown initiative to use SPME as a tool for a variety of purposes. This trend has resulted to numerous novel devices that exploit the features of SPME. Some noteworthy applications are the following: Portable Solid-Phase Microextraction for Field-Air Sampling A great field for future evolution for SPME is seen in field sampling. The technique is easy and convenient, portable, and not space demanding. Sampling may be performed independently of analysis or may also be combined with portable GC [8]. In the former case, innovative portable SMPE devices have been developed for sampling air, aroma, and volatiles from foods and living organisms (e.g., insect pheromones). Additionally, new coatings and methodologies are investigated [9]. The use of SPME fibers coated with adsorptive porous polymer solid phases for quantitative purposes is limited due to interanalyte displacement and competitive adsorption. For air analysis, these problems can be averted by employing short exposure times to air samples flowing around the fiber. In these conditions, a simple mathematical model allows quantification without the need of calibration curves. Portable dynamic air-sampling devices have been designed for application of this approach to nonequilibrium SPME sampling and determination of airborne volatile organic compounds (VOCs). These devices reduced total sampling and analysis time compared to the official methods (trapping in charcoal, extraction with CS2, and GC-FID analysis) [10]. Despite the reduced sampling time, method sensitivity is superior for volatile organic compounds. Hence detection limits as low as 700 parts per trillion (ppt) have been reached. Solid-phase microextraction technology combined with fast portable GC reduced the sampling and analysis time to less than 15 min. The configuration offered the conveniences of on-site monitoring that is not possible with conventional methods [8,11]. An interesting methodology in that direction may be the SPMEdirect FID method. In that scheme, the SPME was connected to an FID system but with no GC column. The idea was to measure rapidly the total sum of volatiles sorbed on the fiber. Using this scheme as an

SPME: A New Tool in Contemporary Bioanalysis



electronic nose, one can easily add a column to obtain qualitative insight of the analyzed samples [12]. Wire or Fiber In-Tube An ingenious approach is the incorporation of wire inside a capillary tube in order to minimize the internal volume of the capillary (compare Fig. 5A and B). A stainless-steel wire (0.20 o.d.20 cm) was inserted in a piece (0.25 mm i.d.20 cm) of a GC capillary column, diminishing its volume to 3.53 AL. The capillary was used as an intube SPME device, connected to micro-LC. Preconcentration of tricyclic antidepressants from human urine was accomplished, using minimal volume of organic solvent for analyte desorption [13]. With a similar experimental setup, the same group studied the configuration of fiber in tube. Approximately 280 Zylon fibers (11.5-Am

Fig. 5 Three types of extraction tubes used (in tube microextraction). (A) Intube, (B) wire-in-tube, and (C) fiber-in-tube configurations. (From Ref. 15.)



Theodoridis and de Jong

diameter) were forced in a PEEK tube (0.25 mm i.d.) as can be seen in Fig. 5C. The tube was used for the enrichment of n-butylphtalates, providing a preconcentration factor of about 160. The authors claim that such schemes employ minimal amounts of organic solvent and facilitate direct coupling to capillary techniques such as CE and micro-LC [14,15]. Protection of the Fiber by a Membrane Protecting the SPME fiber by a membrane may serve as means to prolong fiber lifetime and enable the process of dirty samples. In this objective, a PDMS coated bar was enclosed in a dialysis membrane bag and the sampler was used for the solventless procedure for the preconcentration of triazines from aqueous matrices. In addition to enrichment, hollow fiber-protected microextraction also served as a technique for sample cleanup because of the selectivity of the membrane, which prevented large molecules and extraneous materials (e.g., humic acids) from being extracted [16]. In a similar manner, a bar coated with PDMS was enclosed in a dialysis membrane bag and the device was used for microextraction of hydrophobic analytes (cyclohexanes, PAHs) from aqueous matrices. The concept combined passive sampling with solventless preconcentration of organic solutes. Subsequently, the sampler was desorbed and the analytes were analyzed by capillary GC-MS [17]. Fiber Conditioner Fiber conditioning is performed thermally by its insertion in a GC injection port for a certain time. Usually, this means 1–3 hr for a new fiber or 5 min between different samples at 250–280jC. This may reduce available instrumentation and at the same time introduce unwanted interferences to the GC column. To address these concerns, Koziel et al. [18] developed a fiber conditioner device. The conditioner ` was assembled from a Hamilton syringe cleaner, where a 1000-U ceramic heater and a flow of N2 gas facilitated desorption and conditioning of the fiber. The device performed equal or better than GC injectors for removing test components (alkanes of varying boiling points). Solid-Phase Microextraction Electrochemistry The idea behind the combination was to integrate extraction and electrochemical reaction in a single conductive polymer coating. In this coating (a carbon steel wire with a 10-Am gold coating), the

SPME: A New Tool in Contemporary Bioanalysis



analytes (Hg in this case) are electrochemically oxidized (or reduced) and sorbed. Desorption was accomplished with a dedicated desorption system and analysis by GC-MS. Hg2+ in aqueous solution was reduced to Hg0 which is next determined by mass spectrometry. With this methodology, inorganic mercury and organomercury compounds were differentiated. Another attractive proposal is the construction of a SPME-electrodeposition device for the determination of putrescine and cadaverine [19]. The three-electrode system consisted of a Ag/AgCl reference electrode and a stainless-steel mesh counter electrode, which surrounded a pencil lead; the latter served as both the SPME device and the working electrode. The pencil lead was immersed in a pH 8 borate buffer, and 1.70 V potential vs. the reference electrode was applied, resulting in an electrochemical reduction of buffer solution protons. Subsequently, diamines present in the solution are converted into their free base form and retained on the electrode, which is used as the SPME fiber. The device was then transferred to a capillary GC equipped with a thermionic detector. Solid-Phase Microextraction-Mass/Atomic Spectrometry The combination of SPME with the high sensitivity and selectivity of mass spectrometry may reduce the need for chromatographic separation and allow for very rapid sample processing. Initial approaches have dealt with coupling to ion mobility mass spectrometry [20]. Recently, increased interest in this coupling is seen in different aspects such as bioanalysis and determination of heavy metals. Accordingly, direct coupling of nonequilibrium SPME to ion trap has been reported via static desorption in an SPME–HPLC interface. The 70-AL analyte plug was then directly introduced to an APCI (Atmospheric pressure chemical ionization) or an ESI interface. Polydimethylsiloxane fibers were tested for the extraction of spiked calf urine. Despite the absence of a real liquid phase separation mode, problems such as matrix complexity and ion suppression were overcome by the high selectivity of both SPME and MS. Method linearity (0.4–80 ng/mL), reproducibility (2.5–13.7% RSD), and sensitivity (0.4 ng/mL LOD) were adequate, and the combination has proven an efficient and rapid method for the determination of lidocaine in biological samples [21,22]. In a similar manner, PDMS and PDMS/DVB fibers were tested for the extraction of amphetamines and their



Theodoridis and de Jong

methylenedioxy derivatives from urine and their quantitation by electrospray ionization–high-field asymmetric waveform ion mobility spectrometry–mass spectrometry. Desorption occurred dynamically (0.4 mL/min) within a PEEK tubing (150.5 mm) that was fixed in a stainless-steel T connector. Limits of detection in human urine were between 200 pg/mL and 7.5 ng/mL [23]. Solid-phase microextraction has also been used as an introductory technique for matrix-assisted laser desorption/ionization (MALDI) for mass spectrometry and ion mobility spectrometry. A silanized optical fiber served as the sample extraction surface, the support for the sample plus matrix, and the optical pipe to transfer the laser energy from the laser light source to the sample. Atmospheric pressure MALDI ion mobility spectrometer or quadrupole/time-of-flight mass spectrometer was used for the detection of nicotine, myoglobin, enkephalin, and substance P utilizing 2,5-dihydroxybenzonic acid and alpha-cyano-4-hydroxy cinnaminic acid as the ionization matrix [24]. Finally, SPME has recently been coupled directly with atomic spectroscopy techniques for the determination of metal hydrides (As, Se, Sn, Sb) and Ge hydride and chloride [25,26]. For similar purposes, SPME has been used as a sampling technique combined with radiofrequency glow discharge MS for the determination of tetraethyl lead at ppt concentrations [27]. Coupling of SPME with atomic spectroscopy techniques was so far achieved via GC or HPLC. Taking into account the growing importance of metal determination and speciation in biological systems, such a direct coupling may provide an interesting and advantageous alternative for sampling and determination of organometal compounds in various matrices, opening a new prospect for bioanalysis.

III. SORPTION PRINCIPLES AND PARAMETERS In SPME, the extraction can either reach equilibrium (complete extraction) or last for a defined time. In the former case, extraction is considered to be complete and to follow the rules of liquid–liquid extraction. For the established equilibrium of the analyte between the fiber and the solution equilibrium, the distribution constant Kfs is [28]: Kfs ¼

Cf Cs


SPME: A New Tool in Contemporary Bioanalysis



From Eq. (1), with simple mathematics, one comes to Eq. (2) describing n as the number of moles extracted by the coating phase n¼

Kfs Vf Vs C0 Kfs Vf þ Vs


where Vf is the fiber coating volume, Vs is the sample volume, and C0 is the initial concentration of the analyte. From this equation, it is derived that after equilibrium, the relationship of amount extracted and sample concentration is directly proportional. This relationship enables quantitative analysis. Care should be taken since the linear range of the method is affected not only by SPME, but also by the subsequent analytical method. For liquid absorptive fibers, it is very unlikely to observe saturation phenomena and it is thus assumed that the response of the fiber will be linear for most working concentration ranges. However, solid adsorption coatings provide less active surface and (see discussion in Sec. IV) analyte displacement may occur. It is of utmost importance to validate the method in terms of linearity using standard solutions before applying real samples (spiked or not). When the sample volume is very large, Eq. (1) is simplified to: n ¼ Kfs Vf C0


Equation (3) signifies that in cases where Vs is very large, the amount extracted is independent of the sample volume. This indicates the value of SPME for field analysis. Extraction conditions affect extraction recovery to a great extent. The most critical parameters are sample volume, sample pH value, ionic strength (salt concentration), extraction temperature, extraction time, and finally convection or agitation. Detailed discussion on the effect of these parameters on extraction can be found in comprehensive reviews covering the topic [2,29] and the excellent books published recently on SPME [30–32]. Accuracy and precision of SPME can be easily influenced by the above parameters. Optimization of these conditions may lead to large enhancement of the extraction yield. Salt concentration and pH affect SPME as they also affect any extraction procedure. Salt addition can improve the extraction yield. Salts often employed include NaCl, (NH4)2SO4, and Na2CO3 in varying contents. Typically, an increase in the extraction yield is



Theodoridis and de Jong

observed with increasing amount of salt due to ‘‘salting out’’ effect. This can be followed by a maximum and a decrease in yield with further saline increment. In this case, it is believed that polar analytes contributing to electrostatic interactions in saline environment lose their mobility and mass transfer toward the extracting phase [2]. Adjustment of pH may improve the extraction yield for compounds that can be protonated. In most of the cases, pH is adjusted in order to obtain the analyte in its neutral undissociated form to enhance extraction yield since only this form is extracted in absorptive fiber. Care has to be taken when direct-immersion SPME is used since extreme pH values (lower than 2 and higher than 10) can damage the coating. Sample volume selection should be based on the estimated partition constant Kfs. For compounds with high Kfs values, large sample volumes (z10 mL, if available) should be used. For headspace extraction, the gaseous phase volume should be minimized in order to increase the yield. Agitation of the sample is used in order to enhance the extraction recovery with time or to reduce the equilibrium time. The most common agitation methods are magnetic stirring and fiber vibration. An increase in temperature can increase the extraction yield in nonequilibrium situations as a result of diffusion enhancement. The latter will also result to decrease in the time required to reach equilibrium. However, in principle, increase in temperature decreases the distribution constant (and thus to the amount extracted) due to decrease in partition coefficient to the extraction phase. Extraction time varies greatly with times ranging from 1 to 60 min. Solid-phase microextraction is an equilibrium process, but very often, extraction is ended in a fixed time before reaching equilibrium. Equilibrium time is governed by mass transport between sample and coating and therefore affected by coating thickness, agitation method, temperature, and so forth. An attractive option to accomplish reduction in extraction time could be Multiple SPME under nonequilibrium conditions. Koster and de Jong [33,34] studied the theory and the application of performing multiple SPME experiments on the same sample. Theoretically, the yield of multiple extractions is higher than the yield of one extraction of the cumulative time. This was observed in the SPME-LC and SPME-GC analysis of lidocaine, amphetamine, and related drugs from human urine [33,34]. Alternatively, for a standard extraction time, the total yield obtained by

SPME: A New Tool in Contemporary Bioanalysis



multiple SPME was higher compared to single SPME. Theoretically, this enhancement is evident in the extraction of compounds with rather low Kfs. In contrast for analytes with high values of Kfs (Kfs > 10,000), multiple extraction is not likely to improve extraction performance. Characteristic Kfs values are Kfs = 125 for benzene, Kfs = 831 for xylene [28], Kfs = 221 for clozapine, and Kfs = 2671 for loxapine [35]. As a rule, an indication of the value of Kfs can be obtained by octanol–water partition coefficients (Kow). However, this should be regarded as estimation only and experiments should be made to confirm the fit. Special care has to be taken for the determination of partition coefficients. Very nonpolar compounds, such as polycyclic aromatic compounds (PAHs), may be adsorbed into glass

Fig. 6 Gas chromatogram of blank plasma and plasma spiked with 5 nmol/ mL of diazepam (peak 1) and prazepam (internal standard, peak 2). SPME modified with 1-octanol PA fiber. (From Ref. 37.)



Theodoridis and de Jong

walls of laboratory devices (e.g., extraction vials) and Teflon coatings to a substantial extent. Such interactions must be taken into account when calculating partition coefficients. It was shown that failing to do this may lead to large errors in the value of the partition coefficient, particularly for very nonpolar compounds [36]. Krogh et al. [37] used another approach in order to improve extraction recovery. They proposed a solvent-modified extraction procedure that employs the modification of a PA fiber by sorption of 1-octanol before its direct immersion in blood plasma samples. The amount of diazepam extracted this way was twice higher compared to the amount extracted without the use of 1-octanol. The method was further optimized in a recent publication [38]. Parameters, which were found to influence analyte recovery, were studied in a factorial design and response surface methodology. Figure 6 depicts the application of this extraction scheme in the analysis of drugs in plasma. It should be noted, however, that the potential of the method is limited due to the incompatibility of SPME fibers with organic solvents.

IV. COATINGS The efficiency of a separation method is dependent to a great extent on the stationary phase. In a similar way, the efficiency of a SPME method is subject to the choice of fiber coating. The physical and chemical properties of the extracting phase govern extraction selectivity and yield. So far, six coatings are available commercially in 18 different configurations. The main characteristics of these coatings are depicted tabulated in Table 1. The most common PDMS and PA coatings are liquid polymeric phases, where absorption is the major mechanism (Fig. 7). In contrast, divinylbenzene phases have a more rigid crystalline lattice polymeric structure. In these coatings, extraction of the analyte occurs via its adsorption on the surface of the polymer. Additionally, to commercial phases, many other experimental phases have been developed. The selection of fiber coating is mainly based on the principle ‘‘like dissolves like’’ and is of utmost importance for a successful application. This effect is important especially due to the fact that SPME is (almost) never an exhaustive extraction method. The fundamental properties of the various coatings are described in detail in the following paragraphs. Finally, a parameter that should always be taken into account is the stability of coating (fiber) in organic solvents. Polydimethylsilox-

SPME: A New Tool in Contemporary Bioanalysis



Table 1 Characteristics and Major Properties of the Most Common SPME Fiber Coatings Fiber coating Polydimethylsiloxane (PDMS) Polyacrylate (PA)

Thickness Compatibility/ (Am) recommended for 7a 30b 100b 85



Polydimethylsiloxane/ divinylbenzene (PDMS/DVB)c






75 85d 65




Carbowax/DVB (CW/DVB)c Carbowax/templated resin (CW/TPR)


Target analytes Nonpolar organics (VOCs, PAH, pesticides, drugs, etc.) Polar organics (phenols, triazines) Aromatic hydrocarbons, VOCs Amines, polar compounds VOCs, hydrocarbons Polar organic compounds, alcohols Anionic surfactants


Bonded phase. Nonbonded phase. c Partially cross-linked phase. d On a Stableflex fiber. b

ane and PA are liquid phases that may exhibit swelling and shrinking. Caution is required when using chlorinated solvents as these may dissolve the epoxy glue that holds the fiber. Especially for PDMS/ DVB and CW/DVB fibers, extra caution is required. In extreme cases, the polymer coating may swell and drop off the fiber. Newer developments in fiber manufacturing have enhanced stability and tolerance for HPLC mobile phases.

A. Absorptive Coatings In absorption process, the analyte progresses from the bulk of the sample toward the fiber coating. This phenomenon is a combination of convection and diffusion; thus increasing either of these can enhance absorption. Agitation is the best way to increase convection. Diffusion can be increased by increasing the extraction temperature [2,3]. In



Theodoridis and de Jong

Fig. 7 Scheme of the types of coatings for SPME. Liquid absorptive coatings such as PDMS and PA (left) vs. solid adsorptive coatings (e.g., template resin) where adsorption occurs in either large or small pores. (From Ref. 3.)

absorptive coatings, the analytes partition in to the extracting phase, where analyte molecules are solvated. Diffusion of the analytes in the extracting phase facilitates the penetration of the analyte molecules to the whole volume of the coating. The first coatings developed and commercialized were PDMS and PA; these remain still the most popular since they offer generic selectivity and thus adequate recovery for many types of nonpolar analytes. Furthermore, they are rugged fibers of (generally) long lifetime. Nonpolar analytes have relatively high affinity for the apolar PDMS phases. Polyacrylate is more polar and can be used for the extraction of more polar compounds, such as phenols. Mixed phases are mainly used for the

SPME: A New Tool in Contemporary Bioanalysis



extraction of volatile compounds. The extraction yield of these fibers is higher compared to PDMS, but their lifetime is limited. Coating thickness is selected according to the extraction yield required, the extraction time, and the nature of the analyte. The thinner the coating, the faster the partition equilibrium can be reached. The choice of coating thickness is also related to the molecular mass of the analyte: for small molecular weight compounds, high extraction yields can be obtained with relatively thick coatings [2].

B. Solid Coatings Coatings regarded as solid are the divinylbenzene phases used in combination with both GC and HPLC and other experimental coatings used in combination with HPLC for the in-tube approach. In these phases, penetration of the analyte molecules into the core of the polymeric phase is negligible. Such materials posses a well-defined structure of a highly dense network, which reduces the diffusion of the analyte within its structure. Partitioning generally follows a Langmuir isotherm with the assumptions that: (a) molecules adsorb into an immobile state, (b) sorption active sites are homogenous and capable of one to one interaction with analyte molecules, and (c) no interaction occurs between absorbed molecules and neighboring sites [2,39]. However, in multianalyte samples, competition occurs between the analytes for the coating binding sites. Due to its dense structure, the active volume of the polymer is much less and displacement of analytes of low affinity may be observed, especially during long extraction times. This phenomenon may either be considered as a desired selectivity enhancement or as possible source of inaccuracies. In case when the analyte has low affinity for the coating, nonlinearity is often observed. A way to overcome such problems is to utilize extraction times much shorter than the equilibration time and also lesser amounts of analytes. This displacement effect was seen using a homemade polyacrylic acid-coated fiber for the extraction of proteins (Fig. 8). Analytes with low affinity were extracted only when short extraction times were employed. In such a case, the amount of basic proteins adsorbed onto the fiber was found to be proportional to the concentration of the protein. In contrast, during longer extraction, displacement of week binders occurred. Proportionality was also obtained for longer extraction times provided that the protein content does not



Theodoridis and de Jong

Fig. 8 Cation-exchange microchromatography of a mixture of model proteins. Samples: (a) the original sample consisting of myoglobin (M), cytochrome c (C) and lysozyme (L); (b and c) proteins adsorbed onto and then released from a home-made polyacrylic acid-coated fiber with extraction times of 5 and 240 sec, respectively. (From Ref. 40.)

exceed the binding capacity; otherwise, the extraction of strongly absorbed proteins was favored. In longer extraction, displacement of week binders occurred. Figure 8 shows chromatograms of the analysis proteins obtained with the micro-LC system with and without SPME. Because myoglobulin was almost in its neutral form at the used extraction conditions, it was not adsorbed on the cation-exchangercoated fiber. Besides the selectivity, Fig. 8 also shows that cytochrome c is displaced by lysozyme during extraction; that is, at longer extraction time (compare Fig. 8b and c), the amount of lysozyme is increased as the amount of cytochrome c is decreased [40].

C. Special Coatings Lately, innovative phases for SPME have been developed. Media commonly used in liquid chromatography have been validated as possible SPME media. As such, porous bonded silica LC coatings (C8, C18), sol gel media, carbon graphitized silica, molecularly imprinted polymers, and immunoaffinity media have been used for microextraction. This drive is considered a strong future trend since such combinations enhance the advantages of the corresponding methods whereas, at the same time, they suppress their failings.

SPME: A New Tool in Contemporary Bioanalysis



Production of SPME materials by sol gel has attracted immense interest during the last years. Such phases are reported to exhibit high thermal stability and tolerance to organic solvents. Developed sol gel fibers employ polyethylene glycol (PEG), hydroxydibenzo-14crown-4 (OH-DB14C4)/hydroterminated silicone oil or hydroxydiberizo-14-crown-4 (OH-DB14C4), dihydroxy-substituted saturated urushiol crown ether (DBUD14C4), and 3,5-dibutyl-unsymmetrydibenzo-14-crown-4-dihydroxy crown ether (DBUD14C4) coatings. The fibers were validated for the SPME-GC of several organic pollutants and proved to be very stable at high temperature (up to 340–350jC) and in different solvents [41–44]. Molecularly imprinted polymers (MIPs) are media of predetermined selectivity that have found extensive use in separations and analysis. Molecularly imprinted polymers are produced by copolymerization of the analyte (as a template) within a highly dense polymeric network. At the end of polymerization, the analyte is removed, leaving a specific cavity, which should be complementary to the analyte molecule in terms of shape and chemical interactions. If the analyte is extracted by the polymer in a later stage, selective binding will occur in the binding site due to molecular recognition. Molecularly imprinted polymers actually represent another strong trend for high selectivity in separations. The utilization of MIPs in solid-phase extraction was first reported in 1994 [45]. Now it is by far the best studied and most widespread application area for MIP technologies and the first that made it to the market. An expected development was the expansion to microextraction. This was done by two groups independently. The group of Pawliszyn used bulk polymerization to manufacture MIPs for propranolol. The MIPs were used in the fashion of a miniaturized SPE column. Ground polymer particles were packed in a 80-mm PEEK tube, and the MIP minicolumn was fitted in an HPLC system to be used for in-tube microextraction from spiked serum samples [46]. Researchers in Groningen (The Netherlands) followed the fiber geometry to fetch a templated polymer on the outer surface of a fused optical fiber. The plastic coatings of a silica fiber were removed by burning. The fiber was cleaned and treated subsequently with sodium hydroxide, hydrochloric acid, and silylation reagents. The fiber was next dipped in a prepolymer solution that contained the template clenbuterol, and polymerization with simultaneous coating of the fiber was initiated by UV radiation. The obtained coated fibers were washed with a mixture



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of acetic acid and methanol (10:90 v/v) to remove the template and free the binding active sites. The methacrylate MIP coatings had a film thickness of f75 Am. The MIP fibers were used to trap analog molecules from aqueous solutions. Subsequent washing with acetonitrile (the polymerization solvent) facilitated removal of impurities and selective binding of the template and related molecules on the fiber. As can be seen in Fig. 9, acetonitrile washing removes interfer-

Fig. 9 HPLC-ECD chromatograms following SPME of blank urine (a), urine spiked (100 ng/mL) with brombuterol and washing of the fiber (b), blank urine and washing of the fiber (c). Fibers were washed in 200 AL of acetonitrile. Injection of 20 AL of the desorption liquid. Brombuterol is the peak indicated by the arrow. (From Ref. 39.)

SPME: A New Tool in Contemporary Bioanalysis



ing peaks from urine samples (compare Fig. 9a and c). In contrast, the analyte brombuterol remains on the MIP fiber. The method provided efficient cleanup and a satisfactory yield (40%) [47]. Especially for these phases, capacity and therefore method linearity are limited. Immunoaffinity extraction (IAE) is another way to combine a molecular recognition mechanism with the high-resolution power of the separation techniques. In this method, antibodies specific for a given analyte are immobilized on an appropriate support. The obtained medium should exhibit specificity for the analyte, facilitating very selective binding from a variety of matrices. Immunoaffinity extraction is now established in environmental and biological analysis as a powerful tool for sample purification and analyte preconcentration. The combination of IAE with SPME faces some important limitations: (a) antibodies are proteins, which do not tolerate extreme ionic strength, pH values, and temperatures, (b) desorption should be limited to liquid, and (c) nonspecific binding on the core of the base material should be prevented. Yuan et al. [48] immobilized antitheophylline serum on a silica fiber that had been previously modified with

Fig. 10 Competitive binding of cold theophylline with [3H]theophylline to the antitheophylline antibodies immobilized on a fused silica fiber. The [3H]theophylline was kept at saturation value (4 ng/mL), whereas the concentration of added cold theophylline was varied. (From Ref. 48.)



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3-aminopropyltriethoxysilane and subsequently with glutaraldehyde. The immunofiber was used for the specific binding of theophylline or a radioactive tracer ([3H]theophylline) from human serum. Quantification was accomplished in a scintillation counter, and both competitive and noncompetitive assays were performed (Fig. 10) [48]. Further developments toward this route are expected. Lately, special attention is given to polypyrrole (PPY) coatings for the extraction of ionic analytes. Exploiting its natural anion exchange properties as a conducting polymer, PPY was examined for direct SPME of anionic species from aqueous solutions without derivatization. Polypyrrole is coated on fused silica capillary’s inner surface (GC precolumn) by chemical polymerization. The inherent multifunctionality of pyrrole polymer (k–k electrons, interactions by polar functional groups, and hydrophobic interactions) may enhance extraction efficiency for both

Fig. 11 Effect of coating polymer chemistry on extraction efficiency for intube SPME of a series of h-blockers. (From Ref. 2.)

SPME: A New Tool in Contemporary Bioanalysis



polar and nonpolar aromatics in aqueous samples. Various analytes have been already tested on such coatings: catechins, caffeine, aminecontaining drugs, beta-blockers, organoarsenic compounds, and aromatic compounds [49–53]. Preliminary studies indicate that adsorption governs the extraction mechanism on such polymers. Acid–base interactions and ionic properties of PPY are advantageous features for future applications. Figure 11 depicts an example of the effect of varying coating selectivity on extraction yield. Diversifying extraction efficiency for the four different types of coatings is clearly observed for their use for in-tube SPME of pharmaceuticals. It is evident that PPY provides an overall superior efficiency for the extraction of the drugs of interest. Other innovative approaches include the utilization of polycrystalline graphites in the form of pencil leads for the microextraction of a nonionic alkylphenol ethoxylate surfactant [54], fibers coated with polymeric furelenes for the extraction of BTEX, naphthalene congeners, and phthalic acid diesters from water samples [55], anodized aluminum wire for aliphatic alcohols, BTEX, and petroleum products from gaseous samples [56], and low-temperature glassy carbon films for aromatic hydrocarbons [57].

V. DERIVATIZATION Derivatization is a useful practice often encountered in contemporary analysis in order to enhance the analytical behavior and the signal obtained from certain analytes. The truth is that derivatization is often called ‘‘a necessary evil’’; however, more and more workers tend to study and develop derivatization schemes to improve their analytical results. Currently, analysis of polar compounds is a major challenge since their isolation and analysis is often problematic. Hence in chromatographic separations, derivatization mainly aims at the reduction of polarity. Another chief objective is the introduction of an appropriate moiety to enhance detection sensitivity (e.g., the introduction of fluorophore for HPLC detection). For SPME, the need for derivatization mainly aims at the improvement of chromatographic behavior in GC. Hence polarity reduction is the major goal of the derivatization process. This is achieved by introducing moieties such as alkylsilyl, acetyl, and chloroformates to couple polar groups of the analyte like hydroxyl, amino, and carboxyl active groups.



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Derivatization may be performed prior to extraction, combined with the extraction, or following the extraction procedure. In the first case, derivatization is performed in the sample itself. For derivatization in the sample, the derivatizing agent is added to the sample matrix or to an appropriate extract derived from the sample. Since the majority of the samples analyzed with SPME are aqueous, direct derivatization in situ necessitates the formation of stable derivatives in aqueous environment. As such derivatizing agents, alkylchloroformates seem promising. Several alkylchloroformates have been tested for the derivatization of primary amines in water. The reaction is well known in peptide chemistry as a protecting reaction for peptides and aminoacids. The resulting carbamates are stable in water and are satisfactorily extracted by SPME. The method has been applied to the derivatization of amphetamines according to the reaction equation [58,59]: RNH2 þ CICO  OR2 ! RNH  CO  OR2 þ HCl For the derivatization of organic acids, reagents like borates, chloroformates, and benzyl bromide have shown good results. The reaction of acetic acid with benzyl bromide in aqueous solution resulted in the formation of benzyl acetate. However, reaction of acetic acid with hexylchloroformate did not yield the desired derivative. In contrast, hexylchloroformate successfully derivatized benzoylecgonine [60]. Trimethyloxonium tetrafluoroborate was used as a derivatizing agent to modify 29 organic acids in urine samples via a rather cumbersome procedure [61]. Benzodiazepines have been derivatized in urine to benzophenones by acid hydrolysis. The derivatives can better be extracted by direct immersion SMPE rather than HSSPME [62] because they are not volatile. Alternatively, a fast liquid–liquid extraction may be employed to transfer the analytes of interest to organic environment, which is necessary for conventional derivatization reactions (silylation, alkylation, acylation) [63]. This strategy may seem more convenient and easy to adapt to existing analytical protocols but in fact shrinks the distinctive features of SPME as a solvent-less technique. Lately, however, several derivatization procedures in aqueous environments have been developed utilizing novel reagents. Thus the development of a direct derivatization in the presence of water is not such an obstacle as it used to be.

SPME: A New Tool in Contemporary Bioanalysis



Simultaneous extraction and on-fiber derivatization is a very promising approach. This is a straightforward scheme that may deliver high efficiency for both extraction and derivatization reactions. The best way to perform such a scheme is to introduce first the derivatizing reagent on the fiber either by dipping the fiber in the reagent solution or by exposing the fiber to its headspace. Next, the fiber is introduced to the sample. As the analyte molecules are sorbed on fiber, they are continuously converted to derivatized analogs. Since derivatization occurs on the fiber, extraction cannot proceed toward equilibrium. Notable examples of this approach are the simultaneous HS extraction and derivatization of fatty acids with pyrenyldiazomethane to produce pyrenylmethyl ester [64], formaldehyde with o(2,3,4,5,6,-pentafluorobenzyl)hydroxylamine hydrochloride [65], amphetamines with pentafluorobenzoylcholride [66] and acetic anhydride [63], and aldehydes with pentafluorophenylhydrazine to form hydrazones [67]. On-fiber derivatization after extraction is performed for analytes that exhibit adequate extraction efficiency but require enhancement for their GC analysis. Polar analytes such as carboxylic acids, amphetamines, steroids, and hydroxyl metabolites of PAHs can thus be derivatized on-fiber after extraction to improve peak shape and detection sensitivity. In this case, the fiber with the extracted analytes is exposed to the headspace of the derivatization reagent [68,69]. The enhancement achieved by derivatization is clearly exemplified in Fig. 12 where the chromatograms of high molecular mass carboxylic acids are depicted prior and after on-fiber derivatization. Following extraction, the SPME fiber was exposed to diazomethane. The resulting esters provide sharp peaks in GC (Fig. 12b). On-line derivatization may occur also with SPME-LC configurations. In such schemes, the fiber following extraction is desorbed statically in an organic solvent containing the derivatization reagent. Next, the interface/injection valve is switched driving the derivatized analytes toward the analytical column. The method was tested for the SPME of alcohol ethoxylates and their derivatization with 1-naphthoyl chloride [70]. Another alternative is to perform the derivatization inside the GC injection port during the desorption of the SPME fiber. In one approach, amphetamines were extracted by headspace SPME from whole blood. The analytes were desorbed in the hot GC injection port, where heptafluorobutyric anhydride had been injected. Thus desorp-



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Fig. 12 Improvement of peak shapes by derivatization of carboxylic acids. (From Ref. 2.)

tion and derivatization occurred simultaneously. Such an approach requires fast derivatization kinetics and on-column focusing to avoid peak tailing [71].

VI. BIOANALYTICAL APPLICATIONS Solid-phase microextraction was initially introduced as a new tool for the extraction of organic compounds from environmental samples. However, in the last few years, the method has gained a lot of interest in a broad field of analysis including food, biological, and pharmaceutical samples. Successful coupling of SPME with LC and CE enables the analysis of a variety of polar or macromolecular analytes of biological significance: proteins, polar alkaloids, pharmaceuticals, and so forth. Furthermore, the development of HS-SPME provided a powerful alternative for the sampling and pretreatment of various biological samples such as urine, blood plasma, and hair [72]. Urine is one of the most important samples in bioanalysis and certainly the

SPME: A New Tool in Contemporary Bioanalysis



most important sample for toxicological analysis. As a sample for SPME, urine may be used by either direct immersion or headspace extraction. Regulation of ionic strength and pH value by addition of salts may improve extraction yield. Blood plasma and serum are rather complex samples of great significance for clinical chemistry, toxicology, therapeutic drug monitoring, and other analytical aspects. Solid-phase microextraction is mostly used in headspace mode to trap volatiles or semivolatile analytes. Direct immersion and in-tube SPME protocols have also been used, but they may result to shortened fiber lifetime or capillary clogging. Therefore special attention and thorough protein precipitation may be necessary. Hair sampling has evolved as an attractive noninvasive method especially suited for toxicological analysis; thus hair is now considered the third fundamental biological specimen for drug testing besides blood and urine. Drug metabolites or nonmetabolized drug molecules are distributed in hair either incorporated in the hair shaft from blood or due to adsorption from other media from the environment (sweat, smoke, etc.). As the hair grows with a certain rate, hair specimens may provide a historical record of exposure of the individual and can be later found there when often they are not detectable in other tissue. The application of headspace SPME for hair analysis of organic compounds has recently been reviewed [73]. Noteworthy application areas of SPME in bioanalysis can be found in the following major directions.

A. Analysis of Pharmaceuticals Solid-phase microextraction has found extensive use in the determination of pharmaceuticals in either pharmaceutical preparations or biological samples. Antidepressant drugs, valproic acid, steroids, anorectic agents, anesthetics, and many other types of pharmaceutical agents have all been analyzed by GC or LC following SPME. Solid-phase microextraction provides a powerful alternative to existing methods for the extraction of blood plasma and serum. Hence SPME may also find use in therapeutic drug monitoring. An example is seen in Fig. 13: SPME with a 100 Am PDMS fiber was used to extract spiked plasma samples. Recently, comprehensive reviews on the use of SPME for the analysis of drugs have covered the field [2,72,74–77]. In these reviews, detailed information on applications and methods is given.



Theodoridis and de Jong

Fig. 13 SPME-GC-NPD chromatogram of antidepressant drugs in human plasma. (1) Amitrytyline, (2) trimpramine, (3) imipramine, (4a) cis-doxepin, (4b) trans-doxepin, (5) nortriptylin, (6) mianserine, (7) desipramine, (8) maprotilline, (9) clomipramine, (10) desmethylchlomipramine, (IS) chlomipramine, 375 ng/mL of each analyte, extraction for 30 min. (From Ref. 75.)

B. Toxicological and Forensic Analysis Toxicological analysis is a field where routine and research are integrated to a great extent. Novel methods are often rapidly implemented to advance the tasks of toxicological laboratories (provided that the quality of a new method is evident and undoubtful). Solidphase microextraction offers great advantages to toxicological analysis in both research and routine analysis. Headspace SPME-GC-MS has proven a powerful tool in toxicological analysis. The preconcentration of the analytes obtained on PDMS and PA fibers offers great advantages compared to conventional headspace GC-MS. Therefore many toxicological laboratories have implemented SPME and developed such methods for the analysis of numerous analytes in a variety of matrices: alcohol in blood, VOCs in plasma and blood, poison agents (malathion, cyanide), nereistoxin, chlorophenols, organochlorines persistent in blood, PAHs, and mercury and other heavy metals species in blood and other biological specimens [26,72,77]. Drugs of abuse is probably the widest application field of analytical toxicology and the most common task of such laboratories. The

SPME: A New Tool in Contemporary Bioanalysis



combination of SPME with gas chromatography-mass spectrometry (GC-MS) has found extensive use for the determination of amphetamines, benzodiazepines, barbiturates, methadone, cannabinoids, alkyl nitrites, tricyclic antidepressants, and other drugs of abuse. The field has been covered by comprehensive reviews [72,75–77]. An example of the utilization of SPME in the analysis of drugs in hair is depicted in Fig. 14. GC-MS analysis combined with HS-SPME to recover the drugs from spiked hair [76]. Solid-phase microextraction has also been coupled to HPLC and CE for the analysis of barbiturates, benzodiazepines, and other drugs of abuse [Table 1 in Ref. 72].

C. Clinical Chemistry Solid-phase microextraction has also found use in clinical chemistry. Compared to existing techniques, it shows significant benefits and offers a good alternative to conventional methods [72,74–77]. Although the use of liquid-phase separations has by far outnumbered that of GC in clinical chemistry, SPME-GC has found a niche and has been used for a variety of studies: the investigation of drug metabolism in human keratinocyte cells [78], the study of metabolism and excretion of benzophenone [79], and the determination of putrescine and cadaverine [19], monocyclic aromatic amines in biological fluids in screening for trimethylaminuria (fish odor syndrome) [80], urinary

Fig. 14 GC-MS (single-ion monitoring) following HS-SPME of 10 mg of hair spiked with 16 drugs. Concentrations: 1 ng/mg. (From Ref. 76.)



Theodoridis and de Jong

organic acids in metabolic studies [81], carnitine (an essential factor in the fatty acid metabolism of organisms) [82], and aminoacids [28]. Figure 15 illustrates the potential of SPME in clinical chemistry. Feces from an adult on a normal diet were dried, acidified (pH 1–2), and saturated with NaCl. A 75 Am PDMS fiber was exposed to the headspace for 30 min and desorbed in the GC injector (250jC, 2 min). Compounds derived from food products and end metabolism products (4-methylphenol, dimethylsulfide) were determined [76]. Determination of biomarkers in exhaled human breath attracts an increasing interest in clinical chemistry and diagnosis as an alternative noninvasive method. More than 100 VOCs have been identified in normal human breath by GC-MS. The methods currently used for sampling and preconcentration (chemical interaction, adsorptive binding, cold trapping) are tedious procedures, they require complex devices, and they suffer from particular problems (e.g., excess of water from the breath). Solid-phase microextraction offers an alternative that can overcome such limitations. The fiber can be directly exposed in the mouth of the subject. An inert tubing is added to a commercial SPME device in order to protect the fiber from the subject’s tongue (Fig. 16). The method demonstrates significant

Fig. 15 GC-MS profile of VOCs in the HS offeces of an adult with normal diet. Peak identities: (1) dimethylsulfide, (2) acetic acid, (3) propionic acid, (4) isobutyric acid, (5) n-butyric acid, (6) 2-methylbutyric and isovaleric acids, (7) n-valeric acid, (8) isocaproic acid, and (9) 4-methylphenol. (From Ref. 76.)

SPME: A New Tool in Contemporary Bioanalysis



Fig. 16 Device for the sampling of human breath. (From Ref. 83.)

advantages compared to existing extraction techniques, requiring only 1–3 min for sampling and providing detection limits in the low nanomolars per liter range [83].

D. Affinity Measurements The measurement of binding affinity is a worthy application field for SPME [84–87]. Solid-phase microextraction is rarely an exhaustive extraction method; thus it causes negligible depletion of the analytes. Hence the method is a very well suited method for the quantification of the free quantity of analytes participating in equilibria (e.g., protein binding). In contrast, in exhaustive extractions (employing solvents or a solid-phase bed), the equilibrium between matrix components (proteins) and the drug is disturbed. This leads to a shift of the equilibrium toward the freely dissolved fraction. Vaes et al. [84] used PA-coated fibers to measure the protein binding of four polar drugs (aniline, nitrobenzene, 4-chloro-3-methylphenol, and 4-n-pentylphenol). The determination of binding to bovine serum albumin (BSA) by (nondepletion) SPME gave comparable results to equilibrium dialysis. It was shown that increasing hydrophobicity results to an increase in affinity for BSA [84]. The group extended the concept to predict absorption profiles and kinetics using quantitative structure–activity relationships [85] and to investigate the correlation of membrane/water partition coefficients with free concentrations in in vitro systems [88]. Researchers at the same university employed nonequilibrium SPME for the determination of freely dissolved analytes in complex matrices (chyme) [89]. If protein binding occurs in one to one molar ratio, binding constants can be calculated. This concept was exploited by Yuan



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and Pawliszyn [86] in order to determine binding constants of diazepam to human serum albumin utilizing Scatchard plots. The method may work even in a four-compartment system: matrix (protein), solution, headspace, and fiber. Hence SPME was used to measure the concentrations of alkylbenzenes (volatile drug) in the headspace of a solution containing also BSA [90].

VII. POSSIBILITIES AND LIMITATIONS OF SOLID-PHASE MICROEXTRACTION Solid-phase microextraction exhibits certain advantages that have brought the technique to the forefront of contemporary analytical chemistry. Of these advantages, the most significant are: no use of solvents, ease of handling, in-line coupling to GC, no need for expensive sophisticated instrumentation, automation capabilities, and its nature as a microtechnique. Solid-phase microextraction is very useful in miniaturized systems as is demonstrated for the combination with micro-LC and CE. The fiber geometry allows an efficient and low dead-volume coupling with these techniques’ automation capabilities. The automation capabilities of SPME are a great advantage taking into consideration the continuous drive toward utilization of more controlled and automated methods. Compared with other extraction methods like LLE and SPE, SPME when coupled to GC does not need specific devices and can be easily automated. Direct-immersion SPME can be very easily automated by modification of conventional autosamplers in order to host the SPME fiber instead of the sampling needle. To automate HS-SPME, the autosampler should also allow controlled heating of the sample vial. Yet maybe the most important feature of SPME is the integration of sampling and extraction in one step and the subsequent straightforward sample introduction. The method eliminates steps in the analytical process and thus eliminates the sources of possible errors. Not only time and resources are saved, but also most important precision and accuracy of the method can be controlled to a better extent. However, no matter how attractive SPME seems to the reader, it is not always the same undemanding to the practitioner. The conditions of SPME should be precisely controlled in order to achieve accurate and reproducible measurements. As a dynamic multivariate

SPME: A New Tool in Contemporary Bioanalysis



method, SPME requires control of the most important parameters that affect the process: agitation, sampling time, temperature, sample volume, vial volume (for HS-SPME), sample matrix, and additives. Calibration methods used with SPME are external standard, internal standard, and standard addition. External calibration is probably the most widely used calibration method especially in cases of little variance between samples [2]. For biological samples, care has to be taken in order to maintain constant ionic strength. In cases of high concentrations, dilution may be necessary, whereas in trace analysis, a large urine volume can be used. In such cases, normalization of the ionic strength by salt addition is often performed. Standard addition is another alternative for variable samples. The sample is analyzed, and then a known amount of the analyte is added and the sample is processed again. Extraction can even be made from the same sample amount if negligible analyte depletion occurs in the first extraction. The use of internal standard can work satisfactory in SMPE under some conditions. Extraction time profiles should be determined also for the internal standard. If there are large differences in equilibrium times, large errors may occur. Very precise time programming should be applied to obtain reproducible results. Furthermore, the use of internal standard with adsorptive coatings may result in competitive binding, displacement, and therefore large errors. Finally, when a competing phase is present in the sample (e.g., proteins, humic acids), the use of internal standard faces another limitation. The affinity of the internal standard toward the competing face may be very different from the analyte affinity. Fiber SPME is especially attractive in the case of specific application fields such as the measurement of binding affinity or proteinfree drug concentrations. Coupling of fiber SPME with HPLC and other liquid separation methods is a practical alternative to the use of SPE especially if certain needs are thus covered, e.g., nondepletion extraction and field sampling. In other cases, the use of SPME can hardly compete with SPE since SPE offers much greater array of stationary phases and thus stationary phase selectivities. It is believed, however, that continuous research in that direction will result on the development of new innovative phases/coatings for SPME. Nevertheless, comparing the two extraction modes is a trivial effort since the two processes differ to their very nature. Proper judgment could be done when comparing on-line SPE with SPME. Additionally, SPE is often a multistep procedure employing quanti-



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tative (in most cases) trapping of the analytes on the bed, appropriate washing, and elution in a chosen solvent. Very often, the washing step(s) is the most critical stage. For example, in SPE, the most common approach is to trap the analytes in general (hydrophobic interactions), wash out unwanted impurities in subsequent washing steps, and finally, recover the analyte ofinterest in a final elution step. In contrast, selectivity of SPME seems more based on the diffusion process and the sorption of the analytes on the coating. As a rule, SPME does not employ washing steps, but only a direct desorption step. This simplicity, which is considered SPME’s major advantage, may also prove a drawback. In certain cases, simple SPME protocols may not reach the selectivity and cleanup obtained by three- or fourstage LLE or SPE [35]. Multistep protocols could also be used with SPME and with much easier handling and lower consumption of organic solvents. Such procedures are not yet developed probably because they would lessen the simplicity of the technique. In general, SPME provides low recoveries. However, this problem is overcome by the fact that the total extracted compound is subsequently determined. Solid-phase microextraction should be calibrated carefully (see above), but then, it provides very satisfactory sensitivity, linearity precision, and accuracy. It is unlikely that SPME will become a universal method. Scientists and practitioners should comprehend such methods as useful alternatives to existing methods. Solid-phase microextraction offers improvement in several characteristics of conventional practices. The method has already found a wide application area, and it is seen to find numerous additional utilizations. Furthermore, SPME may expand to cover applications such as the analysis of small samples, analysis of air samples, field sampling affinity measurements, and determination of free analyte concentration (e.g., drug in plasma). For example, as seen in Fig. 1, the increase on publications reporting on SPME originating from food/flavor analysis exhibits the strongest trend of all the fields. Such a trend is easily understood considering the superior advantages that SPME offers for this specific scientific area: sampling from individual organisms, sampling for specific time cycle of the life of the organism, convenient and reproducible field sampling, and no need for calibration of air pumps. An important field for SPME may be the automation of forensic and toxicological analysis. Samples found positive by automated

SPME: A New Tool in Contemporary Bioanalysis



immunoassays need to be confirmed by an independent method. In common practice of this application field, this means GC, employing LLE, SPE, and derivatization for many groups of analytes. Such laborious methods could be integrated in automated SPME protocols, provided that the further development and the validation of such methods will prove them reliable for such tasks. It is thus believed that SPME will become an established methodology in this specific but also in other bioanalytical fields, and that its applications will increase to an even greater extent in the near future.


Benzene, toluene, ethylbenzene, xylene Bovine serum albumin Capillary electrophoresis Carboxen/polydimethylsiloxane Carbowax/divinylbenzene Carbowax/templated resin Direct immersion Enzyme-modulated immunotest Enzyme-linked immunosorbent assay Electron spray ionization Flame ionization detection Fluorescence polarization immunoassay Gas chromatography High-performance liquid chromatography Headspace Immunoaffinity extraction Liquid chromatography Liquid–liquid extraction Molecularly imprinted polymers Mass spectrometry Polyacrylate Polycyclic aromatic hydrocarbon Polydimethylsiloxane Polydimethylsiloxane/divinylbenzene Polyether ether ketone Polyethylene glycol Polypyrrole



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Solid-phase microextraction Solid-phase extraction Volatile organic compounds

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SPME: A New Tool in Contemporary Bioanalysis 69.



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5 Polyelectrolytes as Stationary Phases in Liquid Chromatography Lilach Yishai-Aviram and Eli Grushka Department of Inorganic and Analytical Chemistry, The Hebrew University, Jerusalem, Israel



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I. INTRODUCTION Chemically modified silicas are used ubiquitously as stationary phase support in liquid chromatography (LC). In spite of alternative column packing, such as zirconia, alumina, titania, etc., silica continues to be the most commonly used packing material in modern LC. The main advantages of silica are its high level of mechanical strength, uniformity in terms of size and surface area, and purity. These qualities permit the formation of efficient packed beds that remain stable under high operating pressures for long periods of time [1]. The surface of silica consists of various kinds of silanols and siloxane bonds [2,3]. The siloxane (Si–O–Si) sites are hydrophobic and contribute little or nothing to the retention of polar solutes. However, the hydrophobic nature of the siloxane bond makes it possible to observe some retention of nonpolar solutes [4]. On the other hand, the silanol groups, which can be hydrated by adsorption of water, are polar and are considered to provide strong adsorption sites [3,5,6]. Basic analytes can interact strongly with the acidic silanols. The silanols can exist in three different forms [5]: single (isolated), geminal, or vicinal form. The degree of ionization of the silanols depends on the pKa values of the different silanol groups in the particular mobile phase used and on the pH of the mobile phase. Mendez et al. [7] found that for the two types of columns, silica and C18, there are two types of silanols with pKa values of about 3.6 and 6.3. Thus, the silica surface is negatively charged from a relatively low pH. In silica-based columns (normal phase as well as reversed phase,) it is possible to work only within a relatively narrow pH range, usually between 2 and 7.5. One of the approaches to overcome this limited pH range is to use new types of polymer-based phases [8] including polymer-clad silica gel particles, which are the subject of this review. These new polymeric phases have an added advantage of offering new and unique selectivities that cannot be attained using conventional silica gel. Most of the polymeric stationary phases in use are neutral [9–13]. However, the range of polymeric stationary phases can be expanded to include polyelectrolytes. For example, positively charged polymers [14–18] can be adsorbed on silica particles by electrostatic interactions over a wide range of pH due to the fact that the surface of the silica has partially negative charge. On these positively charged surfaces, it is easy to adsorb negatively charged polyelectrolytes to form a multilayer [19–21].

Polyelectrolytes as Stationary Phases / 275 There are two main approaches for making silica-based polyelectrolyte stationary phases. One approach is to coat the silica gel particles in a batch mode outside the column. Once coated, the column is then packed using conventional high-performance liquid chromatography (HPLC) packing techniques (e.g., see Krokhin et al. [22] and Pirogov et al. [23]). The batch mode of preparing polyelectrolytecoated columns is relatively straightforward. There are three different methods to coat silica with charged polyelectrolytes. The first method forms covalent bonds [24] between the polymer and the support material by refluxing the two components in toluene for several hours [25,26]. The second approach utilizes electrostatic interaction between the silanol groups on the silica support and a cationic polymer, which can be irreversible. The third approach is physical adsorption, which can be accomplished by several different ways: thermal treatment [11], irradiation with microwave and gradiation [27], and self-immobilization [28]. In all these approaches, the stationary phases are prepared outside the column. Once prepared, the columns are packed using slurry packing techniques. The main advantage of preparing the phases outside the column is the wide range of polymers that can be used for coating [e.g., (x,y)-ionene bromide [29] or copolymers such as poly(ethylene-co-acrylic acid) [30]]. Other advantages of the ‘‘outside-the-column’’ approach are the ability to determine the exact amount of polymer bonded to the silica and the capability of characterizing the newly formed stationary phase without having to empty the column. The second approach to prepare silica-based polyelectrolyte stationary phase is to coat the column dynamically in situ. In this approach, the coating solution is passed through the column that has been packed previously with the silica support. Conventional chromatographic equipment is used for transporting the coating solution through the column. Of the two approaches, the batchwise method is, by far, the most prevalent. The dynamic coating technique is an in situ method used to prepare stationary phases for HPLC, capillary electrophoresis, and capillary electrochromatography. In the literature, we often find that the expression ‘‘in situ coating’’ refers to batch-mode methods in which the polymerization proceeds directly on silica gel particles prior to column packing (e.g., Carbonnier et al. [31] and Mao and Fung [32]). In this review, we use the term in situ to indicate a coating process in which a solution containing the coating material is passed

276 / Yishai-Aviram and Grushka through a column already packed with the appropriate chromatographic packing. As mentioned, dynamic coating is not used often to produce polymer-coated stationary phases for HPLC. However, due to its simplicity, the dynamic coating technique has potential benefits in terms of cost, ease of preparation, and stability. As a result, we will discuss the technique in some greater details in Section 2.

II. THE PRINCIPLE OF DYNAMIC COATING The term ‘‘dynamic coating’’ was first employed by Ghaemi and Wall [33] and later by Hansen [34] and Helboe et al. [35] (and references therein). These authors coated dynamically naked silica with a salt of an alkyl quaternary amine. The cationic quaternary amines in the mobile phase are attracted, by electrostatic forces, to the negatively charged silanol. After reaching equilibrium, three phases are present: the adsorbed quaternary ammonium salt as the stationary phase, unadsorbed amines, and micelles in the case where the concentration of the quaternary amines in the mobile phase exceeds the critical micellar concentration (CMC). The amount of adsorbed amine was found to depend on the silica surface and on the amine’s alkyl chain length [36]. In general, dynamic coating can be carried out on any column packed with conventional chromatographic medium (e.g., silica gel, reversed-phase material, etc.) by passing through the column a solution containing the new stationary phase component. The additive to the mobile phase adsorbs on the existing stationary phase, thus changing the nature of the stationary phase. Usually, but not necessarily, the coating procedure continues until the stationary phase is saturated with the adsorbed components. The adsorbing stationary phase (the old stationary phase) can be naked silica or a bonded phase, depending on the desired new stationary phase. Ion-pair chromatography, a well-established technique used to separate charged analytes, also takes advantage of dynamic coating [37–39]. Negatively or positively charged surfactants are added to the mobile phase to create the new stationary phase. Most often, the column contains a hydrophobic bonded phase (e.g., RP8 or RP18) and the surfactant additives are either negatively charged or positively charged, depending on the application at hand. Frequently, alkyl sulfates or sulfonates are used as negative surfactants, and tertiary

Polyelectrolytes as Stationary Phases / 277 or quaternary amines are used as positive ion-pair reagent. In ionpair chromatography, the additive is present in the mobile phase both during the stationary phase modification stage and the separation stage. On the other hand, in classical dynamic coating situations, the mobile phase additive is there only for the new stationary phase generation and is absent in the separation stage. Although ion-pair chromatography is an important variant of dynamically coated chromatographic systems, it will not be discussed here. Many reviews are devoted solely to ion-pair chromatography (e.g., see Refs. 40 and 41). In the context of this chapter, dynamically coated columns are columns coated with polyelectrolytes. The mobile phase in these cases does not contain the modifying polymers. We can expend the ‘‘classical’’ dynamic coating techniques by working with polyelectrolytes. Silica columns are easiest to coat due to the presence of negative charges. A positively charged polymer is added to a suitable mobile phase, which is then passed through the column using the chromatographic pump. As the polymer passes through the column, its positive charges interact with the Si–O groups on the silica packing. Once the column is loaded, the polymer is no longer present in the mobile phase. It should be noted that during the polyelectrolyte loading stage, the pump pressure is high due to the viscosity of the polymer-containing solution. However, during the separation part, because the polyelectrolyte is no longer present in the mobile phase, the pressure is typical of HPLC systems. Due to the strong electrostatic interactions between the polyelectrolytes and the charged silanols groups on the silica, the modified column is highly stable. The dynamic coating technique is very common in capillary electrophoresis (e.g., Refs. 42–49) and in capillary electrochromatography (viz. Refs. 50 and 51). The use of a quaternary ammoniumbased polymer, which interacts strongly with the surface of the silica, has been proven successful. Figure 1 describes the adsorption behavior of poly(diallyldimethylammonium chloride) (PDADMAC), a polycationic electrolyte, on negatively charged silica [52]. The amount of adsorbed PDADMAC increases, irrespective of the molecular weight, with an increase in the pH of the coating solution. The increase in adsorption is due to rising surface charge density caused by the ionization of silica silanol groups. In addition to the pH, the ionic strength of the polyelectrolyte coating solution has a strong influence on the adsorption of the

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Fig. 1 The pH dependence of PDADMAC adsorption on silica gel. (From Ref. 52. nElsevier.)

polymer [53,54]. Increase of the ionic strength increases the adsorption of the positively charged polymer (see Fig. 2) [52]. The salt has two effects: it changes the structure of the polyelectrolyte in solution, and it changes the adsorption of the altered polyelectrolyte to the silica [15]. Thus, it is highly important to maintain constant ionic strength. As in the ‘‘classical’’ dynamic coating technique, the mobile phase can be of any kind. Most often, it is a buffer mixed with methanol, acetonitrile, or tetrahydrofuran. Juskowiak [55] suggests that the pH of the ‘‘conditioning mobile phase’’ during the initial treatment of silica is a crucial factor in governing surface coverage. For the dynamic coating technique to be effective, it is important to understand the factors governing the adsorption of the coating material, such as the amount of modifier in the coating solution, its pH, the molecular weight of the polymer, and the charge of the polymer [56]. Polyelectrolytes should be charged over a wide pH range. The polymer should be soluble in the mobile phase and should not affect the detection of the analytes. There are no special requirements from the column being coated over and above the conventional chromatographic requirements such as being well packed. The dynamic coating technique has several advantages as follows. It is easy to perform and does not need any additional instru-

Polyelectrolytes as Stationary Phases / 279

Fig. 2 The ionic strength dependence of PDADMAC adsorption on silica. (From Ref. 52. nElsevier.)

mentation over and above a routine liquid chromatograph. The columns thus prepared can be applied for the separation of ionic and nonionic solutes. Last but not least, the columns prepared by dynamic coating are reproducible irrespective of the original brand of the column.

III. COLUMN CHARACTERIZATION Coated stationary phases can be characterized chemically, physically, and chromatographically (e.g., see Tonhi et al. [57,58]). Although the coated packing material described in these references was prepared outside the column (not dynamically in the context of this review), the methods of characterization used are universal and can be applied for in situ cases as well. Among the physical and chemical approaches to the characterization of the polymeric phases, we find the following: Carbon content: The percent carbon in the silica plus polymer phase can be obtained through elemental analysis, which is

280 / Yishai-Aviram and Grushka carried out before and after the polymer coating. In this way, we can evaluate the amount of stationary phase in the column. Thermogravimetric analysis (TGA): TGA allows us to ascertain the thermal stability of the coated polymer vs. the polymer by itself. Infrared spectroscopy (IR): IR evaluates the presence of residual silanols and thus indicates the efficiency of the coating procedure. In addition, IR can shed light on the interactions between the polymeric coating and the silica gel matrix underneath. Nuclear magnetic resonance (NMR): 13C cross-polarization magic angle spinning (CP-MAS) NMR can be used to analyze possible interactions between the polymer and the silica gel support. Scanning electron microscopy (SEM): SEM analysis provides morphological information on the coated polymeric stationary phase. Atomic force microscopy (AFM) [59,60]: Similar to SEM, AFM yields information on the morphology of the coated layer. X-rays techniques [31,60]: Various X-ray spectroscopy methods can be used to obtain information on the chemical composition of the coated phase as well as on the nature of the coated surface. Small-angle neutron scattering (SNAS) [61]: This technique provides a direct determination of the stationary phase thickness and bonding density. A different kind of characterization is obtained by examining the interaction of the coated polymeric stationary phase with different test solutes. This approach is the chromatographic characterization and it is complementary to the physical and chemical methods described above. The chromatographic interactions that can be examined include hydrophobic interactions, hydrogen bonding, ion exchange capacity, steric selectivity, silanol activity, etc. Kimata et al. [62], Galushko [63,64], Czok and Engelhardt [65], as well as Classens et al. [66] offer a list of solutes that can be used for evaluating these interactions. In general, these evaluations are empiric in nature, but they allow quick classification of the major interactions that will determine the elution times. An example on the use of some

Polyelectrolytes as Stationary Phases / 281 of the above chromatographic interactions can be obtained from the work of Tonhi et al. [58]. A more rigorous approach to chromatographic interactions and characterization is the linear free energy relationship. However, this approach fails for charged stationary phases including coated polyelectrolytes. More conventional chromatographic parameters, such as plate height and plate number, have also been used to characterize polymeric-coated columns [58]. We next detail the use of various polyelectrolytes to obtain new charged stationary phases. We will describe the preparation of the various columns, their characterization, and their use. Tables 1 and 2 give the names, abbreviations, and structures of the polymers described in this review. Also given in are the references of the papers using these polyelectrolytes.

Table 1 Positively Charged Polymers Polymer



Poly(dimethyldiallylammonium chloride) (PDADMAC)


Poly(N-ethyl-4-vinyl pyridinium bromide) (PEVP)


Poly(hexamethyleneguanidium hydrochloride) (PHMG)




Poly(N-chloranil, N,N,NV,NV-tetramethylethylene diammonium dichloride) (PCED)


Polyethyleneimine (PEI)



282 / Yishai-Aviram and Grushka Table 2 Negatively Charged Polymers Polymer



Dextran sulfate (DS)




Poly(styrene sulfonate) (PSS)


IV. POSITIVELY CHARGED POLYELECTROLYTES AS STATIONARY PHASES A. Coating Procedures Several groups have prepared positively charged stationary phases with polyelectrolytes. Krokhin et al. [22] used reversed-phase packing (Silasorb’s C8) to form several anion exchange columns using batchmode procedures. First, they mixed the packing material (C8) with a solution of dodecylbenzenesulfonic acid (DBSA). The DBSA adsorbs on the C8-bonded phase, forming a negatively charged surface layer. Then, a positively charged polymer solution was added to the freshly prepared negatively charged packing. Due to strong electrostatic interaction, the polymer adsorbs on the surfactant, yielding an anion exchange material. After the stationary phase is prepared, a chromatographic column is packed using conventional slurry techniques. In their study, they have prepared four different anion exchangers using four different charged polymers: poly-(dimethyldiallylammonium chloride) (PDADMAC), poly(N-ethyl-4-vinyl pyridinium bromide) (PEVP), poly(hexamethyleneguanidinium hydrochloride) (PHMG), and 2,5-ionene (ionene). They found different ion exchange capacities, stabilities, and selectivities for each of the new stationary phases. The columns were used to separate a variety of inorganic

Polyelectrolytes as Stationary Phases / 283 anions as well as some heavy metal ions using an ethylenediaminetetraacetic acid (EDTA)-containing mobile phase. Pirogov et al. [23] continued the study of Krokhin et al. [22]. They also used DBSA to ‘‘activate’’ reversed-phase packing material followed by coating with a positively charged polyelectrolyte. In later works, Pirogov et al. [67,68] extended the approach and used several ionenes with various functional groups to prepare a series of anion exchange packing. In their procedure, they applied the cationic polymer coating solution directly on the commercially available cation exchange materials. Because the cation exchange material has on it sulfonic groups, the DBSA step is eliminated from the procedure. Ionenes are water-soluble linear cationic polyelectrolytes consisting of dimethylammonium charge centers. Pirogov et al. compared several types of cation exchange material at two temperatures of ionene coating. They found that higher coating temperature gave higher ion exchange capacity. They used the polymeric anion exchange columns to separate various inorganic anions. They found that they can manipulate the selectivities by varying the ionene used to prepare the ion exchange material. Suzuki et al. [69] also used several ionenes to prepare positively charged polymeric stationary phases. In this case, the ionenes were covalently attached to the silica surface via bonded propyl amine. They characterized the chromatographic characteristics of the newly made column and compared it with conventional C18 and phenylbonded phases. The batch-mode approach was used for the preparation of the ionene stationary phase. Gupta and Prasad [70] bonded poly(N-chloranil N,N,NVNV-tramethylene diammonium dichloride) (PCED(Cl)2) to silica in batch mode and then packed the newly created stationary phase in a corning glass tube. The polycationic polymer was synthesized by them. They used this column for molecular recognition of h-lactam antibiotic. Millot et al. [71] prepared three differently charged polymeric phases. Two of the three were cationic and the third was anionic and will be described in a later section. One of the polycationic phases was obtained by mixing silica gel with a solution of polyethyleneimine (PEI) in methanol. The adsorption was carried out using sonication for 10 min at 0jC followed by shaking for 25 hr. The amount of PEI on silica was found to be 50 mg/g silica. The silica-coated PEI was then crosslinked by suspending it in 1,4-butanedioldiglycidylether

284 / Yishai-Aviram and Grushka (BUDGE) solution and sonicating the mixture for 2 hr at 60jC. After cooling and filtering, it was slurry-packed to the column. A second phase was obtained by mixing silica gel and hexadimethrine bromide (HB) in water. This mixture was kept under agitation for 24 hr, and then washed, dried, and slurry-packed. The amount of adsorbed HB per gram of silica was found to be 29 mg/g. All the polycationic stationary phases described above were prepared in a batch-mode outside the column. Once the support was coated, the columns were then packed. Recently, Aviram and Grushka [72] dynamically coated a silica gel column with PDADMAC. The PDADMAC was added to a coating solution that was passed through the silica column using an HPLC pump. PDADMAC adsorbs strongly on the silica particles due to electrostatic interactions between the negatively charged silanol groups and the positive centers of the polyelectrolyte. After the column is loaded with the polyelectrolyte, the mobile phase, which no longer contains PDADMAC, is introduced, and once the column reaches equilibrium, separations can be preformed. They found that the magnitude of the capacity factors is directly related to the amount of the adsorbed PDADMAC in the column. The capacity factors of the negatively charged solutes increased dramatically as the amount of PDADMAC increased. On the other hand, the capacity factor of the positive solutes decreased as the PDADMAC in the column increased.

B. Properties of the Phases and Retention Mechanism In all the works quoted in Section 4.1, the chromatographic behavior of the polyelectrolyte-modified columns was compared to that of conventional HPLC columns and, in every case, it was found that retention behaviors and selectivities changed markedly in the newly created stationary phases. The retention mechanism of the solutes is affected by the type of the solutes and the stationary phase. In cases discussed here, the stationary phase contains positively charged centers on the polymers, functional groups of the polymer, and nonbonded silica. Most of the articles cited above consider the positive polymers as anion exchangers and the retention mechanism is taken to be typical of ion exchange columns. Suzuki et al. [69] extended the chromatographic characterization of their ionene-based stationary phases by using some of the test compounds of Kimata et al. [62]. They found that the new phases have significant solute shape recognition ability. They showed that their

Polyelectrolytes as Stationary Phases / 285 ionene-based column can be used either as reversed-phase or as ion exchange column, depending upon the nature of the components of the analyte mixture. Krokhin et al. [22] characterized their positive polyelectrolyte columns by checking their ion exchange capacity. As might be expected, they found that the capacity of the anionic exchangers depends on the functional group density of the polymer chain. Thus,

Fig. 3 Isotherms of sorption of 4,6-ionene at different temperatures on Silasorb-S and observed chromatograms of inorganic anions: (1) at 70jC and (2) at 20jC. (From Ref. 68.)

286 / Yishai-Aviram and Grushka

Fig. 4 The retention time of a-Lact on (a) HB-based column; (b) triple-layer of adsorbed HB, DS, and HB; (c) crosslinked PEI column. (Reprinted with permission from Ref. 71. nFriedr. Vieweg and Sohn Verlagsgesellschaft mbH, 1999.)

poly(N-ethyl-4-vinylpyridinium bromide) (PEVP) has higher capacity (0.032 mmol/g) than ionine (0.010 mmol/g). The PEVP phase has one quaternary ammonium group per two atoms in the chain, whereas ionene has two groups of quaternary ammonium per nine atoms. Subsequent work from the same group [68], where ionenes were adsorbed directly on cation exchange material, showed that the amount of polyelectrolyte adsorbed is a function of the charge density of the adsorbing medium. Also, it was shown that higher adsorption temperature results in greater adsorption (see Fig. 3).

Polyelectrolytes as Stationary Phases / 287

Fig. 5 Separation of structural isomers of phenylphenol on (3,16)-ionene column. (1) o-Phenylphenol; (2) m-phenylphenol; and (3) p-phenylphenol. (From Ref. 25. nAmerican Chemical Society, 2001.)

Millot et al. [71] have also calculated the ion exchange capacity of their columns. The anion exchange capacity of the silica/HB phase was 0.05 mEq/g, whereas the silica/crosslinked PEI phase was 0.19 mEq/g for the same silica support. The adsorbed crosslink PEI was very effective in screening the underlying silanol groups. On the other hand, the surface coverage of HB was low and the underlying silica was exposed for interactions with the solutes, resulting in mixed retention mechanisms. This behavior is seen in Fig. 4, where the retention time of a-lact is shown on the HB-based column and on the crosslinked PEI column (plus on another column that will be dis-

Fig. 6 Separation of some inorganic anions on ionene modified columns. a) least hydrophobic ionenes; b) ionenes of intermediate hydrophobicity; c) most hydrophobic ionenes. (Reprinted from J. Chromatogr. A, 850, A.V. Pirogov, M.M. Platonov, O.A. Shpigun, Polyelectrolyte sorbents based on aliphatic ionenes for ion chromatography, pp. 53–63, 1999, with permission from Elsevier.)

Polyelectrolytes as Stationary Phases / 289 cussed shortly). Panel a in Fig. 4 is the HB-based phase and panel c is the crosslinked PEI phase. As can be seen in Fig. 4, the retention time is longest on the HB column even though its ion exchange capacity is the smallest. The severe tailing seen in the HB column is also indicative of mixed retention mechanism. Aviram and Grushka [72] found that on PDADAMAC, which was adsorbed (dynamically) on silica gel, the retention mechanism for positively charged solutes and for the neutral solutes is similar to than in reversed-phase chromatography. Negatively charged solutes (acids) exhibited a retention behavior that was a combination of reversed-phase and ion-pair chromatography.

C. Applications Suzuki et al. [25] found that bonded ionene stationary phases have the ability to separate positional and geometric isomers. They separated solutes with small structural differences. For example, Fig. 5 shows a baseline separation of o-phenylphenol, m-phenylphenol, and p-phenylphenol on (3,16)-ionene column under isocratic condition using a methanol/water (65:35 vol/vol) mobile phase. This separation was not possible on a reversed-phase column under the same conditions. Krokhin et al. [22,49] as well as Pirogov et al. [23,67,68] and Pirogov and Buchberger [50] used their positively charged polymeric stationary phases for the separation of inorganic anions and metal cations (as their EDTA complexes). For the separation of inorganic anions, indirect photometric detection was used. Figure 6 shows an example of the separation of some inorganic anions on ionene-modified columns [67]. The figure shows that the selectivity can be manipulated by changing the nature of the ionene stationary phase.

V. NEGATIVELY CHARGED POLYELECTROLYTES AS STATIONARY PHASES A. Coating Procedures Because silica surface is negatively charge, it is not practical to adsorb anionic polyelectrolytes on it. The most common way to prepare an anionic polyelectrolyte stationary phase is by adsorbing the positive polyelectrolyte on silica gel or on an anion exchanger and then coating the resultant (positively charged) packing with the anionic polyelec-

290 / Yishai-Aviram and Grushka trolyte. Huhn and Muller [73] prepared a cationic exchange column by first coating a vinyl-modified silica with polystyrene or with poly(glycidyl methacrylate) (PGMA) and then sulfonating the coated silica gels with concentrated sulfuric acid to achieve strong cationic exchange (SO3). Sulfite solution was also used to sulfonate the coated polymers by ring opening. For example, the PGMA-coated silica gels were sulfonated with 1 M sodium sulfite solution in the presence of tetrabutylammonium bromide as catalyst. The result of the reaction with the sulfite is also strong cationic exchange column. Figure 7 shows the two forms of the new coated cation exchangers. Takeuchi et al. [74,75] and Safni et al. [76] dynamically coated an anion exchange column with dextran sulfate (DS). Dextran sulfate has sulfate groups in each D-glucopyranosyl unit, which interact strongly with the positively charged groups of the original stationary phase. They passed [75] aqueous solution of 1.0% sodium dextran sulfate through the column at 4.2 Al/min for 2 hr followed by washing with water until the baseline was stabilized. It was found that the amount of dextran sulfate retained on the anionic exchanger depends on the size of the dextran sulfate. The smaller is the molecular weight of the dextran, the more of it is retained on the column during the coating process. Thus, the pore size of the original anionic exchanger influences the ion exchange properties of the resulting anionic polymer stationary phase. Safni et al. [77] extended the method and dynamically coated a silica-based anion exchanger with heparin. Heparin, a mucopolysaccharide, possesses carboxyl, sulfate, and aminosulfonate groups as ionic moieties. Although the resulting new stationary phase is a cation exchanger, they used it to separate inorganic anions.

Fig. 7 Polymeric cation exchangers formed by (a) direct sulfonation, and (b) sulfite-induced ring opening.

Polyelectrolytes as Stationary Phases / 291 Millot et al. [71] prepared a double-layer polymer coating by adsorbing first HB on silica (as discussed in the previous chapter) and then adsorbing on the HB layer anionic DS. Similarly, they coated previously prepared crosslink PEI on silica with DS. The DS coating procedure calls for mixing the components overnight with gentle shaking. The HB-DS or PEI-DS packing was washed and packed in the column. Aviram and Grushka [72] used dynamic coating technique to adsorb on silica gel first positively charged PDADMAC (as discussed in the previous chapter) and then negatively charged poly(styrenesulfonate) (PSS) on the PDADMAC layer. The resulting doublelayered column could be used as a cation exchanger and also to separate neural species as well.

B. Properties of the Phases and Retention Mechanism The negatively charged polyelectrolyte stationary phase can be characterized using all the tools discussed previously. Huhn and Muller [73] confirmed the presence of the anionic polymers on the stationary phase by doing elemental analysis. From the results, they calculated the average polymer film thickness, which is used to characterize the polymer bonded to the silica gel surface. Huhn and Muller [73] found that, after the polymer coating, the average polymer thickness was 0.25–0.5 nm. After sulfonation, the film thickness was 0.12–0.28 nm. The PGMA layer was thicker than the polystyrene and, therefore, had higher pH stability as shown in Fig. 8. Conventional silica gel columns cannot be used at pH above 7.5. However, the PGMA-coated column can be operated at pH values up to 11. Huhn and Muller [73] checked the performance of the newly coated column packing material by generating reduced van Deemter plot (i.e., reduced plate height h vs. the reduced velocity m). Figure 9 shows two reduced van Deemter plots obtained by them. Some of the minimum h values that they measured on their negatively charged polymeric stationary phases were 4 when Na+ was used as the test solute and 5 when K+ was the test solute. These values demonstrate the good efficiencies that can be realized with polymer-coated silicas. Also, the gentle increase of h with increasing m above the minimum values indicates favorable resistance to mass transfer.

292 / Yishai-Aviram and Grushka

Fig. 8 pH stability on cationic column. (5) Polystyrene column; (o) poly(glycidyl methacrylate) column. (From Ref. 73. nElsevier.)

Huhn and Muller [73] measured the column resistance parameter /, which is indicative of the ‘‘goodness’’ of the column packing. Typical values for well-packed silica gel columns are between 500 and 800. The values found by Huhn and Muller for three different columns were 790, 890, and 850. These values indicate that the columns were well packed and had good flow properties.

Fig. 9 The van Deemter plot; reduced plate height (h) vs. reduced velocity (m) on PGMA column: (5) 6 mg/L Na+; (o) 8 mg/L K+. (From Ref. 73. nElsevier.)

Polyelectrolytes as Stationary Phases / 293 Takeuchi et al. [75] probed the nature of their dextran sulfatemodified column using nitrate ions. They monitored the retention behavior of nitrate as a function of the concentration of sodium sulfate in the mobile phase. They found that the unmodified column behaved as expected from an anion exchanger; namely, the retention of the nitrate decreased as the concentration of the sodium sulfate in the mobile phase increased. However, the dextran sulfate-modified columns, with the exception of the one modified with the largest dextran sulfate, behaved in the opposite direction; kV increased with increasing sodium sulfate in the eluent. Figure 10 shows this behavior. Takeuchi et al. [75] suggest that nitrate is repelled by free sulfate groups. The behavior of the 50,000 dextran sulfate-modified column was explained by its inability to cover completely all the pores of the underlying packing. Figure 10 also shows that the kV values for all the modified columns are smaller than those values obtained with the unmodified columns. The decrease in kV is attributed to the decrease in anion exchange sites after the modification with dextran sulfate. Takeuchi et al. [75] found that the retention behavior of inorganic anions was altered by the modification with dextran sulfate. Safni et al. [77] characterized their heparin-modified column, which is also a cation exchanger. They found that the retention time of nitrate (the

Fig. 10 log kV vs. log sodium sulfate in the mobile phase on modified column with different average Mw of dextran sulfate. 1 (o) = 50,000; 2 (5) =25,000; 3 (4) = 15,000; 4 (.) = 8000; 5 (n) = 5000; 6 (E) = without modification. (From Ref. 75. nFriedr. Vieweg and Sohn Verlagsgesellschaft mbH, 1999.)

294 / Yishai-Aviram and Grushka probe solute) behaved differently in the presence of inorganic salts (sodium sulfate and magnesium sulfate) in the mobile phase than in the presence of organic acids (citric acid, glutamic acid, oxalic acid, and tartaric acid) in the mobile phase. With inorganic salts in the mobile phase, the retention of the nitrate changed little when the concentrations of the salts were changed. However, with the organic acids in the mobile phase, it was found that as the concentration of the acids increased, the retention time of the nitrate increased as well. Figure 11 shows the behavior of nitrate retention as a function of the various salts in the mobile phase. Safni et al. [77] explain the behavior depicted in Fig. 11 by the existence of both cationic and anionic sites in the heparin-modified column. The cationic exchange sites are due to the heparin coverage, whereas the anionic exchange sites are due to the underlying quaternary amine groups in the original anion exchange column. The solutes can interact with both exchange centers. The strength of these interactions depends on the constituents of the mobile phase. The organic acids in the mobile phase are more effective in shielding the heparin groups, thus increasing the interactions of the nitrate

Fig. 11 Log retention time vs. log concentration of the salts in the eluent. (From Ref. 77. nElsevier.)

Polyelectrolytes as Stationary Phases / 295

Fig. 12 Separation of monovalent and divalent cations (a) in guinea pig serum, and (b) bovine serum. (From Ref. 76. nElsevier.)

296 / Yishai-Aviram and Grushka solute with the underlying anion exchange sites. The authors maintain that the retention behavior of cations is expected to be normal because the cations should interact with the cation exchange sites without any repulsion from the anionic exchange sites. Millot et al. [71] determined the ion exchange capacity for their negatively charged double-layer phases. They found that the stationary phase containing HB-DS is a cation exchanger, whereas the stationary phase consisting of PEI-DS is an anion exchanger. This behavior was explained by incomplete charge neutralization by the DS layer. As a result, a mix retention mechanism (anionic exchange from the PEI surface and cationic exchange from the DS polymer layer) exists. They also found that the ion exchange capacity is a function of the silica gel porosity; the higher is the porosity, the lower is the ion exchange capacity.

C. Applications Safni et al. [76] used their anion exchanger column modified with dextran sulfate to separate various alkali and alkaline-earth cations. They applied the technique to separate monovalent divalent cations present in guinea pig serum and bovine serum. Figure 12 shows the resulting chromatograms.

Fig. 13 Separation of anions on anion exchanger modified with heparin. (From Ref. 77. nElsevier.)

Polyelectrolytes as Stationary Phases / 297 In their paper on the heparin-modified column, Safni et al. [77] show the separation of inorganic anions. For the separation to take place, the mobile phase included tartaric acid (see discussion in Section 5.2). The detection was done indirectly using an ultraviolet (UV) detector. Figure 13 shows the resulting chromatogram. Millot et al. [71] used their negatively charged HB-DS composite column to separate some basic proteins using gradient elution. The mobile phase was a Tris buffer at pH 7 and the gradient was a NaCl gradient. Figure 14 shows the separation obtained.

VI. COMPLEX POLYELECTROLYTE LAYERING This review describes the use of polyelectrolytes to coat an existing stationary phase and generate a new stationary phases with different chromatographic properties, selectivities, and efficiencies. The coating can be done in a batch mode or by dynamic coating. The review discussed the use of both negatively and positively charged polymers to prepare new columns. The newly coated columns often provide a platform for complex retention mechanism as well as for unique selectivities. The use of polyelectrolytes to modify stationary phases opens the door to generate complex combinations for specific separa-

Fig. 14 Separation of positively charged proteins on negatively charged HB-DS composite column. (1) TRYP; (2) a -CHYMO; (3) MYO; (4) LYSO. (From Ref. 71. nFriedr. Vieweg and Sohn Verlagsgesellschaft mbH, 2003.)

298 / Yishai-Aviram and Grushka tions. A step in this direction is reported by Millot et al. [71], who describe the generation of a triple-layer polyelectrolyte-coated column. The three layers were HB–DS–HB and because the topmost layer is positively charged, the resulting column is an anion exchanger. The triple layer masked well the residual silanol groups on the silica gel particles, resulting in improved peak shapes. Although the polyelectrolyte columns provide charge centers for ion exchange-based separations, they can also provide sufficient hydrophobic centers to allow for the separation of uncharged solutes. Thus, the polyelectrolyte-coated column can separate mixtures of solutes with diverse chemical properties.








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Absorptive coatings, 247–248 Acetic anhydride, 145 Acetonitrile-water mobile phase, 83 dependencies of constants, 85 Acetyl, 255 Actinides, 146 Acylation agents used in SFE/SFR, 145 Adsorbent activity, 29 Adsorbents SFE, 135–138 Adsorption chromatography, 26, 66 Adsorption isotherm equation, 52 Aflatoxin B1 extraction, 123, 163–164 AFM, 280 Airborne volatile organic compounds, 238

Alcoholysis, 147 Alkylbenzenes, 264 gradient elution reversed-phase separation, 60, 61 Alkylsiyl, 255 Aluminas, 135, 136 American Oil Chemical Society (AOCS) Official Method G3-53, 158 fatty acid content, 159 Amino-bonded silicas, 140 Aminopropyl, 26 Ammonia NH2-Mega Bond Elut, 162 Amphetamine, 244 Analyte collection, 130 Analyte molecules, 201 expression of maximum number, 226–228 number, 204





Analyte peak, 190 Analyte polar group, 255 Analyte retention factor, 195 Analyte trapping efficiency, 129 Analytical derivatization SFR, 144 Analytical determination sample size, 122 Analytical gradient-elution chromatography retention theory, 9–18 Analytical SFE applications, 150 lipid or lipid derived volatile and semivolatile compounds, 157 detect irradiated foodstuffs, 165 drug analysis, 150 features, 117 instrumentation, 117 integration of adsorbents, 135 reactions and derivatization applied, 143 triangle, 116 yielding crude fractionations, 131 Analytical toxicology application, 260–261 Anion exchangers ionene, 282 PDADMAC, 282 PEVP, 282 PHMG, 282 Anion separation, 296 Antidepressant drugs SPME-GC-NPD chromatogram, 260 AOAC methods organic solvents, 161 AOCS Official Method G3-53, 158 fatty acid content, 159 APCI, 241 Applied Separations, Inc., 121 a priori parameters, 192 Aroma volatiles, 157

Aspergillus flavus, 123 Association of Official Analytical Chemists (AOAC) methods organic solvents, 161 Atmospheric pressure chemical ionization (APCI), 241 Atomic force microscopy (AFM), 280 Automated SFE/SFR/GC analyzer fat content determination, 156 Bandwidths calculation, 33 gradient elution chromatography liquid column, 17–18 Bandwidths increase isocratic conditions, 64 Batch-equilibrium conditions and chromatography, 195 Batch mode PCED, 283 Behavior-gradient preelution, 43 Benzene, 161 Binary gradients, 5 reversed-phase chromatography, 19–24 Binary solvent mixture distribution equilibrium, 51 Bioanalytical applications, 258–263 Biological matrices, 135 Biomarkers determination exhaled human breath, 262 Bonded ionene stationary phases, 289 Bonded nitrile column gradient elution weak solvent, 67–68 Breakthrough curves calculated, 53 BUDGE solution, 284 Butanedioldiglycidylether, 283–284 Caffeine extraction, 127 Candida antarctica, 148

Index Capillary electrochromatography, 275, 278 Capillary electrophoresis (CE), 233, 278 SPME coupling, 237 Carbon content silica plus polymer phase, 279 Carbon dioxide, 140 phase diagram, 113 SC-CO2 extraction, 132–140 Carbon graphitized silica, 250 Carboxylic acids peak shape improvements, 258 Cation(s) separation of monovalent and divalent, 295 Cation exchange material compared, 283 ionine, 286 Cation-exchange microchromatography, 250 Cationic column pH stability, 292 CE, 233, 278 SPME coupling, 237 Celite, 135, 151 Central limit theorem, 199 Chip technology, 182 Chiral separation, 200 Chloroform, 161 Chloroformates, 255 Cholesteryl stearate, 148 Chromatographic column frequency distribution of sojourn time, 215 polar solvent adsorbed, 52 Chromatographic interactions, 280 Chromatographic migration, 190 Chromatographic optimization function (COF), 71–72 Chromatographic process kinetics, 15



Chromatographic quantities and equilibrium distribution constant K, 197 Chromatographic retention, 182 Chromatography batch-equilibrium conditions, 195 under critical conditions, 87–88 equilibrium conditions, 195–196 polar adsorbents, 28 polar compounds, 33 preparation prior, 110 stochastic approach, 183–188 stochastic description, 182 ternary gradients, 78–80 CHROMDREAM, 73, 75 CHROMSWORD, 73, 75 Classical dynamic coating technique, 277, 278 CMC, 276 Coating(s), 246–254 Coating polymer chemistry extraction efficiency, 254 Coating procedures polyelectrolytes, 282–283, 289–290 Coating solution PDADMAC, 284 Coextractives and water, 125–127 COF, 71–72 Column characterization, 279–281 Column hold-up volume, 48 effect, 46 preelution, 46 Column uptake of polar solvents correction of retention volume, 104–106 Complex polyelectrolyte layering, 298 Composition window, 86 Confocal Raman spectroscopic analysis, 237 Constant mobile phase velocity, 213 Corn extraction of aflatoxin B1, 123




Cosolvent, 127 addition capability, 118 Critical concentration interactive LC of copolymers, 88 Critical fluids sample preparation applications, 149–166 Critical micellar concentration (CMC), 276 Critical pair of adjacent peaks, 72 Cyanopropyl, 26 Dalea spinosa, 125 DBSA, 282, 283 2-DCB, 166 Dehydrated meat matrices FAME distributions, 155 Dense gas chromatography, 114 Derivatization, 255–257 analytical SFE, 143 on-fiber after extraction, 257 on-line SPME-LC configurations, 257 organic acids, 256 peak shape improvements, 258 postcolumn HPLC, 144 SFE, 144–145 and simultaneous extraction, 257 Desorption, 235 Dextran sulfate, 290 modified column, 293 structure, 282 DI, 234 SPME, 234–235 Diatomaceous earth, 135 Dibutyl-unsymmetry-dibenzo-14crown-4-dihydroxy crown ether, 251 Dihydroxy-substituted saturated urushiol crown ether, 251 Dioxane volumes, 66

Dirac function, 214 Direct immersion (DI), 234 SPME, 234–235 Direct sulfonation polymeric cation exchangers, 290 Distribution equilibrium binary solvent mixture, 51 Divinylbenzene phases, 246, 249 Dodecylbenzenesulfonic acid (DBSA), 282, 283 2-dodecylcyclobutanone (2-DCB), 166 Double-layer polymer coating, 291 Drug analysis analytical SFE, 150 off-line SFE, 158 Drugs of abuse, 260–261 Dry test meter, 119 Dynamic coating defined, 276 polymer-coated stationary phases, 276 principle, 276–278 Dynamic desorption, 235 ECD, 156 chromatogram pesticides extracted using fluoroform, 141 Edgeworth-Crame´r series expansion, 218 EDTA, 283 Egress time, 183–185 Einstein equation, 184 Electrochromatography, 14 Electron capture detector (ECD), 156 chromatogram pesticides extracted using fluoroform, 141 ELSD, 158, 166 Eluent salts retention time vs. concentrations, 294 ELUEX, 73, 75 Elution chromatography, 183

Index Elution peak, 190 Elution strength ternary gradients, 79 elution separation resolution window diagram, 80 Elution time of analyte peak, 228 Elution volumes calculation, 33 corrected, 55 gradient dwell volume, 44, 45 gradients 0% polar solvent and overestimated data, 67 Elutropic solvent, 135 Environmental Protection Agency (EPA) Pollution Prevention Act, 110–111 EO-PO, 88 cooligomer gradient elution reversedphase separation, 89 EPA Pollution Prevention Act, 110–111 Equilibrium conditions chromatography, 195–196 Equilibrium constants, 206 Equilibrium distribution, 182 constant K and chromatographic quantities, 197 Ergodic hypothesis, 196 Error on kV, 230 ESI interface, 241 Esterification reactions organic solutes, 145 Ethers butanedioldiglycidylether, 283–284 dibutyl-unsymmetry-dibenzo14-crown-4-dihydroxy crown, 251 dihydroxy-substituted saturated urushiol crown, 251



[Ethers] octadecylethers separation, 30 oligoethylene glycol alkyl, 83 coelute, 87 oligoethylene glycol nonylphenyl coelute, 87 separation, 29 Ethylenediamine-tetraaectic acid (EDTA), 283 Ethylene oxide-propylene oxide (EO-PO), 88 cooligomer gradient elution reversed-phase separation, 89 Evaporative light scattering detector (ELSD), 158, 166 Everett’s equation, 51 Exhaled human breath biomarkers determination, 262 Extracted analyte collection, 128–130 Extraction aflatoxin B1, 123, 163–164 polar analytes, 162 Extraction cell pesticide recovery, 136 Extraction conditions vs. extraction recovery, 243 Extraction efficiency coating polymer chemistry, 254 Extraction fluid density, 131 cleanup, 134 preferred, 121–122 type or composition variation, 140–141 Extraction mode and coupling, 234–241 novel devices, 238–241 Extraction rates vs. flow rates, 131




Extraction recovery vs. extraction conditions, 243 Extraction tubes types, 239 Extraction yield increase temperature, 244 Extractor design, 118 False separation, 38 FAME, 145 distributions dehydrated meat matrices, 155 synthesizer automated on-line, 155 Fast gradients, 69–70 Fat band, 126 Fatty acid content AOCS Official Method G3-53, 159 Fatty acid methyl esters (FAME), 145 distributions dehydrated meat matrices, 155 synthesizer automated on-line, 155 FDA, 160 Femtosystem, 203–205 Fiber conditioner device, 240 Fiber-in-tube extraction, 239–240 Fiber SPME, 265 Flame photometric detector (FPD), 156 Florisil, 135 Florisil trap, 152 Flow programming HPLC, 3 Flow rates vs. extraction rates, 131 Fluid composition pesticide recovery and lipid extracted, 142 Fluid density-based fractionation, 132–134

Fluorescence imaging methods, 185 Fluorocarbons, 140 Fluoroform, 140 Food and Drug Administration (FDA), 160 Food Safety and Inspection Service (FSIS), 160 Fourier-transform infrared spectroscopy (FTIR), 112 FPD, 156 Frenkel-de Boer equation, 184 FSIS, 160 FTIR, 112 Gas chromatography (GC), 112, 232 dense, 114 pesticides extracted using fluoroform, 141 SFE, 156–157 Gas totalizer device, 119 Gaussian shape peak shape, 199 GC. See Gas chromatography (GC) Giddings-Eyring model of chromatography, 190, 207, 226 Gradient(s) effect of delayed migration, 41 linear, concave, and convex examples, 6 optimization, 71–77 Gradient delay, 38 Gradient dwell volume determined, 39–40 effect, 42, 44, 45 elution volume, 44, 45 increases, 38 Gradient elution, 5 IC separations of polymers, 83 ideal, 15 method development, 55–77

Index [Gradient elution] optimization spreadsheet program, 107–108 retention data, 9 reproducibility, 34 retention volumes calculation, 11 reversed-phase separation alkylbenzenes, 60, 61 ethylene oxidepropylene oxide cooligomer, 89 silica gel and bonded nitrile column weak solvent, 67–68 theory, 90–91 Gradient elution chromatography analytical retention theory, 9–18 changing column diameter, 59–60 changing column length, 61–62 changing flow rate mobile phase, 58–59 ion exchange chromatography (IEC), 34–35 liquid column bandwidths and resolution, 17–18 effects of dwell volume on, 37–47 optimization of separation, 3–93, 104–108 prediction of retention, 3–93, 104–108 symbols, 92–96 polymer liquid mechanism, 82 retention, 7 volumes, 54 Gradient elution separation elution strength ternary resolution window diagram, 80 high-molecular compounds, 81–89


[Gradient elution separation] LSS model, 8 optimization, 69–77 Gradient function, 11 linear gradients, 14 Gradient instruments function, 16–17 Gradient methods transfer, 56–57 Gradient preelution illustrated, 43 Gradient profile changing, 64 Gradient program isocratic steps, 5–6 Gradient retention delay calculated, 40 Gradient rounding, 37–38 Gradient RPC optimization, 75 Gradient separation accelerated, 71 Gradient shape effect, 12 Gradient steepness changing, 65 prediction of effect, 62–68 Gradient volume calculated, 41 Gravimetric balance, 115 Hair spiked GC-MS following HS-SPME, 261 Ham SC-CO2 extraction moisture content, 128 Hamilton syringe cleaner, 240 HB, 284 Headspace (HS) extraction, 234 SPME, 234–235, 258 SPME-GC-MS, 260





Heparin structure, 282 Heptafluorobutyric anhydride, 144 Hewlett Packard Model HP 7680, 130 Hexadimethrine bromide (HB), 284 Hexafluorobutyric anhydride derivative, 160 High-performance liquid chromatography (HPLC), 14, 112, 232 designs in-tube coupling, 236 flow programming, 3 isocratic accelerated, 71 elution mode, 3 normal phase gradient elution, 50 correction of retention volume, 104–106 retention volumes, 68 off-line SFE, 158 postcolumn derivatization method, 144 reversed-phase optimization, 73 SFE, 158–163 Holdup time marker selection, 206 Homogeneous columns moving phase velocity, 213–221 peak splitting, 213–221 peak tailing, 213–221 Homopolymers coelution, 87 Hot ball kinetic model, 116 HPLC. See High-performance liquid chromatography (HPLC) HS. See Headspace (HS) Human breath sampling device, 263 Hydrolysis of vitamin A, 148 Hydrolytic activity of lipases, 148

Hydromatrix, 125, 135, 137, 158 soybean oil, 161 Hydroterminated silicone oil, 251 Hydroxydibenzo-14-crown-4, 251 Hyphenated supercritical fluid techniques, 164 IAE, 253 IC, 81 separations of polymers gradient elution, 83 Ideal gradient elution, 15 IEC, 34 ionic compounds, 8 retention, 35 slab model, 36 Immunoaffinity extraction (IAE), 253 Immunoaffinity media, 250 Imperfect mixing mobile phase components, 37 Infrared spectroscopy (IR), 280 on-line with SFE determine iodine number, 165 Ingress number distribution, 188 Ingress time, 183–185 Initial isocratic step, 41 Initial mobile phase retention factor, 40 retention factors, 40 Injection, 201 Injection process error resulting, 228–229 Instantaneous retention factors, 18 changing, 10 Instrumental gradient dwell volumes, 56 Integration limits, 17 Interactive chromatography (IC), 81 separations of polymers gradient elution, 83 In-tube coupling HPLC designs, 236

Index In-tube SPME, 236 Inverse SFE, 139 examples, 139 sequence of steps, 139 Iodine number determine infrared spectroscopy on-line with SFE, 165 Ionene anion exchangers, 282 isotherms of sorption, 285 modified columns separation of inorganic anions, 288 prepare positively charged polymeric stationary phases, 283 stationary phases bonded, 289 structure, 281 Ion exchange chromatography (IEC), 34 ionic compounds, 8 retention, 35 slab model, 36 Ionic strength dependence PDADMAC adsorption on silica, 279 Ionine cation exchange material, 286 Ion-pair chromatography, 276–277 IR, 280 on-line with SFE determine iodine number, 165 Isco, Inc., 120, 121 Isocratic conditions bandwidths increase, 64 Isocratic elution mode HPLC, 3 Isocratic elution retention factor, 58 Isocratic HPLC accelerated, 71 Isocratic LC, 9



Isocratic retention calculation, 33 factors, 7 gradient-elution behavior prediction, 9 Isocratic RPC optimization, 75 Isocratic separations, 48 Isocratic steps gradient program, 5–6 Isohydric organic solvents, 29 Iso-selective gradients, 73 Iso-selective multisolvent gradients, 78 Iso-selective ternary gradients, 79, 80 Isotherms of sorption 4,6-ionene, 285 Joule-Thompson effect, 127 Kinetic tailings, 192 Langmuir isotherm, 32, 249 Langmuir model, 51 Lanthanides, 146 Leco Corporation, 121 Lidocaine, 244 Linear chromatography, 200 Linear concentration gradients, 12 Linear gradients gradient function, 14 Linear solvent strength (LSS) binary gradients, 7 Lipase(s) hydrolytic activity, 148 Lipase-catalyzed hydrolysis, 147 Lipase-catalyzed methanolysis for SFE/SFR, 149 Lipids conversion, 149 Lipid solutes in SC-CO2 solubility data, 125




Liquid absorptive coatings scheme, 248 Liquid chromatography under critical conditions, 87 exclusion-adsorption, 83 polyelectrolytes stationary phases, 273–298 Liquid–liquid extraction SPME, 242 LSS binary gradients, 7 MALDI, 242 Martin rule, 82, 88 Martire model, 31 Mass spectrometry (MS), 112 Matrix-assisted laser desorption/ ionization (MALDI), 242 Matrix solid phase dispersion (MSPD), 124 Mean desorption time, 184 Mean egress time, 184 Meat samples concentration of naphthalene, 154 Methanol with oleic acid, 148 polyethyleneimine (PEI), 283 in water, 22 Methylene chloride, 161 Microchromatography cation-exchange, 250 Microsystem, 203–205 Millisystem, 203–205 Minichromatographic columns, 137 MIP, 250–252 Mobile phase acetonitrile-water dependencies of constants, 85 components, 183 imperfect mixing, 37, 38 prediction of effect, 62–68

[Mobile phase] constant velocity of analyte molecules, 185 flow rate effects, 57 sodium sulfate, 293 time by analyte, 195 visits effective average time, 188 volume, 195 determination, 16 Molecular dynamic quantities, 206 Molecularly imprinted polymers (MIP), 250–252 Monolithic silica gel-based columns, 70 Monte Carlo simulation, 193 Moving phase velocity homogeneous columns, 213–221 MS, 112 MSPD, 124 Mycotoxin extraction, 163–164 Nanosystem, 203–205 Naphthalene concentration meat samples, 154 Naphthalene in SF-CO2, 114 solubility, 114 Naphthalene sulfonic acid separation, 24 Naphthoylene-benzimidazole aklylsulphonamides reversed-phase separation, 4 gradient elution, 63 Near critical fluids, 113 NH2-Mega Bond Elut, 162 Nitrile column gradient elution weak solvent, 67–68 NLEA, 154, 155 NMR, 280 Nonideal retention behavior instrumentation effects, 36–54

Index Normal phase chromatography (NPC), 25, 66 advantages, 27–38 with binary gradients, 25–33 solvents, 27 Normal phase gradient elution HPLC, 50 retention volumes, 68 optimization window diagram, 76 separation, 29, 30, 39 Normal phase HPLC correction of retention volume, 104–106 Normal phase systems separation selectivity and retention, 31 Novanik 600/20 sample, 89 Novozyme 435, 148, 161 NPC. See Normal phase chromatography (NPC) Nuclear magnetic resonance (NMR), 280 Nutritional Labeling and Education Act (NLEA), 154 based method determining fat content, 155 solvent-based-extraction protocol, 154 Octadecylethers separation, 30 Off-line SFE drug analysis, 158 and HPLC or SFC, 158 Off-line trapping, 137 Oligoethylene glycol alkyl ethers, 83 coelute, 87 nonylphenyl ether coelute, 87 separation, 29 separation, 30



Oligomers separations, 25 Oligostyrenes normal-phase gradient-elution separation, 13 On-fiber derivatization after extraction, 257 On-line derivatizations SPME-LC configurations, 257 Optimization reversed-phase HPLC, 73 Organic acids derivatization, 256 Organic solutes esterification reactions, 145 Organic solvent preferential adsorption, 49 Organochlorine pesticides, 151 Overlapping resolution map, 72 Packed column comparison, 138 Packing particle diameter, 70 PAH, 245 Parallel multisample SFE unit simultaneous, 119 Parameters, 243 Partitioning, 249 PCED batch mode, 283 structure, 281 PDADMAC. See Poly (diallyldimethylammonium chloride) (PDADMAC) PDMS coated bar, 240 fiber, 237 Peak capacity, 69–70 Peak shape features and experimental errors retention factor determination, 189–194




Peak splitting, 198, 216–218 homogeneous columns, 213–221 Peak tailing, 199–200, 218–221 homogeneous columns, 213–221 PEEK tubing, 240, 242 PEG, 251 separation, 19–20 PEI methanol, 283 structure, 281 Pelletized celite, 125 Pesticide recovery extraction cell, 136 Pesticide recovery and lipid extracted fluid composition, 142 Pesticides organochlorine, 151 PEVP anion exchangers, 282 quaternary ammonium group, 286 structure, 281 PGMA-coated column, 291 pH adjustment extraction yield, 244 dependence PDADMAC adsorption on silica, 278 stability cationic column, 292 Phase-adsorption technique, 136 Phases properties, 284–288 Phenylphenol separation of structural isomers, 287 Phenylurea optimization window diagram, 76 Phenylurea herbicides, 32, 68 resolution window diagram, 77

Phenylurea herbicides NP-gradient elution separation resolution window diagram, 74–75 PHMG anion exchangers, 282 structure, 281 Phosphatidylcholine, 148 Pico-chip system, 203–205 Pico-tube system, 203–205 Plant sterols, 161 Plasma gas chromatography, 245 Poisson law, 187–188 Polar adsorbents chromatography, 28 Polar analytes, 257 extraction, 162 Polar compounds chromatography, 33 Polarity and elution strength, 27 Polarity reduction, 255 Polar solvent adsorbed chromatographic column, 52 Polar solvents column uptake correction of retention volume, 104–106 Poly(diallyldimethylammonium chloride) (PDADMAC), 277–278 adsorption on silica ionic strength dependence, 279 pH dependence, 278 anion exchangers, 282 coating solution, 284 layer, 291 structure, 281 Poly(hexamethyleneguanidium hydrochloride)(PHMG) structure, 281

Index Poly(N-chloranil, N,N,N ,V N V-tetramethylethylene diammonium dichloride) (PCED) batch mode, 283 structure, 281 Poly(N-ethyl-4-vinyl pyridinium bromide)(PEVP) anion exchangers, 282 quaternary ammonium group, 286 structure, 281 Poly(styrene sulfonate)(PSS), 282, 291 Polyacrylic acid-coated fiber, 249 Polycationic electrolyte, 277–278 Polycationic phases, 283 Polycationic polymer, 283 Polycationic stationary phases, 284 Polycyclic aromatic compounds (PAH), 245 Polydimethylsiloxane (PDMS) coated bar, 240 fiber, 237 Polydispersity of synthetic polymers, 82 Polyelectrolyte layering, 298 Polyelectrolytes applications, 297 coating procedures, 282–283, 289–290 stationary phases liquid chromatography, 273–298 negatively charged, 289–297 positively charged, 282–288 Polyethylene glycol (PEG), 251 separation, 19–20 Polyethyleneimine (PEI) methanol, 283 structure, 281 Polymer-coated stationary phases dynamic coating, 276



Polymeric cation exchangers direct sulfonation, 290 Polymers separations, 25 Polypyrrole (PPY) coatings, 254 Polystyrene separation, 39 Poor retention data reproducibility, 5 Population, 192 Porous bonded silica LC coatings, 250 Portable solid-phase microextraction for field-air sampling, 238 Positively charged polymers, 281 Positively charged proteins separation, 297 Postcolumn derivatization method HPLC, 144 Post-SFE trapping, 137 Poultry fat pesticide recoveries lipid extracted, 142 PPY coatings, 254 Preelution behavior-gradient, 43 Preferential adsorption, 49 organic solvent, 49 Programmable fluid ‘‘wash’’ cycles, 121 Propanol in dichloromethane calculated breakthrough curves, 53 in heptane, 53, 68 in hexane, 68 volumes, 66 Proximate fat analysis, 153–155 Pseudomonas cepacia, 148 PSS, 282, 291 Pulsed field gradient nuclear magnetic resonance, 181 Purospher Star RP-18e, 60




Quaternary ammonium group PEVP, 286 Raman microspectroscopic analysis, 237 Raman spectroscopic analysis, 237 RBD soybean oil, 161 RCRA, 111 Real-tome single-molecule observations, 205 Refined, bleached, deodorized (RBD) soybean oil, 161 Relative error on kV, 223 Relative errors residence time, 222–223 Relative random errors, 221 Resolution gradient elution chromatography liquid column, 17–18 Resource, Conservation, and Recovery Act (RCRA), 111 Retention effects of adsorption of strong solvents, 48–54 gradient elution chromatography, 7 instrumentation effects, 36–54 liquid chromatography modes, 64 ternary mobile phases, 81 Retention behavior small and large molecules differences, 82 Retention chromatographic quantities, 206 Retention data calculating, 17 Retention factor, 189 dependence, 22, 32 determination peak shape features and experimental errors, 189–194

[Retention factor] initial mobile phase, 40 injection effect, 194 peak splitting effect, 190 peak tailing effect, 191 vs. solute concentration, 16 stochastic bias effect, 192–193 unretained tracer selection effect, 195 Retention function, 11 Retention mechanism and NPC phases, 26 properties, 284–288, 291–296 Retention prediction selectivity ternary gradients, 79–81 Retention theory analytical gradient-elution chromatography, 9–18 Retention time alpha-Lact, 286 calculation, 9–16 determined, 191 Retention volume calculation, 9–16 correction column uptake of polar solvents, 104–106 differences window diagram, 76 errors, 65 gradient elution chromatography, 54 normal-phase gradient elution HPLC, 68 Reversed-phase chromatography (RPC), 44, 45 adsorption and partition mechanism, 23 binary gradients, 19–24 elution times, 21 gradient optimization, 75

Index [Reversed-phase chromatography (RPC)] ion-pair or salting-out, 23 isocratic optimization, 75 retention, 209 Reversed-phase gradient elution, 69 separation resolution window diagram, 77 Rhizomucor miehei, 148 Rotameter, 119 RPC. See Reversed-phase chromatography (RPC) Salatrim characteristic, 166 Salting out effect, 244 Salts in eluent retention time vs. concentrations, 294 Sample size extraction time and precision, 124 SARA, 111 Scanning electron microscopy (SEM), 280 Scatchard plots, 264 SC-CO2, 110, 111, 125 extraction, 132–140 Scott-Kucera model of adsorption, 32 SEC, 81 Seed oils sterol concentration, 162 Selectivity ternary gradients, 78 retention prediction, 79–81 SEM, 280 Separation conditions effects, 57 Separation efficiency increase, 61



Separation engineering renewal, 181 Separon SGX, 13 Nitrile, 32 resolution window diagram, 74–75, 77 RPS column, 24 silica gel column, 53 Sequential optimization methods with COF sum optimization criterion, 72 SF. See Supercritical fluid (SF) SFCU technique, 138, 139 SFE. See Supercritical fluid extraction (SFE) SFR. See Supercritical fluid reaction (SFR) Short packed columns, 70 Silanized optical fiber, 242 Silanols, 274 Silasorb SPH C8, 22 Silica, 135 carbon graphitized, 250 Silica-based polyelectrolyte stationary phases approaches for making, 275 Silica gel and bonded nitrile column gradient elution weak solvent, 67–68 Silica plus polymer phase carbon content, 279 Siloxane bonds, 274 Silyated silicas, 135 Silylation, 144–145 Simultaneous extraction and on-fiber derivatization, 257 Simultaneous predictive optimization advantage, 72–73 Single molecule mutual independence, 186–187




Single-molecule chromatography, 201 Single-molecule dynamic quantities, 182 Size-exclusion chromatography (SEC), 81 Slovanik 320, 89 Small-angle neutron scattering (SNAS), 280 Snyder, 26 Snyder model, 31 Snyder-Soczewinski model, 31 Soczewinski displacement model of retention, 26 Sodium sulfate mobile phase, 293 Sol gel media, 250 Solid coatings, 249 Solid phase extraction (SPE) materials, 137 Solid-phase microextraction (SPME), 231–268 accuracy and precision, 243 application area, 266 CE coupling, 237 clinical chemistry, 261 description, 232 designs in-tube coupling, 236 determination of pharmaceuticals, 259 device, 235 electrode position, 241 schematic, 232 DI, 234–235 electrochemistry, 240–241 fiber, 265 fiber coatings characteristics and properties, 247 filter protecting, 240 GC-NPD chromatogram antidepressant drugs, 260

[Solid-phase microextraction (SPME)] Headspace GC-MS, 234–235, 258, 260 in-tube, 236 LC, 235–236 LC configurations on-line derivatizations, 257 liquid-liquid extraction, 242 low recoveries, 266 mass/atomic spectrometry, 241–242 publications reporting, 233 references possibilities and limitations, 264–267 Solubility data lipid solutes in SC-CO2, 125 Solubility parameters characteristic, 133–134 Solute removal using SF, 115 Solute’s maximum solubility, 115 Solute trapping, 130 Solvent breakthrough curves calculate, 52 Solvent demixing, 48 effect, 104–106 Solvent-modified extraction procedure, 246 Sorbent-based SFE, 139 Sorbent collection device integration, 137 Sorbent-filled collection device, 130 Sorbents, 135 fractionation of extract, 135 Sorbent trap option supercritical fluid extraction apparatus, 152 Sorption principles and parameters, 242–245 Soxhlet extraction technique, 111

Index Soybean oil Hydromatrix, 161 triglycerides solubility, 126 Spectroscopic analysis confocal Raman, 237 SPE materials, 137 SPME. See Solid-phase microextraction (SPME) Static desorption, 235 Stationary phase, 183 identify sites, 187 mean time, 189 Steep gradients with wide concentration range, 86 Sterol concentration seed oils, 162 Stochastic approach of chromatography, 183–188 aspects, 183–184 Stochastic bias, 201 effect, 221 Stochastic model, 185–188 Stochastic theory of chromatography, 225 Stoichiometric parameter value, 66 Structural isomers separation phenylphenol, 287 Structure-based predictive software, 73, 75 Sulfite-induced ring opening polymeric cation exchangers, 290 Supelco, 232, 235 Supercritical-carbon dioxide (SC-CO2), 110, 111 extraction, 132–140 Supercritical fluid (SF), 151 extract cleanup, 151–152 for off-line sample preparation in food analysis, 110–167



[Supercritical fluid (SF)] sample preparation, 110–111 solute removal, 115 Supercritical fluid chromatography (SFC), 111 fatty acid content, 159 off-line SFE, 158 SFE, 158–163 Supercritical fluid cleanup (SFCU) technique, 138, 139 Supercritical fluid-derived extract simplifying, 131–132 Supercritical fluid extraction (SFE), 111–130 acylation agents, 145 adsorbents, 135–138 apparatus sorbent trap option, 152 collecting nonvolatile and volatiles device schematic, 129 commercial instrumentation, 120 coupling reaction chemistry derivatization, 142–148 extraction of volatiles and semivolatiles, 135 fatty acid content, 159 gas chromatography (GC), 156–157 ham sample extraction time function, 116 with HPLC or SFC, 158–163 integrated with selected chromatographic/ spectroscopic techniques, 164–165 integration of cleanup step, 131–141 lipase-catalyzed methanolysis, 149 optimizing selectivity, 134 pesticides analyzed, 151




[Supercritical fluid extraction (SFE)] principles, 112–116 sample matrix and preparation, 122–124 with SFR combining, 143 sorbent-based, 139 technique inversed, 148 two-step fractionation method soybean oil, 162 types of extraction and instrumentation, 117–121 unit design, 118 utilizing SFR metals and radioactive species analysis, 146 Supercritical fluid reaction (SFR), 112, 143 acylation agents, 145 analytical derivatization, 144 catalysts, 146–148 fatty acid content, 159 inversed technique, 148 lipase-catalyzed methanolysis, 149 reactions, 142–143 with SFE combining, 143 Supercritical fractionation in seed oils, 162 Superfund Amendments and Reorganization Act (SARA), 111 Suprex Autoprep 44, 130 Synergist in facilitating extraction, 127 Synthetic resins, 135 Tailings, 192 Tandem off-line and in-line trapping, 137

2-TCB, 166 Tenax trap, 129 Ternary gradients chromatography, 78–80 Ternary mobile phases retention, 81 Tetraalkylammonium salts, 147 2-tetradecylcyclobutanone (2-TCB), 166 Tetrahydrofuran in water, 22 Tetrahydrofuran-water mobile phases dependencies of constants, 85 TFA, 163 TGA, 280 Theophylline competitive binding, 253 Thermogravimetric analysis (TGA), 280 Thin layer chromatography (TLC), 21, 48, 183 spot test, 115 Three-block PO-EO-PO cooligomer, 88 Threshold pressure, 114, 115 TLC. See Thin layer chromatography (TLC) Total Fat Analyzer, 121 Total petroleum hydrocarbons (TPH), 150 Toxicology analytical application, 260–261 TPH, 150 Trace components analysis, 150–152 Transesterification, 145 Transesterified rapeseed oil, 47 Trapping efficiency, 130 Trifluroacetic acid (TFA), 163 Triglycerides, 147 Trimethyloxonium tetrafluoroborate, 256

Index 2-dodecylcyclobutanone (2-DCB), 166 Two-parameter Langmuir isotherm, 51 Two-step gradient elution reversed phase separation, 47 Two-step SFE fractionation method soybean oil, 162 2-tetradecylcyclobutanone (2-TCB), 166 Unretained tracer, 224 improper selection, 230 Urine HPLC-ECD chromatograms following SPME, 252



Van Deemter equation, 70 Van Deemter plot, 292 Volatile organic compounds (VOC) airborne, 238 GC-MS profile, 262 Volumetric mobile phase flow rate, 193 Wald equation, 189 Wheat pesticide recoveries, 153 Window diagram, 72 Wire-in-tube extraction, 239–240 X-rays spectroscopy methods, 280 X-rays techniques, 280