Magnetically Enhanced Quadrupole Mass Spectrometer Thesis submitted in accordance with the requirements of the University of Liverpool for the degree of Doctor in Philosophy by Simon Maher Department of Electrical Engineering and Electronics University of Liverpool September 2013 Synopsis The Quadrupole Mass Filter (QMF) is the key component of a Quadrupole Mass Spectrometer (QMS) first described by Nobel laureate Wolfgang Paul and co- worker Helmut Steinwedel in 1953. The QMS remains a widely used analytical tool for separating charged species in space according to their mass-to-charge ratio, with an extensive range of applications in both industry and research. In the original work of Paul and Steinwedel much emphasis was placed on the fact that the QMF separates ions due to the quadrupolar electric field (comprising dc and ac components) and without the use of magnetic fields. In the present thesis both experimental and theoretical work is presented, to demonstrate that the application of a magnetic field to a QMS enhances device performance. Theoretical work has focussed on the analytical investigation of the Mathieu equation for this particular case. This has led to an extensive simulation study of a QMS under the application of static and dynamic magnetic fields. A method is described that enables the three-dimensional (3D) fields of a simple QMF to be determined to a high accuracy. The technique produces accurate field values and was used to investigate fringe field effects particularly at the entrance to the QMF where they can often be detrimental to performance. Moreover, a two- dimensional (2D) software model was used to study the behaviour of the QMF and modified to incorporate the effect of applying a magnetic field. The software model is capable of accurate simulation of spectra allowing the user to specify QMF dimensions and various applied input signals including, electrode geometries, dimensions and operating parameters. A new performance method has been developed that allows the effective stability diagram of the QMS to be mapped numerically for given operational i conditions. This method generates an effective stability diagram which enables instrument behaviour to be predicted and provides a means for optimising performance. Using this method the stability diagram has been effectively mapped for a QMS with a static transverse magnetic field applied in zone 1. This provides an insight into the fundamental workings of this device therefore allowing operating parameters to be optimised accordingly. The ability to scan a range of ion masses and provide uniformity of the effect of the magnetic field is a necessary requirement for a viable mass spectrometer instrument. The proof-of-concept for this novel instrument is demonstrated using a dynamic magnetic field. In order to implement the magnetic field with the conventional scanning method a Helmholtz coil electromagnet was used; this allowed the magnetic field intensity to be altered by varying the current. A custom current ramp was designed and built to operate the Helmholtz coil. This was manually synchronised with a commercial quadrupole mass spectrometer to provide a constant peak width mass scan demonstrating the proof-of-concept for a magnetically enhanced QMS. A magnetically enhanced QMS is a novel instrument that has improved performance with more powerful monitoring and sensing capabilities than conventional QMS instruments available hitherto. One of the challenges of developing and deploying portable MS is that of reducing the size (to render the MS system portable), whilst at the same time maintaining instrument performance in terms of resolution, sensitivity and mass range. Such an instrument in deployment should find a range of applications. ii Acknowledgements The University of Liverpool coat of arms depicts an open book inscribed with the Latin phrase “fiat lux” (which is translated “let there be light”) the first words spoken by God at the beginning of time in the book of Genesis. This is an expression that incorporates so many facets relevant to science: knowledge, truth, wisdom, design, creativity, energy and so much more. It is in this light that my PhD training has been undertaken. This process has not been without its struggles and I have received significant help and guidance from so many to whom I am indebted and sincerely grateful for their kindness. First and foremost my thanks is aimed heavenwards to the Lord God Almighty for all that He has given me. I owe a huge debt of gratitude to my supervisor, Prof. Stephen Taylor, who gave me the opportunity to undertake research in his group and continues to provide a constant flow of support and encouragement. It has been a great privilege to work under his guidance. I am very thankful to Dr. J. R. Gibson, acting as my secondary supervisor, who has provided a wealth of advice and assistance throughout this work. I am also extremely grateful to the Department of Electrical Engineering & Electronics at the University of Liverpool and the Engineering and Physical Sciences Research Council (EPSRC) for awarding me a Doctoral Training Grant without which I would not have been able to undertake this research. I offer my sincerest thanks to the many past and present members of the Mass Spectrometry group for their help and whole-hearted support: Dr. S. U. Syed, Mr. F. P. Jjunju, Dr. B. Brkic, Dr. T. J. Hogan, Dr. F. Salarzaei, Dr. J. Sreekumar, Dr. K. Evans, Dr. V. Leus, Mr. S. Giannoukos and Mrs. M. Juno. iii I would like to express my thanks for the help and technical assistance received from the staff at Q-Technologies (Liverpool, UK): Dr. N. France, Mr. D. Taylor, Mrs. A. Standish and Mr. A. Taylor. Many thanks to Dr. R. T. Smith who has been a great source of advice and encouragement and to Mr. D. M. Hughes from the Department of Mathematical Sciences (University of Liverpool) for his advice, suggestions and assistance. Special thanks to Mr Jonathan Maher, Mr Graham Swift and Dr. R. T. Smith for proof reading this thesis. This version of the thesis is that corrected in response to the comments of the examiners following the viva. The contribution of the examiners, Prof. John F. J. Todd and Prof. Simon Maskell, in this respect is acknowledged. I would like to acknowledge the help and assistance provided by technical staff at the University of Liverpool. From the Department of Electrical Engineering: Mr. A. Roby, Mr. R. Wratten, Mr G. Cook, Mr. J. Carrick, Ms. J. Anson, Mr. J. Lynch and Mr. A. Edwards; from the School of Engineering: Mr. D. Atkinson and Mr. M. Jahme; from the e-Science team thanks are due to Dr. Ian Smith for his assistance in utilising the Condor High Throughput Computing Service. I would like to thank Dr. M. Egan of the Ultra Mixing and Processing Facility (Department of Chemistry) for his kindness in lending specialist equipment and Ms. Zelda Chatten at the Harold Cohen Library for her assistance in locating several obscure research articles. I am very grateful for the abundance of love and wholehearted support received from my family and friends. For my wife, Amy, who has always been a great encouragement and has been so supportive and patient with me. For my beloved son Timothy who brings such joy to my heart. For my parents, the late & great David and Susan, who have been an inspiration and have always, supported, taught, encouraged iv and prayed for me – whose example and guidance has influenced all my endeavours. As well to David, Jonathan, Hannah, Rebecca, and David, Jenny, Billy, Sue; Maria and Billy; John and the late Anne; the late John (Spud) and Gertie (3G) – thank you all for your warmth, encouragement, generosity and banter. To all the saints at Larkhill for their encouragement, prayers and support – thank you. Thank you all so very much! “Blessed be the Lord, who daily loadeth us with benefits, even the God of our salvation. Selah.” (Psalm 68:19) v Contents Chapter 1 : Introduction ................................................................................................. 1 1.1 Mass Spectrometry .......................................................................................... 1 1.1.1 Performance Criteria ................................................................................ 4 1.1.2 Mass Analyser Comparison ..................................................................... 7 References ................................................................................................................ 10 Chapter 2 : Literature Review ...................................................................................... 11 2.1: A Century of Mass Spectrometry ...................................................................... 11 2.1.1 Laying the Foundations ............................................................................... 12 2.1.2 The Birth of Mass Spectrometry ................................................................. 15 2.1.3 The Growth of Mass Spectrometry ............................................................. 19 2.1.4 The Future for Mass Spectrometry .............................................................. 28 2.2 Focusing on Quadrupole Mass Spectrometry and Allied Topics ....................... 30 2.2.1 Laying the Foundations ............................................................................... 31 2.2.2 Initial Development of the Quadrupole Mass Filter .................................... 31 2.2.2.1 Circular Cross-Section Electrode Geometry ........................................ 33 2.2.2.2