Transform Techniques in Chemistry PDF
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Transform Techniques in Chemistry MODERN ANALYTICAL CHEMISTRY Series Editor: David Hercules University of Pittsburgh ANALYTICAL ATOMIC SPECTROSCOPY By William G. Schrenk PHOTOELECTRON AND AUGER SPECTROSCOPY By Thomas A. Carlson MODERN FLUORESCENCE SPECTROSCOPY, VOLUME 1 Edited by E. L. Wehry MODERN FLUORESCENCE SPECTROSCOPY, VOLUME 2 Edited by E. L. Wehry APPUED ATOMIC SPECTROSCOPY, VOLUME 1 Edited by E. L. Grove APPLIED ATOMIC SPECTROSCOPY, VOLUME 2 Edited by E. L. Grove TRANSFORM TECHNIQUES IN CHEMISTRY Edited by Peter R. Griffiths ION-SELECTIVE ELECTRODES IN ANALYTICAL CHEMISTRY Edited by Henry Freiser Transform Techniques in Chemistry Edited by Peter R. Griffiths Ohio University, Athens Plenum Press· New York and London Library of Congress Cataloging in Publication Data Main entry under title: Transform techniques in chemistry. ~Modern analytical chemistry) Includes bibliographical references and index. 1. Fourier transform spectroscopy. I. Griffiths, Peter A., 1942- QD96.F68T7 543'.085 77-29271 ISBN 978-1-4684-2405-8 ISBN 978-1-4684-2403-4 (e9ook) 001 10.1007/978-1-4684-2403-4 ® 1978 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1978 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 AU rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, me<:hanical, photocopying, microfilming, re<:ording, or otherwise, without written permission from the Publisher Contributors Michael B. Comisarow, Chemistry Department, University of British Columbia, Vancouver, B.C., Canada V6T lW5 James W. Cooper, Department of Chemistry, Tufts University, Medford, Massachusetts 02155 Thomas C. Farrar, Chemistry Division, National Science Foundation, Washington, D.C., 20550 Charles T. Foskett, Digilab, Inc., Cambridge, Massachusetts 02139 Peter R. Griffiths, Department of Chemistry, Ohio University, Athens, Ohio 45701 Martin Harwit, Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853 Peter C. Jurs, Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802 Russell D. Larsen, Department of Chemistry, University of Nevada Reno, Reno, Nevada 89507. Present address: Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 John O. Lephardt, Phillip Morris U.S.A., Research Center, P. O. Box 26583, Richmond, Virginia 23261 Alan G. Marshall, Chemistry Department, University of British Columbia, Vancouver, B.C., Canada V6T 1W 5 Charles L. Wilkins, Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68501 v Preface The application of the Fourier transform is being seen to an increasing extent in all branches of chemistry, but it is in the area of chemical analysis that the greatest activity is taking place. Fourier transform infrared and nuclear magnetic resonance spectrometry are already routine methods for obtaining high-sensitivity IR and NMR spectra. Analogous methods are now being developed for mass spectrometry (Fourier transform ion cyclo tron resonance spectrometry) and microwave spectroscopy, and Fourier transform techniques have been successfully applied in several areas of electrochemistry. In addition the fast Fourier transform algorithm has been used for smoothing, interpolation, and more efficient storage of data, and has been studied as a potential method for more efficient identification of samples using pattern recognition techniques. Linear transforms have also been shown to be useful in analytical chemistry. Probably the most important of these is the Hadamard transform, which has been applied in alternative methods for obtaining IR and NMR data at high sensitivity. Even though measurements involving this algorithm will probably not be applied as universally as their Fourier transform ana logs, in the area of pattern recognition application of the Hadamard trans form will in all probability prove more important than application of the Fourier transform. In this book, distinguished investigators in the various fields mentioned above have written on their area of expertise at a level that should be understandable to graduate analytical chemists and to the advanced under graduate, as well as the professional maintaining and updating research skills. It is hoped that the similarities between the various spectroscopic and data manipulation techniques will become evident throughout the book. We have omitted treatment of crystallographic applications because they seem outside the mainstream of analytical interests. After a brieflook at the history of transform techniques in chemistry and an editorial forecast of their applications in the future (Chapter 1), the mathe- vii viii Preface matical basis of the Fourier transform is introduced by Charles Foskett of Digilab, Inc., in Chapter 2. In Chapter 3, Alan Marshall and Melvin Comisa row of the University of British Columbia discuss the foundation of multi plex methods in spectroscopy, showing the origin of the advantages of instruments that do not measure a spectrum directly, but rather generate a signal that is related to the spectrum through the Fourier or Hadamard transform. In Chapter 4, James Cooper of Tufts University discusses the nature of the data-handling and computer capabilities required for on-line Fourier transform spectrometry. The next six chapters describe the theory, instrumentation, and appli cations of several different types of multiplex spectroscopy. In Chapters 5 and 6 the editor describes Fourier transform infrared spectrometry, and in Chapter 7 Martin Harwit of Cornell University describes Hadamard transform infrared spectrometry, including how this technique may be used to multiplex information both spectrally and spatially. In Chapter 8, Thomas Farrar of the National Science Foundation introduces Fourier transform-NMR spectrometry, and some of the more recent advances in this subject are described in the subsequent chapter (Chapter 9) by James Cooper. In Chapter 10, the nature of Fourier transform ion cyclotron res onance spectrometry is introduced by Melvin Comisarow. Several of the more important applications of the Fourier transform in data processing are discussed in Chapter 11 by John Lephardt of Philip Morris U.S.A., and in Chapter 12, the application of transform techniques in pattern recognition is described by Charles Wilkins of the University of Nebraska and Peter Jurs of Pennsylvania State University. Chapter 13, by Russell Larsen of the University of Nevada at Reno, describes poten tial applications of binary transforms for very rapid data processing; to a greater extent than the previous chapters, this represents a look into the future and is written to a slightly more advanced audience than the earlier chapters. We believe it represents an important new transform technique of the future and merits a more advanced treatment since there is little readily available reference material on this subject. Finally, the editor has summar ized the applications of the Fourier transform in electrochemistry in a chapter that illustrates not only the sensitivity advantage obtained through acquiring data at several frequencies simultaneously but also shows how the information content of different types of electrochemical data may be enhanced by the application of the Fourier transform independently of the manner in which the data were acquired. That a volume such as this may be compiled is a tribute to the many pioneers in all the areas covered in this book. The fact that so many of the techniques that are described here are now available in the market place is similarly a tribute to the individuals and companies who had faith that transform techniques were of sufficient value to be developed commercially. On a more personal level, the editor and many of the authors would like Preface ix to thank the various agencies that, in such timely fashion, supported their research and the many co-workers without whose cooperation and hard work many of the results described in this book would not have been found. Finally, the secretarial assistance so valuable in preparing the manuscripts of these chapters is gratefully acknowledged. Peter R. Griffiths Contents Chapter 1 Transform Techniques in Chemistry: Past, Present, and Future Peter R. Griffiths 1.1. The Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Optical Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 .2. NMR Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.3. Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2. .T he Present. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3. The Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 References .............................................. 8 Chapter 2 The Fourier Transform and Related Concepts : A First Look Charles T. Foskett 2.1. Introduction: Guitar Tuning ................................ 11 2.2. Differences in Space and Time: Phase ......................... 14 2.3. Sums, Integrals, and Orthogonality. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4. Various Expressions of Fourier Transform Relationships. . . . . . . . . . . 17 2.5. Concepts and Corollaries for Fourier Transforms ................ 19 2.6. More on Phase and Phase Correction. . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.7. Apodization and Resolution Enhancement. . . . . . . . . . . . . . . . . . . . . . 30 2.8. The Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.9. Walsh and Hadamard Transforms ........ . . . . . . . . . . . . . . . . . . . . 35 2.1 O. Summary ............................................... 36 References .............................................. 37 xi xii Contents Chapter 3 Multichannel Methods in Spectroscopy Alan G. Marshall and Melvin B. Comisarow 3.1. Introduction............................................. 39 3.2. Spectrometer Sources and Detectors. . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2.1. Terminology....................................... 40 3.2.2. Single-Channel (Scanning-Type) Spectrometer. . . . . . . . . . . . . 40 3.2.3. Multidetector Spectrometer ........................... 41 3.3. Weights on a Balance: The Multichannel Advantage. Multiplex Methods. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 45 3.3.1. One-at-a-Time Weighing: The Scanning Spectrometer. . . . . . . 45 3.3.2. Many Balances: The Multidetector Spectrometer. . . . . . . . . . . 46 3.3.3. Half the Weights on the Balance at Once: Hadamard Multiplexing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3.4. All the Weights on the Balance at Once: The Fourier Advan tage ........................................ 48 3.4. Hadamard Multiplexing of Spatially Dispersed Spectra. . . . . . . . . . . . 49 3.5. Advantages of Coherent Radiation in Spectrometer Detection. . . . . . . 53 3.6. Fourier Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.6.1. Fourier Multiplexing: The Multichannel Advantage ........ 55 3.6.2. Fourier Analysis of Detector Response: Spectral Line Shape. . 58 3.6.3. Pulsed Monochromatic Coherent Radiation as a Broad-Band Radiation Source ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.7. Summary: Relations Between Different Spectrometers. . . . . . . . . . . . . 61 3.8. Appendix. Noise Considerations for Multichannel Spectrometers .... 63 3.8.1. NB oc (signal)l/2: "Source-Limited" Noise. . . . . . . . . . . . . . . . 65 3.8.2. NA = constant: "Detector-Limited" Noise ............... 65 3.8.3. NC oc signal: "Fluctuation" Noise. . . . . . . . . . . . . . . . . . . . . . 65 References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Chapter 4 Data Handling in Fourier Transform Spectroscopy James W. Cooper 4.1. The Computer System ..................................... 69 4.1.1. Introduction to Computers ........................... 69 4.1.2. Data Acquisition ................................... 71 4.1.3. Timing in Data Acquisition. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.1.4. The Sampling Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.1.5. Digital Phase Correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.1.6. Signal Averaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.1.7. Signals Having High Dynamic Range. . . . . . . . . . . . . . . . . . . . 79 4.1.8. Other Computer Requirements. . . . . . . . . . . . . . . . . . . . . . . . . 81 4.1.9. Disk-Based Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.1.10. Comparison of Data System Requirements in NMR and IR .. 83 4.2. The Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
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