Temperature-Programmed Gas Chromatography E-Book

Leonid M. Blumberg

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 655

Veröffentlichungsjahr: 2011

Beschreibung

This book provides a comprehensive up-to-date overview of temperature-programmed gas chromatography (GC). The first part of the book introduces the reader to the basics concepts of GC, as well as the key properties of GC columns. The second part describes the mathematical and physical background of GC. In the third part, different aspects in the formation of a chromatogram are discussed, including retention times, peak spacing and peak widths. An invaluable reference for any chromatographer and analytical chemist, it provides all the answers to questions like: * At what temperature does a solute elute in a temperature-programmed analysis? * What is the value of the retention factor of eluting solute? * How wide are the peaks? * How large is the time distance between two peaks? * How do all these parameters depend on the heating rate?

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Preface

Constants, Abbreviations, Symbols

Part One: Introduction

Chapter 1: Basic Concepts and Terms

References

Chapter 2: A Column

2.1 Retention Mechanisms

2.2 Structures

2.3 Operational Modes

2.4 Specific and General Properties of a Column

2.5 Boundaries

References

Part Two: Background

Chapter 3: Linear Systems

3.1 Problem Review: Metrics for Peak Retention Time and Width

3.2 Chromatograph as an Information Processing System

3.3 Properties of Linear Systems

3.4 Mathematical Moments of Functions

3.5 Properties of Mathematical Moments

3.6 Pulses

References

Chapter 4: Migration of a Solid Object

4.1 Velocity of an Object

4.2 Parameters of Migration Path

4.3 Relations between Path Parameters and Object Parameters

References

Chapter 5: Solute–Liquid Interaction in Gas Chromatography

5.1 Distribution Constant and Retention Factor

5.2 Chromatographic Parameters of Solute–Liquid Interaction

5.3 Alternative Expressions of Ideal Retention Model

5.4 Linearized Retention Model

5.5 Relations Between Characteristic Parameters

Appendix 5.A Relative Errors in Power Functions

References

Chapter 6: Molecular Properties of Ideal Gas

6.1 Theory

6.2 Gas Viscosity and Related Parameters – Empirical Formulae

6.3 Empirical Formulae for Solute Diffusivity in a Gas

Appendix 6.A

References

Chapter 7: Flow of Ideal Gas

7.1 Flow of Gas in a Tube

7.2 Pneumatic Parameters

7.3 Relations Between Pneumatic Parameters

Appendix 7.A

References

Part Three: Formation of Chromatogram

Chapter 8: Formation of Retention Times

8.1 Solute Mobility

8.2 Solute–Column Interaction and Solute Migration

8.3 General Equations of a Solute Migration and Elution

8.4 Uniform Solute Mobility in Isobaric Analysis

8.5 Scalability of Retention Times in Isobaric Analyses

8.6 Dimensionless Parameters

8.7 Boundaries of the Linearized Model

Appendix 8.A

References

Chapter 9: Formation of Peak Spacing

9.1 Static GC Analysis

9.2 Closely Migrating Solutes in Dynamic Analysis

9.3 Isobaric Linear Heating Ramp and Highly Interactive Solutes

9.4 Properties of Generic Solutes

Appendix 9.A Elution Temperature Interval

References

Chapter 10: Formation of Peak Widths

10.1 Overview

10.2 Local Plate Height

10.3 Solute Zone in Nonuniform Medium

10.4 Apparent Plate Number and Height

10.5 Thin Film Columns

10.6 Thick Film Columns

10.7 Temperature-Programmed Analyses

10.8 Temperature-Programmed Thin Film Columns

10.9 Packed Columns

10.10 Scalability of Peak Widths in Isobaric Analyses

10.11 Plate Height: Evolution of the Concept

10.12 Incorrect Plate Height Theory

References

Index

Leonid M. Blumberg

Temperature-Programmed Gas Chromatography

Further Reading

Hübschmann, H.-J.

Handbook of GC/MS

Fundamentals and Applications

2009

Hardcover

ISBN: 978-3-527-31427-0

McMaster, M.

GC/MS

A Practical User’s Guide

2008

E-Book

ISBN: 978-0-470-22834-0

Rood, D.

The Troubleshooting and MaintenanceGuide for Gas Chromatographers

2007

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ISBN: 978-3-527-31373-0

Cserhati, T.

Multivariate Methods in Chromatography

A Practical Guide

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ISBN: 978-0-470-05820-6

Kuss, H.-J., Kromidas, S. (Eds.)

Quantification in LC and GC

A Practical Guide to Good Chromatographic Data

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ISBN: 978-3-527-32301-2

Fritz, J. S., Gjerde, D. T.

Ion Chromatography

4th completely revised and enlarged edition

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ISBN: 978-3-527-32052-3

The Author

Dr. Leonid M. BlumbergFast GC ConsultingP.O. Box 1243Wilmington, DE 19801 19801USA

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

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© 2010 Wiley-VCH Verlag & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

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Print ISBN: 978-3-527-32642-6 ePdf ISBN: 978-3-527-63215-2 ePub ISBN: 978-3-527-63226-8 Mobi ISBN: 978-3-527-64045-4

To Irena, who made this book possible

Preface

1952 was the year when James and Martin published two papers demonstrating partition gas chromatography [1, 2]. And it was also the year of Griffiths’, James’, and Phillips’ lecture on gas chromatography (GC) [3]. The main topic of the lecture at the First International Congress on Analytical Chemistry (Oxford, September 4–9, 1952) was the evaluation of alternatives to a thermal-conductivity cell. The authors mentioned that, by the way, “With a mixture containing components with a wide range of boiling points, the later components tend to spread themselves out to give long bands of low concentration. This can be overcome by varying the temperature (Fig. 3).” A linear heating ramp from 0 to 50°C in 40min and a five-peak chromatogram were shown in Figure 3 [3]. That was all for the beginning of the temperature-programmed GC.

After 50 years, Cramers and Leclercq estimated that 80% of GC analyses are conducted with temperature programming [4].

One can distinguish two groups of studies in temperature-programmed GC. One is concerned with the prediction of retention times of particular solutes. The focus of the other is a general theory whose object is general trends (such as effect of heating rate on retention of all peaks) and the effects of those trends on performance characteristics (such as the largest possible number of resolved peaks) of GC.

Foundation of general theory of temperature-program GC can be attributed to Giddings who outlined the theory and came close to solving the problem of optimal heating rate [5]. A book entirely dedicated to general theory of temperature-programmed GC was published by Harris and Habgood in 1966 [6]. Nothing on the same subject that was as comprehensive as that book has been published since then.

This book is an attempt of an overview of the more recent state of general theory of temperature-programmed GC. The book consists of three parts. Part one is introductory. It introduces the basic terminology of GC and briefly describes the key properties of GC columns.

Part Two, Background, outlines mathematical and physical background of GC. The titles of its chapters – Linear Systems, Migration of a Solid Object, Solute–Liquid Interaction in Gas Chromatography, Molecular Properties of Ideal Gas, and Flow of Ideal Gas – speak for themselves. The book provides probably the broadest coverage of these topics that can be found in a single volume on GC.

The core topics of the book are covered in Part Three, Formation of Chromatogram. Here too, the chapter titles – Formation of Retention Times, Formation of Peak Spacing, and Formation of Peak Widths – speak for themselves.

Chapter 10 on peak-width formation deserves additional comments. The chapter is based on Golay’s 1958 plate height theory [7] in capillary columns. Unfortunately, widely accepted perception of the theory, while being attributed to Golay, is a significant distortion of his theory. The distortion was introduced at the same symposium (Amsterdam, May 1958) where Golay presented his theory. This time, plate height theory in packed columns published 2 years earlier by van Deemter et al. [8] has been distorted, but 2 years later the distortion spread to Golay’s theory as well.

In the true van Deemter and Golay theories, plate height was expressed as a function of local velocity of a carrier gas. Due to gas decompression along the column, its local velocity is a coordinate-dependent quantity which is not easy to measure. It is much easier to measure the time-averaged gas velocity (briefly, average velocity). And so, for practical convenience, local gas velocity in Golay and van Deemter formulae was replaced with average velocity. The incorrectness of this distortion has been almost immediately recognized. Several leading experts in GC who adopted the distortion published the retractions. However, this was not enough. The distorted theory, being practically attractive, took on the life of its own. Since then, the pseudotheory dominated the GC literature including the textbooks and universality curricula on GC.

In majority of typical applications having weak or moderate gas decompression along the columns, the difference between actual dependence of plate height on gas average velocity and that dependence predicted from distorted theory was not alarmingly large. This was probably the key reason for the resilience of the distorted theory. However, in GC-MS with its vacuum at the column outlet, in high-resolution GC using long small-bore columns, and in other applications incurring strong gas decompression along the column, the difference is large. The fact that the accepted theory was not taken to the task of explaining experimental observations is an indication of a disregard for the theory among its own followers.

There is nothing wrong in expressing a column plate height as a function of a gas average velocity. However, the correct expressions of that kind are complex – much more so than the conveniently modified van Deemter and Golay formulae are. Also complex are the formulae for optimal average velocity. Much simpler are the formulae for the plate height as a function of a gas flow rate and the formulae for optimal flow rate. All that has been discussed in the literature. Although this simpler approach is based on sound theory and numerous experimental verifications, its acceptance lags its potential usefulness for scientifically based optimization of conventional GC and new techniques such as comprehensive multidimensional GC.

Of course the incorrect theories of GC were not the only ones. Development of correct theories by many workers never stopped. And this is what made this book possible. However, it is fair to say that the wide proliferation of the incorrect plate height theory – the theory of the most basic concept in chromatography – corrupted the trust in all theories in GC.

Recognizing that the theory presented in Chapter 10 is different from widely accepted theory, the material of the chapter is delivered differently than the material of the previous two chapters. While temperature programming is addressed from the very beginning of Chapters 8 and 9, Chapter 10 builds its case from historical perspective starting from simpler and gradually escalating to more complex issues eventually involving gas decompression and temperature programming. Both, the average gas velocity and the flow rate as independent variables in the formulae for plate height are explored. The readers who prefer to rely on the average velocity as the independent variable can see for themselves how complex the correct theory based on the average velocity is compared to its counterpart with flow rate as independent variable. Only after that, average velocity was removed from further considerations.

A special section in Chapter 10 is dedicated to the analysis of the incorrect plate height theory. This includes the motivation and evolution of the theory as well as the examples of its adoption, retractions, and criticism.

The book has a large number of mathematical formulae. Majority of them were derived from basic principles. All formulae with the exception of the simple ones were derived with the help of Mathematica® software (Wolfram Research, Champaign, IL, USA). Without Mathematica, management of this number of formula with the confidence in their correctness would be hardly possible.

A few words about myself. Educated in the USSR as electrical engineer, I immigrated to the US in 1977 and joined Avondale division of Hewlett-Packard Co. Having by the time of immigration an expertise in theory and design in low-noise electronics, I was involved for 10 years in the design of signal-processing hardware and software for GC integrators. And then began my rapid drift into GC. Ray Dandeneau, the R&D manager at that time, lured me in GC. Terry Berger was my local guide. Although I never met Golay, I consider myself to be his and Giddings’ student. I met Giddings once and was lucky to have a lengthy discussion with him. I also learned a good deal from the works of Cramers and Guiochon. There was time when Cramers and I communicated on a more or less regular basis.

One of my first GC publications was a two-part series (part 1 with Berger) on theory of plate height in nonuniform time-varying chromatography [9, 10]. Although this work remains mostly unknown, I think that it was my most significant contribution to chromatographic theory (GC, LC, etc.). Thus, Giddings’ formula for plate height in GC with gas decompression [11, 12] along the column and Giddings’ pressure correction factor follow directly from that theory. Some results of the theory are incorporated in the text of Chapter 10.

June 2010

Leon Blumberg

References

1 James, A.T. and Martin, A.J.P. (1952) Biochem. J., 50, 679–690.

2 James, A.T. and Martin, A.J.P. (1952) Analyst, 77, 915–932.

3 Griffiths, J., James, D., and Phillips, C.S.G. (1952) Analyst, 77, 897–904.

4 Cramers, C.A. and Leclercq, P.A. (1999) J. Chromatogr. A, 842, 3–13.

5 Giddings, J.C. (1962) Gas Chromatography (eds N. Brenner, J.E. Callen, and M.D. Weiss), Academic Press, New York, pp. 57–77.

6 Harris, W.E. and Habgood, H.W., (1966) Programmed Temperature Gas Chromatography, John Wiley & Sons, Inc., New York.

7 Golay, M.J.E. (1958) Gas Chromatography 1958 (ed. D.H. Desty), Academic Press, New York, pp. 36–55.

8 van Deemter, J.J.J., Zuiderweg, F.J., and Klinkenberg, A. (1956) Chem. Eng. Sci., 5, 271–289.

9 Blumberg, L.M. and Berger, T.A. (1992) J. Chromatogr., 596, 1–13.

10 Blumberg, L.M. (1993) J. Chromatogr., 637, 119–128.

11 Stewart, G.H., Seager, S.L., and Giddings, J.C. (1959) Anal. Chem., 31, 1738.

12 Giddings, J.C., Seager, S.L., Stucki, L.R., and Stewart, G.H. (1960) Anal. Chem., 32, 867–870.

Part One

Introduction

Chapter 1

Basic Concepts and Terms

Chromatography is a technique of separation of compounds – components of a mixture. Chromatography can be analytical [1], or – as in the case of preparative chromatography [2–4] – it can be other than analytical. The purpose of analytical chromatography is to obtain information regarding a mixture and its components rather than to make a product. Here the analytical chromatography has been considered only. How clean is the air in this room? What are the major components of the gasoline in this container? Is this pesticide present in the soil at this location, and, if yes, how much of it is there? To answer these and similar questions, one can analyze a representative sample of a mixture in question – a test mixture.

A chromatograph or a chromatographic instrument consists of several devices. The key device is the separation device – the one where the separation takes place. In column chromatography, the separation device is a chromatographic column – a tube that either has a special material along its inner walls (an open tubular column) or is packed with small particles (packed column) or with a porous material. The separation occurs due to different levels of nondestructive interactions of different components (analytes, species) of a test mixture with the material inside the column. As the subject of this book is the column analytical chromatography, from now on, the term chromatography will always infer that technique.

In addition to a column, a typical chromatograph includes, Figure 1.1, a sample introduction device [5–10] and a detector [5,6,10,11]. A chromatograph also requires a fluid (eluent [6, 12], mobile phase) that flows through the column from its inlet to the outlet transporting components of a test mixture in the same direction. In gas chromatography (GC), the mobile phase is an inert carrier gas, in liquid chromatography (LC), the mobile phase is a liquid. To emphasize the fact that the components of a test mixture are soluble in the mobile phase, they are also called the solutes.

Figure 1.1 Block-diagram of a chromatograph.

A set of conditions for the execution of a chromatographic analysis (a run) – the column type and temperature, the carrier gas type and its flow rate or pressure, the sample introduction device and the detector together with their operational conditions, and so forth – comprise a method of the analysis.

A chromatographic analysis starts with a quick (ideally, instantaneous) injection of a test mixture into the column inlet. While being transported through the column, different solutes differently interacting with the column interior migrate through the column with different velocities. As a result, each solute is retained (resides) in the column for different amount of time, known as the retention time or the residence time. Different retention times cause the solutes to elute – to pass through the column outlet – separately from each other constituting the separation of the solutes.

When an eluite [6, 13] (a solute eluting from a column) mixed with effluent [12] (mobile phase leaving a column) passes through a detector, the latter generates a response indicative of the presence of the solute in the detector. Ideally, a detector response to each solute should be proportional to the solute amount or concentration.

A way to observe the separation result is through a chromatogram representing a plot of a detector signal – the detector response as a function of time elapsed since the injection of a test mixture. A simple chromatogram resulted from analysis of a two-component mixture is shown in Figure 1.2. Ideally, it should be a line chromatogram [14–16] shown in Figure 1.2a. Unfortunately, no matter how quick was the injection, each solute migrating along the column occupies a zone (a band) whose width gradually increases with time. As a result, each eluite and a corresponding peak have nonzero width as shown in Figure 1.2b.

Figure 1.2 Chromatograms of a two-component mixture. The markers, tR1 and tR2, are the retention times of respective components. (a) A line chromatogram that would occur if there were no broadening of the solute zones during the solute migration along the column. (b) A realistic two-peak chromatogram resulted from the separation and the broadening of the solute zones.

Usually, a chromatographic analysis does not end with the generation of a chromatogram. A contemporary chromatographic system might include a chromatograph and a data analysis subsystem. The latter might quantify and identify the peaks and report retention time, width, area, height, amount, concentration, and other information regarding each peak.

Two different concepts – a solute zone and a peak – have already been mentioned in the preceding text. A zone, Figure 1.3, is a space occupied by a solute migrating in a column. The distribution of a solute zone along a column can be described (Figure 1.3b) by the solute’s specific amount, a(z), – the solute amount (mass, mole, and so forth) per unit of length. The width of a zone is measured in units of length along the column. A peak, on the other hand, can be a zone elution rate [06], a detector signal in response to elution of the zone, or a portion of chromatogram (Figure 1.2b) representing that signal. In either case, the width of a peak is measured in units of time. The distinction between the terms a zone and a peak is recognized throughout the book. Typically, both a zone and a peak representing the zone have similar pulse-like shape with a clearly identifiable maximum.

Figure 1.3 Solute zone within a L-long column (a), and the distribution, a(z), of its amount along the z-axis (b). The proportions of the column and the zone shown here are not typical. Typically, a column is several orders of magnitude longer than its internal diameter, and the longitudinal width of a zone – its spread along the z-axis – is hundreds of times larger than the diameter.

Throughout the book, the width of a pulse (a peak or a zone) is identified with its standard deviation defined later. For now, it is sufficient to assume that standard deviation of a pulse (denoted as σ for a peak and for a zone) is equal to about 40% of its half-height width [12].

Quality of separation of two peaks depends on their spacing [15, 17, 18] – the difference between the peak retention times – and widths. For the peaks of the same width, Figure 1.4, the further they are apart from each other the better they are separated. On the other hand, for the same spacing, Figure 1.5, the narrower are the peaks the better is their separation.

Figure 1.4 Four pairs of peaks. The peaks (dashed lines) in each pair have the same width and shape, but different distances between their apexes. The distances increase from (a) to (c) and so does the appearance of the peak separation in each pair.

Figure 1.5 Pairs, (a) and (b), of peaks. In both pairs, the distance between the peaks (dashed curves, – – –, in pair (b)) is the same. However, the two peaks in pair (a) are 10 times narrower and appear to be more separate than the peaks in pair (b).

References

1 Giddings, J.C. (1991) Unified Separation Science, John Wiley & Sons, Inc., New York.

2 Biblingmeyer, B.A. (1987) Preparative Liquid Chromatography, Elsevier, Amsterdam.

3 Guiochon, G., Shirazi, S.G., and Katti, A.M. (1994) Fundamentals of Preparative and Nonlinear Chromatography, Academic Press, San Diego.

4 Schmidt-Traub, H. (2005) Preparative Chromatography of Fine Chemicals and Pharmaceutical Agents, Wiley-VCH, Weinheim.

5 Lee, M.L., Yang, F.J., and Bartle, K.D. (1984) Open Tubular Gas Chromatography, John Wiley & Sons, Inc., New York.

6 Guiochon, G. and Guillemin, C.L. (1988) Quantitative Gas Chromatography for Laboratory Analysis and On-Line Control, Elsevier, Amsterdam.

7 Klee, M.S. (1990) GC Inlets – An Introduction, Hewlett-Packard Co., USA.

8 Jennings, W., Mittlefehldt, E., and Stremple, P. (1997) Analytical Gas Chromatography, 2nd edn, Academic Press, San Diego.

9 Grob, K. (2001) Split and Splitless Injection for Quantitative Gas Chromatography – Concepts, Processes, Practical Guidelines, Sources of Error, Wiley-VCH, Weinheim.

10 Poole, C.F. (2003) The Essence of Chromatography, Elsevier, Amsterdam.

11 McNair, H.M. and Miller, J.M. (1998) Basic Gas Chromatography, John Wiley & Sons, Inc., New York.

12 Ettre, L.S. (1993) Pure Appl. Chem., 65, 819–872.

13 Haidacher, D., Vailaya, A., and Horváth, S. (1996) Proc. Natl. Acad. Sci. USA, 93, 2290–2295.

14 Davis, J.M. and Giddings, J.C. (1985) Anal. Chem., 57, 2168–2177.

15 Giddings, J.C. (1990) in Multidimensional Chromatography Techniques and Applications (ed. H.J. Cortes), Marcel Dekker, New York and Basel, pp. 1–27.

16 Giddings, J.C. (1995) J. Chromatogr., 703, 3–15.

17 Dolan, J.W. and Snyder, L.R. (1998) J. Chromatogr. A, 799, 21–34.

18 Dolan, J.W. (2003) LC-GC, 21, 350–354.

Chapter 2

A Column

In this chapter, the most prominent structures, retention mechanisms, and operational modes of GC columns are discussed with the main purpose of introducing the relevant terminology. A more detailed information can be found in many sources [1–13].

2.1 Retention Mechanisms

As mentioned earlier, the root cause of separation of solutes – components of a test mixture – in chromatography is the different levels of nondestructive interaction of the solutes with the column interior. In GC, that interaction is the sorption (absorption or adsorption) of the solutes by stationary (not moving) sorbent – a column stationary inner material also known as the stationary phase. The sorption is balanced by the opposing process of a solute desorption into the inert carrier gas – the mobile phase or the eluent. At their sorption/desorption equilibrium, different solutes become differently distributed between the mobile and the stationary phase. As a result, different solutes are carried by the carrier gas toward the column outlet with different net velocities. This causes different time of retention (residence) of the solutes in the column, and their subsequent separation.