Quadrupole Mass Spectrometry and its Applications PDF
Preview Quadrupole Mass Spectrometry and its Applications
PETER H.DAWSON (editor) QUADRÜPOLE MASS SPECTROMETRY and its applications ELSEVIER SCIENTIFIC PUBLISHING COMPANY AMSTERDAM-OXFORD-NEW YORK 1976 ELSEVIER SCIENTIFIC PUBLISHING COMPANY 335 Jan van Galenstraat P.O. Box 211, Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017 With 189 illustrations and 21 tables ISBN: 0-444-41345-6 Copyright © 1976 by Elsevier Scientific Publishing Company, Amsterdam All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, Jan van Galenstraat 335, Amsterdam Printed in The Netherlands To the pioneering group from the University of Bonn PREFACE There has been a rapid proliferation of quadrupole mass spectrometers in the last decade. Quadrupoles are dynamic mass analysers and, while very simple in their physical geometry, are very complex in their behaviour. Recent theoretical and experimental advances have now provided a basic under standing of real (that is to say, imperfect) quadrupole devices. This book proceeds from a general explanation of the action of radio- frequency quadrupole fields to the description of their utilization in mass analysers such as the quadrupole mass filter, the monopole, the three- dimensional quadrupole ion trap and various time-of-flight spectrometers and finally to the characteristic applications of quadrupoles. A multi-author format was adopted, even though the intention was to produce a systematic text rather than a series of reviews. This provides a broader-than-usual viewpoint in the book and while there is, of necessity, a certain amount of recapitulation in various chapters, repetition has been avoided by the circulation of drafts between authors and many cross- references have been added. Chapters I-V provide a unified approach to explaining the principles of operation of quadrupole devices. Chapter II is largely a qualitative account, illustrated by ion trajectories and computer simulations of performance. The mathematical background is dealt with in Chapter III. Chapter IV furnishes a detailed description of numerical methods of calculation of performance, including the recently developed application of phase-space dynamics. The very important and sometimes controversial subjects of fringing fields and other field imperfections are discussed in Chapter V. Chapters VI-IX provide design and performance evaluations of the mass filter, the monopole, ion traps and time-of-flight instruments. These chapters have been contributed by authors with extensive practical experience with the respective instruments. The approach each takes is quite different, but this reflects the very different state of development in each field. For the mass filter, there is a considerable body of design data available. For the monopole, little data of any kind has been published and Chapter VII is largely a description of a particular design and its performance. For ion traps the present emphasis is on understanding the properties of the stored ions. Chapter IX is more speculative since quadrupole time-of-flight devices are in their infancy. Chapters X-XIII are descriptions of tour areas of application where quad rupole devices have made the greatest impact because of their particular advantages and disadvantages. A project of this kind has involved the co-operation and assistance of many people. We are indebted to our colleagues who have provided data and illu strations used in the book. I would like to thank Rey Whetten for reading much of the manuscript and making many helpful suggestions and, especially, for the pleasure and inspiration that I derived from the years that we worked together on quadrupoles. There follows a list of further acknowledgements and the detailed addresses of the authors. Chapters I-V P.H. Dawson, Division of Physics, National Research Council of Canada, Ottawa, Canada. I gratefully acknowledge the help of Alain Laverdiere of Laval University and Ryoichi Matsumura of NRC in preparing the illustrations and of Colette Verrette of Laval University in typing early drafts. I am deeply indebted to Jill Baker for the preparation of the final manuscript. Chapter VI W.E. Austin, A.E. Holme and J.H. Leek, Department of Electrical Engineering and Electronics, University of Liverpool, Brownlow Hill, Liverpool, U.K. Chapter VII R.F. Herzog, Department of Physics and Astronomy, University of Southern Mississippi, Southern Station Box 5202, Hattiesburg, Mississippi 39401, U.S.A. Chapter VIII J.F.J. Todd and G. Lawson, Chemical Laboratory, University of Kent, Canterbury, Kent, U.K. R.F. Bonner, Department of Chemistry, Trent University, Peterborough, Ontario, Canada. We are indebted to our colleagues in the "dynamic" mass spectrometry group at the University of Kent for their helpful comments and criticisms, and particularly to Roger Mather who obtained some of the data quoted. The assistance of Maree PoUett and Joy Bower-Smith in typing and preparing the manuscript is gratefully acknowledged. Chapter IX J.P. Carrico, Bendix Research Laboratories, Bendix Center, Southfield, Michigan 40875, U.S.A. Discussions with Dr. R.K. Mueller are gratefully acknowledged. The assis tance of S. Miller in the preparation of the manuscript is deeply appreciated. Chapter X J.F.J. Todd, Chemical Laboratory, University of Kent, Canterbury, Kent, U.K. It is a pleasure to acknowledge the help of my colleague Graham Lawson in preparing some of the material for the chapter, and of Maree Pollett, Sheila Cousins, and Linda Lawson in typing sections of the manuscript. Chapter XI G.R. Carignan, Space Physics Research Laboratory, Department of Electrical and Computer Engineering, University of Michigan, Ann Arbor, Michigan 48105, U.S.A. The author is indebted to Wilson Brubaker, Rocco Narcissi, Nelson Spencer, and Ulf von Zahn for their thoughtful assistance in preparing the historical section of the chapter. I am especially indebted to Marti Moon for transforming my handwriting into a final manuscript. Copyright for Figs. 3-5 belongs to the American Geophysical Union. Chapter XII M.S. Story, Finnigan Corporation, 845 West Maude Avenue, Sunnyvale, California 94086, U.S.A. I would especially like to acknowledge the tremendous creative and elec tronic contributionsi of William J. Fies of Finnigan Corporation without which much of the work discussed here would not have been possible. Chapter XIII Graham Lawson, Chemical Laboratory, University of Kent, Canterbury, Kent, U.K. I am indebted to my colleagues in the mass spectrometry group at the University of Kent for their many contributions to and criticisms of the earlier drafts of the chapter. I am particularly grateful to my wife for typing the manuscript. PRINCIPAL SYMBOLS a parameter in the Mathieu equation of motion which depends upon U a stability limit in the Mathieu diagram (even solutions) m a parameter in the calculation of C 2n 2n b parameter in the equation of motion which depends on an auxiliary field b stability limit in the Mathieu diagram (odd solutions) m b parameter in the calculation of C 2n 2n d integer used to specify exact focusing conditions as in ß = p/d d height of the monopole entrance aperture { d height of the monopole exit aperture 2 e electronic charge f applied frequency (in hertz) /o lens focal length g parameter in the equation of motion which depends on an auxiliary magnetic field constant relating the resolution to n2 parameters in the Meissner equation of motion ion trap signal at saturation parameter representing viscous drag minor axis of the acceptance ellipse ionic mass (kg) unit atomic mass (kg) 12> m2i > m22 elements of the matrix M number of rf cycles an ion spends in the field number of rf cycles in a quarter wavelength of the fundamental ion motion p gas pressure g p integer used to specify exact focusing conditions as in ß = p/d q parameter in the Mathieu equation of motion which depends upon V r radial coordinate r field radius 0 s an integer t time in seconds £j arrival time u coordinate parameter representing x, y, z or r 9 ü du/άζ v velocity in the axial direction z x transverse coordinate direction (conventionally that towards the positively biased electrodes) x maximum value of x during a trajectory m y transverse coordinate direction (conventionally that towards the negatively biased electrodes) y maximum value of y during a trajectory m z axial coordinate direction z field size parameter for the ion trap = r /20·5 0 0 z distance of the focusing point in the focusing monopole t A parameter representing gravity in the equation of motion of macro- particles suspended in a field A weighting factor in the general expression for potential N B magnetic field strength C, C ' components of a matrix representing a fringing field C constants in the solution to the equation of motion depending on 2n a and q .D rod diameter D pseudo-potential well depth E electric field E' auxiliary electric field eE ion energy in the axial direction z F force F, F particular solutions to the equation of ion motion { 2 G,G parameters in the general solution to the equation of motion l 2 depending on u and ώ, respectively / ion current in amperes L length of the analyser field 1/ major axis of the acceptance ellipse M specific ionic mass in amu AM peak width M matrix representing one cycle of ion motion N ion density AT«, ion density at saturation P power loss Q quality factor of a coil R resolution (M/AM) S, S' components of a matrix representing the fringing field T a small time interval (<€ 1 rf cycle) T ion temperature { U d.c. voltage applied between opposite sets of electrodes U* system constant for the monopole V zero-to-peak rf voltage applied between opposite sets of electrodes W the Wronksian determinant Z ion displacement averaged over one rf cycle a ratio of the frequency of an auxiliary field to co 0 a\ a" integration constants in the solution to the Mathieu equation β parameter characterizing the nature of ion motion in the stable region 7 weighting factor for the z direction of the field δ displacement due to the ion micromotion δ duty cycle of a rectangular waveform 0 e emittance or acceptance of the mass filter 6j 2u/v e permittivity 0 e', e" construction tolerances 77 viscosity coefficient Θ angular coordinate 0 parameters in the Hill equation of motion r λ weighting factor for the x direction of the field X angular momentum about the z axis a μ parameter characterizing the nature of the ion motion (= iß in the stable region) £ time expressed in terms of the applied field (= cot/2) £ initial phase of the rf field 0 £j phase when G becomes zero 2 p the ratio between electron beam width and 2z 0 p terms in the recursion relationships between C values n 2n p' parameter representing the relative magnitude of an auxiliary field PMAX maximum space charge σ weighting factor for the y direction of the field r characteristic period in the ion oscillation Tj characteristic period for ion loss φ pseudo-potential co angular frequency of the applied field co fundamental frequency of ion motion 0 ω, ω higher frequency components of the ion motion { 2 co' angular frequency of an auxiliary field C0p plasma resonance frequency A parameter of the acceptance ellipse B parameter of the acceptance ellipse Γ parameter of the acceptance ellipse Φ electric potential Φ potential applied between opposite sets of electrodes 0 Φ , Φ third and fourth order terms in the potential 3 4
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