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New methods of mass analysis with quadrupoles with added octopole fields Moradian, Annie 2007

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NEW METHODS OF MASS ANALYSIS WITH QUADRUPOLES WITH ADDED OCTOPOLE FIELDS by ANNIE MORADIAN  B.Sc., Sharif University of Technology, 1994 M.Sc., University of British Columbia, 2002  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Chemistry)  THE UNIVERSITY OF BRITISH COLUMBIA December 2007  © Annie Moradian, 2007  Abstract Mass selective axial ejection of ions and mass analysis with a stability island with linear quadrupoles with added octopole fields are described. With mass selective axial ejection, quadrupoles with 2.0% and 2.6% added octopole fields have been tested and compared to a conventional quadrupole. The effects of trapping ions at different q values, excitation voltage, scan direction, balanced and unbalanced rf voltages on the rods, and dc applied between the rods have been investigated. The highest scan speeds and highest resolution are obtained with resonant excitation and ejection at high q (q = 0.8). With axial ejection, the quadrupole with a 2.0% added octopole field provides mass resolution and ejection efficiencies similar to a conventional rod set. Quadrupole, dipole and simultaneous dipole-dipole excitation between the x and y rod pairs were compared and no advantage was found with quadrupole or dipole-dipole excitation. The effects of scan speed were investigated and a resolution at half height of about 1600 is possible at scan speeds up to 5000 Th/s. Mass analysis using islands of stability was investigated with a quadrupole with 2.0% added octopole field. The island of stability is formed with auxiliary excitation. The experiments confirm the predictions of the simulations. With the resolving dc applied to the quadrupole so that the Mathieu parameter a>0, conventional mass analysis with applied rf and dc and no auxiliary excitation is possible. In this case use of an island of stability yields similar peak shape and resolution. However with the polarity of the resolving dc reversed so that a<0, only very low resolution can be obtained; the added octopole prevents conventional mass analysis. By using a stability island when a<0, the resolution is substantially improved.  ii  ^  Table of Contents ^Abstract^  ii  Table of Contents ^ List of Tables ^ List of Figures ^  vi  List of Symbols and Abbreviations ^  ix  Acknowledgement ^ Dedication ^ Chapter 1^Introduction ^  xiii xv 1  1.1^Theory and background ^ 2 1.1.1^Quadrupole Mass Filter^ 2 1.2^Mass Analysis with Quadrupole rod sets ^ 6 1.2.1^Mass Filter ^ 6 1.2.2^Fringing fields ^ 8 1.3^Quadrupole Ion Traps ^ 9 1.3.1^The Three Dimensional Quadrupole Ion Trap ^ 9 1.3.2^Linear Ion Traps ^ 11 1.3.3^The Secular Frequency and Resonant Excitation ^ 13 1.4^Quadrupoles with Added Multipoles ^ 14 1.4.1^Multipole Potentials ^ 14 1.4.2^Higher Order Fields in 3-D and Linear Ion Traps ^ 16 1.5^Linear Ion Traps as Mass Analyzers ^ 19 1.5.1^Linear Quadrupole Ion Trap with Radial Ejection ^ 20 1.5.2^Linear Quadrupole Ion Trap with Axial Ejection ^ 21 1.5.3^Islands of Stability ^ 25 1.6^Outline of This Thesis ^ 26  Chapter 2 Experimental Methods ^ 2.1^Instrument ^ 2.2^Linear Ion Trap Experimental Set Up ^ 2.2.1^Sample preparation ^ 2.2.2^Data Analysis ^  28 28 34 43 43  ^Chapter 3^Mass Selective Axial Ejection of Ions Without Trapping ^ 46 3.1^Introduction ^ 3.2^Experimental ^ 3.3^Results and Discussion ^ 3.3.1^Experiments with a Conventional Quadrupole Rod Set ^ 3.3.2^Experiments with a Quadrupole Rod Set with a 2.6% Added Octopole Field ^ 3.4 Summary ^  46 46 49 49 58 64 iii  ^  Chapter 4 Mass Selective Axial Ejection of Trapped Ions from a Linear Quadrupole ^  65  4.1^Introduction ^ 4.1.1^Review of the Theoretical Treatment of MSAE of Ions from Linear Ion Traps ^ 4.2^Experimental ^ 4.3^Results and discussion ^ 4.3.1^Dipole Excitation ^ 4.3.2^Quadrupole Excitation ^ 4.3.3^Dipole-Dipole Excitation ^ 4.4 Summary ^  65 65 68 68 68 73 75 75  Chapter 5 Mass Selective Axial Ejection of Trapped Ions from a Quadrupole with a 2.0% Added Octopole Field ^ 76 5.1^Introduction ^ 76 5.1.1^Octopole Potential and Frequency Shifts ^ 76 5.1.2^Mass Resolution and Frequency Resolution ^ 78 5.2^Experimental ^ 80 5.2.1^Mass Calibration ^ 80 5.3^Results and Discussion ^ 81 5.3.1^Dipole Excitation with a Quadrupole with a 2.0% Added Octopole Field8l 5.3.2^Quadrupole Excitation with a Quadrupole with a 2.0% Added Octopole Field ^ 92 5.3.3^Dipole - Dipole Excitation with a Quadrupole with a 2.0% Added Octopole Field ^ 95 5.3.4^Optimum Operating Mode with a Quadrupole with a 2.0% Added Octopole field^ 96 5.3.5^Ejection Efficiencies ^ 99 5.4^Summary ^ 101  Chapter 6^Mass Analysis Using an Island of Stability with a Quadrupole with a 2.0% Added Octopole Field ^ 102 6.1^Introduction ^ 6.1.1^Theory and Background ^ 6.2^Experimental ^ 6.3^Results and Discussion ^ 6.3.1^Positive a ^ 6.3.2^Negative a ^ 6.3.3^Apparent Mass and Island Positions ^ 6.4^Summary ^  102 102 107 111 111 115 117 119  Chapter 7 Summary and Future Work ^  120  References ^  122  iv  List of Tables Table 1.1 Summary of the potential for each multipole. ^ 16 Table 2.1 Instrumentation. ^ 30 Table 2.2 Multipole amplitudes. ^ 33 Table 2.3 Operating voltages. ^ 41 Table 3.1 Initial operating voltages. ^ 47 Table 3.2 Final operating voltages ^ 47 Table 5.1 Modes of applied rf, excitation and dc. ^ 80 Table 5.2 Apparent mass of reserpine with different scan directions with trapped ions excited between the smaller and larger rods at q 0.8 and a scan speed of 10 Th/s. ^ 89 Table 5.3 Ejection efficiencies (%) with the system optimized for the highest resolution^ 100 Table 5.4 Ejection efficiencies with a quadrupole with a 2.0% added octopole field and the system optimized for the highest sensitivity at R 112 r■:: 1000 ^ 100 Table 6.1 Operating Voltages. ^ 108 Table 6.2 a and q values from experiments and simulation. ^ 118  List of Figures Figure 1.1 Conventional circular quadrupole rods in a quadrupole mass filter^ 2 Figure 1.2 First stability region of a quadrupole mass filter with iso-13 lines. The points m l , m2, m3 represent ions with different masses on an operating line 7 Figure 1.3 Schematic cross section of a 3-D quadrupole ion trap. ^ 10 Figure 1.4 A round rod quadrupole with a 2.0% added octopole field ^ 19 Figure 1.5 Schematic of the ESI-triple quadrupole mass spectrometer system: N2, nitrogen curtain gas; C, curtain plate; 0, sampling orifice; SK, skimmer; QO, rf only quadrupole; Ql, mass-analyzing quadrupole; Q2, collision cell; Q3, mass-analyzing quadrupole; D, detector. 24 Figure 2.1 Schematic of the single quadrupole instrument. ESI, electrospray ionization; QO, ion guide; Ql, quadrupole mass filter; IG, ionization gauge; PG, Pirani gauge; CEM, channel electron multiplier ^ 29 Figure 2.2 Circuit diagram of the detector circuit for detection of positive ions ^ 32 Figure 2.3 Cross sections of the electrodes of a quadrupole with an added octopole field. ^ 34 Figure 2.4 Block diagram of the ion trapping experimental set up. ^ 36 Figure 2.5 Pulse sequence for counting injected ions ^ 37 Figure 2.6 Injected ion count vs. injection time ^ 37 Figure 2.7 Injected ion count vs. injection time for injection at q = 0.4 ^ 39 Figure 2.8 Schematic of the timing parameters for MSAE experiments. ^ 40 Figure 2.9 Cross section view of the two exit lenses and the pair of the quadrupole rods that are capacitively coupled to exit lens 1. ^ 42 Figure 2.10 MSAE data analysis software GUI ^ 44 Figure 2.11 MSAE data analysis software GUI ^ 45 Figure 3.1 Block diagram of the experimental set up to add rf to the exit lens ^ 48 Figure 3.2 Mass analysis of reserpine ions with operation at the tip of the stability region with a conventional quadrupole rod set and a scan speed of 5 Th/s. ^ 50 Figure 3.3 MSAE of reserpine ions at q = 0.908 obtained with balanced rf and a scan speed of 0.8 Th/s. ^ 51 Figure 3.4 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the A-pole pair has 15% lower rf voltage than with balanced rf^ 52 Figure 3.5 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the A-pole pair has 15% higher rf voltage than with balanced rf^ 53 Figure 3.6 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the B-pole pair has 15% higher rf voltage and —3V dc^ 54  vi  Figure 3.7 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the A-pole pair has 15% higher rf voltage and +3V dc^ 55 Figure 3.8 Intensity vs. the exit lens voltage for reserpine ions obtained using different combinations of unbalanced rf and added dc. ^ 56 Figure 3.9 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 'Th/s. The rf was balanced and 110 Vp-p rf applied to the exit lens ^ 57 Figure 3.10 Conventional rf/dc mass analysis with a quadrupole with a 2.6% octopole field and a scan speed of 5 Th/s. ^ 59 Figure 3.11 MSAE of reserpine ions from a quadrupole rod set with a 2.6% added octopole field at q = 0.908 and a scan speed of 0.8 Th/s. ^ 60 Figure 3.12 Calculated stability boundaries of a quadrupole with a 2.6% added octopole field (calculated by W. Xiao). ^ 61 Figure 3.13 MSAE of reserpine ions at q = 0.8765 with 4.0 Vp_p dipole excitation applied to the larger rods ^ 62 Figure 3.14 MSAE of reserpine ions at q = 0.8765 with 4.0 Vp_p dipole excitation applied to the smaller rods. ^ 63 Figure 4.1 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation. a) forward scan, ejection at q = 0.80 , 15 Th/s b) reverse scan, ejection at q = 0.80 , 15 Th/s. ^ 70 Figure 4.2 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation. a) forward scan, ejection at q = 0.80 , 5000 Th/s b) reverse scan, ejection at q = 0.80 , 5000 Th/s. ^ 72 Figure 4.3 Peak shapes and resolution with axial ejection of trapped ions, and quadrupole excitation. a) reverse scan, ejection at q = 0.7002 , 15 Th/s b) reverse scan, ejection at q = 0.7002 , 3300 Th/s ^ 74 Figure 5.1 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation between the larger (y) rods. a) reverse scan, ejection at q = 0.40 , 10 Th/s b) reverse scan, ejection at q = 0.80 , 10 Th/s. ^ 83 Figure 5.2 Peak shapes and resolution with axial ejection and dipole excitation between the smaller (x) rods. a) forward scan, ejection at q = 0.40 , 10 Th/s b) forward scan, ejection at q = 0.80 , 15 Th/s. ^ 84 Figure 5.3 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation between the larger (y) rods. a) forward scan, ejection at q = 0.80 , 15 Th/s b) reverse scan, ejection at q = 0.80 , 15 Th/s. ^ 87 Figure 5.4 Peak shapes and resolution with axial ejection and dipole excitation between the smaller (x) rods. a) forward scan, ejection at q = 0.80 , 15 Th/s b) reverse scan, ejection at q = 0.80 , 15 Th/s. ^ 88 Figure 5.5 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation between the larger (y) rods. a) reverse scan, ejection at q = 0.80 , 1570 Th/s b) reverse scan, ejection at q = 0.80 , 5000 Th/s.... 90  vii  Figure 5.6 Peak shapes and resolution with axial ejection and dipole excitation between the smaller (x) rods. a) forward scan, ejection at q = 0.80 , 1500 Th/s b) forward scan, ejection at q = 0.80 , 5000 Th/s. ^ 91 Figure 5.7 Peak shapes and resolution with axial ejection of trapped ions, and quadrupole excitation between the rods. a) forward scan, ejection at q = 0.7002 , 15 Th/s b) reverse scan, ejection at q = 0.7002 , 15 Th/s 93 Figure 5.8 Peak shapes and resolution with axial ejection of trapped ions, and quadrupole excitation between the rods. a) reverse scan, ejection at q = 0.7002 , 1800 Th/s b) reverse scan, ejection at q = 0.7002 , 4200 Th/s. ^ 94 Figure 5.9 Resolution vs. scan speed with different excitation modes, with a conventional quadrupole and a quadrupole with a 2.0% added octopole field. ^ 96 Figure 5.10 Axial ejection of +3 ions of renin substrate tetradecapeptide with dipole excitation applied to a) conventional rods with a forward scan and ejection at q = 0.80 , b) the smaller rods of a quadrupole with a 2.0% octopole field with a forward scan and ejection at q = 0.80 and c) the larger rods of a quadrupole with a 2.0% octopole field with a reverse scan and ejection at q = 0.20. The scan speed in all cases is 3000 Th/s. ^ 98 Figure 6.1 Stability boundaries and islands of stability (q' = 0.02 , v = 9/10) for a quadrupole with 2.0% added octopole field with a > 0 ^ 105 Figure 6.2 Stability boundaries and islands of stability (q' = 0.02 , v = 9 / 10) for a quadrupole with 2.0% added octopole field with a < 0 . ^ 106 Figure 6.3 Quadrupole excitation circuit. ^ 109 Figure 6.4 Mass analysis with a > 0 and (a) with no excitation (b) with the stability island at the tip with the greater la and (c) with the stability island at the tip with the lesser  112  Figure 6.5 Mass analysis of reserpine ion in different stability islands with a > 0 . Peaks are labeled with the name of the corresponding island used for mass analysis ^ 114 Figure 6.6 Mass analysis with a < 0 (a) with no excitation (b) with the stability island at the tip with the greater la! and (c) with the stability island at the tip with the lesser  116  viii  List of Symbols and Abbreviations Symbol or^Definition Abbreviation rf^Radio frequency dc^Direct current 3-D^Three dimensional ESI^Electrospray ionization MALDI^Matrix assisted laser desorption ionization R112^  Resolution at half peak height  LIT^Linear ion trap FTICR^Fourier transform ion cyclotron resonance LC^Liquid chromatography MS^Mass spectrometry TOF^Time of flight MS/MS^Mass spectrometry/mass spectrometry 2-D^Two dimensional RIT^Rectilinear ion trap MSAE^Mass selective axial ejection QO^Quadrupole ion guide Q1^First quadrupole Q2^Collision cell Q 3^Third quadrupole  ix  DAC  Digital to analog converter  MCS  Multichannel scaler  CEM  Channel electron multiplier  GUI  Graphic user interface  QPS  Quadrupole power supply  CAD  Collisionally activated dissociation  CPS  Counts per second  U  Direct current voltage  V  Radio frequency voltage  x, y, z  Cartesian co-ordinates  C2  Angular frequency  113  Field radius  z  Number of charges  e  Electron charge  m  Ion mass  t  Time  a,q  Mathieu parameters  a' a"  Integration Constants  u0  Initial velocity  14 0  Initial radial velocity Function of a and q parameters  w„  Ion oscillation frequency  x  m / z^Mass to charge ratio n^Number of rf cycles h^Constant for each stability region d^Distance from the end of the rods  co ex^Quadrupole excitation frequency K^Quadrupole excitation resonance order  AN^Dimensionless amplitude of the electric potential multipole N^The electric potential multipole order  r„,.„,^Normalization radius Re[f (4)]^Real part of the complex function f (C) Ry , R x^Radius of y-pole and x-pole pairs  Th/s^Thomson per second IG^Ionization gauge PG^Pirani gauge E0^Initial ion kinetic energy Ion kinetic energy after collisions CD^Drag coefficient  A^Collision cross section n^Gas number density 1^Ion  mass  m2^Collision  gas mass  1^Length that an ion travels  xi  (1) FF  Potential in the fringing region  Ez,qttad  Axial component of the electric field  E z ,lens  Electric field of the exit lens  (E z )  Averaged total axial field  Veff  Effective potential  wo  Secular frequency  Ow  Frequency shift  V'  Amplitude of quadrupole excitation voltage Ratio of angular frequencies of excitation to drive rf  q  Ratio of excitation voltage to rf voltage  A,B,C,D  Stability islands  xii  Acknowledgement My graduate years in Don Douglas' lab have been one of the best experiences in my life. Don is the best advisor and teacher I could have wished for. I'm grateful to Don for his commitment to helping see my project through to its final completion, and his equally generous and wise guidance during every step of the work from experiments to publishing papers. I also thank Don for prompt reading of this thesis with lots of comments and advice. I would like to express my gratitude to my supervisory committee members, especially Dr. Michael Blades for his help throughout my studies and for review of this thesis. I'm grateful to all members of Chemistry mechanical and electronic engineering services for their help especially Dave Tonkin for his technical expertise and great assistance with quadrupole power supply electronics. I gratefully acknowledge NSERC and SCIEX through an Industrial chair for financial support of this research. I would also like to acknowledge Dr. Jim Hager and Dr. Bruce Collings from MDS-SCIEX for their helpful comments and suggestions throughout the course of this research. I express my gratitude to Douglas' lab former and present members for their help and support throughout my studies in the lab. My heartfelt thanks go to Chuanfan for assisting me through first stages of my experiments and for always being ready to help. I would like to thank Xianzhen for initiating the simulation studies of "Stability islands for quadrupoles with added octopole fields", which provided me the opportunity to investigate them experimentally. I thank Winnie (Z.) for calculating the stability boundary that was needed for my paper and thesis. I'm grateful to Milica, Kevin,  Anthony, Ori and John for all their friendship, for being patient to hear my outrage or joy at the day's current events and for their support whenever it was needed. More special thanks to Milica and Kevin for becoming my family's close friends. I thank my mother for all her love, sacrifices, encouragements and teaching me to always push harder for success. I would like to thank my brother for always being there for me. I'm indebted to my mother-in-law and father-in-law for their unconditional help and support. Their loving help in raising my two daughters that were born during my graduate studies enabled me to complete my degree. I highly appreciate their kindness and love. My daughters, Beaina and Lara enlighten my life and give me more strength for my day-to-day endeavors. Finally, I would like to acknowledge my husband Ara for his enormous contribution in developing the data analysis software package for my experiments I thank him for his company through this journey, for his love, faith and most of all his friendship that is my inspiration.  xiv  Dedication  To Ara, Beaina and Lara and in loving memory of my father Ardzrooni Moradian.  xv  Chapter 1 Introduction In 1989 the Nobel Prize in Physics was awarded one half to Norman Ramsey, for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks, and one half jointly to Hans Dehmelt and Wolfgang Paul, for the development of ion trapping techniques. The first experiments on trapping ions were performed by Paul and his collaborators in the 1950s [1, 2], who showed that ions with different mass to charge ratios could be separated by a four-pole static (dc) electric field with a superimposed radio frequency field. This was developed into a standard method for mass separation, now widely used, the quadrupole mass filter. The three-dimensional (3-D) quadrupole ion trap, also included in Paul's original patent [3], was first developed as a mass selective detector by Fischer in 1959 [4]. This work was representative of a turning point in the development of ion traps and the technology associated with them. The 3-D quadrupole ion trap and its linear counterpart, the quadrupole mass filter became extremely useful instruments. Over the past two decades, the development of soft ionization techniques such as electrospray ionization (ESI) [5] and matrix-assisted laser desorption ionization (MALDI) [6] have turned mass spectrometry into a powerful method for the characterization of biological molecules. A flourishing industry has been developed around these instruments and the demand for higher performance systems has driven research in this area. Today, high precision mass spectrometry has become a billiondollar industry, with a vast and expanding market in the biomedical and pharmaceutical sectors.  1  1.1 Theory and background  1.1.1 Quadrupole Mass Filter  The basics of quadrupole mass filter operation including the quadrupole potential and ion motion, have been described in detail by Dawson [7], and March and Hughes [8]. A quadrupole field is produced by a set of four parallel hyperbolic rods. Many mass filters employ circular rods instead of hyperbolic rods due to the difficulty of manufacturing hyperbolic rods to high precision [7]. This introduces slight perturbations to the pure quadrupole field but it has been shown that these are insignificant near the axis of the beam [9] and can be minimized with the proper selection of the rod radius r A constant direct current (dc) voltage U and a radio frequency (rf) voltage V cos [)t are applied to the rods as shown in Figure 1.1.  --• — (U — Vcos0t) •^  Figure 1.1 Conventional circular quadrupole rods in a quadrupole mass filter.  2  The potential cl)(x,y) at any point inside the quadrupole is described by x2 -2  y2  (1)(x, y, t) = ^OW ro where x and y are Cartesian co-ordinates and ro , the field radius, is the distance from the centre of the quadrupole to any rod. The potential OW is given by: = (U. – V cos Sgt)^  (1.2)  where U is the dc voltage, V is the zero-to-peak amplitude of the rf voltage applied from each quadrupole rod to ground, and C2 is the angular frequency of the rf voltage. The ion motions in the x and y directions in the quadrupole field are independent and are determined by the following equations: 2ze x+^(U –V cos0t)x = 0 mro2  (1.3)  ._2ze 2 ^ (U –V cosC2t)y =0 Y mr  d2x  .  2 ^  where I= dt 2 and j) = ^ z i s the number of charges on an ion, e is the electron —  dt2^  charge, m is the ion mass and t is time. These differential equations can be written with dimensionless parameters, and are then the Mathieu equation: du 2 de  (1.4)  +(au –2qu cos2Ou = 0 .0t ^u = x 2  or y^  (1.5)  By comparison with equation (1.3) a and q are: 8eU aX =–ay=^ mro2 C2 2  qX^qy =  4eV mro2K-2 2  (1.6)  3  The Mathieu equation has been discussed in many books [7, 8], and only the solutions to the equation will be presented here:  uW= cr'e 4 E c2ne 2 ni' + a ffe -4^C2ne -2ni^(1.7) n=—oo^  n=—co  where a' and a" are integration constants depending on the initial position u 0 and initial radial velocity /4 0 . The constants C 2n and p depend only on the a and q values. Therefore the nature of an ion's motion is determined by its ( a , q) value, regardless of the initial conditions. The solutions represented by equation (1.7) can further be divided into two subcategories; stable and unstable. Stable solutions arise only when p is imaginary such that p = ifi and )61 is not an integer. In this case ions oscillate in the x— y plane with limited amplitudes and pass through the quadrupole field without hitting the rods. Integer values of/3 form a series of solutions, which are periodic and unstable. Ion amplitudes grow exponentially in the x, y or in both directions, and ions are lost. Substituting  p= 1/3 into equation (1.7) and simplifying it, gives the equation of motion for stable ions = A E c2 „ cos(2n + /3) + B E c2 „ sin(2n + fl)4 n=—co^  ^  (1.8)  n=—co  where A = a' + a" and B = i(a' +a"). From equation (1.8), /3 is an important parameter that determines the oscillation frequencies of the ions. The relation of ,6 to (a , q) is given by the recursion formula [8].  4  2  p2 = a +  2  (2 + 16) 2 a (4+13) 2 a  2  (6 + ,6) 2 – a –  (1.9)  2  (,6 -22)) 22 a  q2  – 4) 2 a  q  – 6) 2  2 -  a–•  When q .^ 0.4, can be approximated by [7, 8]. 2  q p 2a + — 2  (1.10)  For given rf and dc voltages, ions in a quadrupole field have oscillatory motion (according to equation (1.8)) that is characterized by frequencies unique to their mass-tocharge ratio. The lowest frequency is termed the "secular frequency". Higher frequencies are not simple harmonics of the lowest frequency. These frequencies can be calculated using equation (1.11). °). = ( 2 n ± fl)  2  ,n=  The stability of solutions to the Mathieu equation depends on the a and q values. Therefore a diagram in the a and q plane consists of regions of stability and instability. This is called the stability diagram. In the stability diagram there is an infinite number of regions where ion motion is stable in both the x and y directions. The first overlapping region for combined x and y stability with iso-,6 lines is plotted in Figure 1.2. Because a x and a y (and equally q x and q y ) are symmetric with respect to the origin of the a–q  plane as shown in equation (1.5), the first quadrant is enough to represent the entire  5  stability diagram. Almost all commercial quadrupole mass filters are operated in first stability region.  1.2 Mass Analysis with Quadrupole rod sets  1.2.1 Mass Filter  In a quadrupole mass analyzer for fixed values of ro , C2 , U and V all ions with the same m / z have the same operating point ((a , q) values) in the stability diagram. Since a / q is equal to 2U / V and does not depend on m , all masses lie along an operating or scan line a / q= constant as shown in Figure 1.2. By scanning the U and V values along this line (i.e. with a fixed ratio), ions with different masses will be transmitted in sequence of mass-to-charge ratio and will reach a detector in order, producing a mass spectrum. Each operating line with specific slope (a / q) corresponds to one resolution setting. In theory the resolution is calculated from the width of the stability region for each of the operating lines. By increasing the U/ V ratio, the operating line approaches closer to the tip of the stability region and only a small range of m / z values will be stable. This corresponds to higher resolution. Usually resolution is defined as R112 M/AM 1/2 ,  where Am i , 2 refers to a measured peak width at half height.  6  0.3  0.2  a 0.1  Operating Line  0.0 0.0^0.1^0.2^0.3^0.4^0.5^0.6^0.7^0.8^0.9^1.0  q Figure 1.2 First stability region of a quadrupole mass filter with iso-13 lines. The points m2, m3 represent ions with different masses on an operating line.  In theory, as the operating line in the stability diagram approaches the tip of the stability region, the resolution will increase without limit. In these theoretical treatments two assumptions have been made which cannot be completely valid. These are (1) all ions stay in the quadrupole field for a sufficiently long time, i.e. the rods are infinitely long and (2) circular rods give an adequate approximation to a hyperbolic field. Considering the finite length of a real quadrupole rod set, the resolution can be expressed as [10, 11] R 112 = n2 /h  ^  (1.12)  7  where n is the number of rf cycles that ions spend in the quadrupole field and the h is a constant that is different for different stability regions. For the first stability region h 'A:10 - 20 [11]. An rf— only quadrupole is a quadrupole which is operated with no dc voltage between the pole pairs (U = 0). This allows the largest possible range of mass-to-charge ratios to pass through the quadrupole. An ion has a stable trajectory when 0 q. 0.908 . Therefore, if V and CI are fixed, there is a lower limit to the mass-to-charge ratio of ions which have stable trajectories in the quadrupole. Consequently rf — only quadrupoles are used as ion guides and high pass mass filters.  1.2.2 Fringing fields In a practical quadrupole mass analyzer the field does not end abruptly at the ends of the quadrupole rods. Usually an end plate is positioned at a distance, d , from the ends of the rods. Penetration of the potential of the end plate into the region between the quadrupole rods will cause a distortion of the ideal quadrupole field. The field in this region is referred to as the fringing field [12]. The quadrupole field grows from zero (on the end plates) to its full value within the quadrupole. In the fringing field region, x, y, and z motion become coupled and the ion motion is very complicated. Normally, this fringing field might be expected to extend over a distance of at least the order of the field radius of the quadrupole rod set [13]. Brubaker first recognized the importance of fringing fields in the mass filter. From his studies two qualitative results were drawn for the effects of the entrance fringing fields on the amplitudes of ion motion [12]. 8  1. Short fringing fields give lower amplitudes of ion oscillation, than perfect fields for both the x and y directions. 2. Long fringing fields (many rf cycles) give large amplitudes of oscillation in the y direction. In this case fringing field defocuses the ions. Brubaker described the fringing field with a linear model and proposed a "delayed dc ramp" to avoid the defocusing of the ions caused by the large y trajectories [12]. With operation in the first stability region and without the "delayed dc ramp", there is an optimum fringing field length of about two rf cycles which was verified theoretically and experimentally to increase the transmission [14, 15]. Hunter and McIntosh modeled the fringing field and concluded that an exponential function describes the field more realistically than a linear model [16]. All the above-mentioned studies for fringing fields were focused on the entrance fringing fields for rf/dc mass filters. Little work has been done to investigate the effect of the exit fringing fields on ion motion. Brinkman reported the first rf-only operation of a quadrupole rod set as a mass spectrometer. The method was based on the exit fringing fields [17]. Others expanded on his work. Details of this will be given in Section 1.5.2.  1.3 Quadrupole Ion Traps  1.3.1 The Three Dimensional Quadrupole Ion Trap  The quadrupolar field in a 3-D ion trap can be produced by three hyperbolic electrodes, a ring electrode in the middle with cap electrodes on each end as shown in  9  Figure 1.3. The electric potential cD(x, y, z) in the 3-D ion trap is similar to the electric potential in the quadrupole mass filter (130(x, y, z, t) =  (x 2  +y 2 rp2  -  2z 2 )  (1.13)  Figure 1.3 Schematic cross section of a 3-D quadrupole ion trap.  where x , y and z are Cartesian co-ordinates and r o is the distance from the centre of the trap to the ring electrode. The potential 1(t) is given by equation 1.2. The quadrupole field still depends on the square of the distance from a reference point, in this case the center of the trap. Ion motion in the  x,  y and z directions are independent. The  equations of motion can be written and solved as in section 1.1. In the quadrupole ion trap, the rf voltage is typically applied to the ring electrode and the two end cap electrodes are typically held at ground potential. Within a selected range of m / z ratios, determined by the applied voltages, the device traps ions within the space bounded by the electrodes. Typically, a mass spectrum is produced by scanning the applied rf voltages to 10  eject ions in the axial direction through an end cap opening, sequentially, with increasing m / z ratio, for detection [8]. This scanning method is called a "mass selective instability scan" and it was introduced by Stafford and co-workers in the first commercial 3-D ion trap [18]. Because the mass-to-charge ratio of the ion that is ejected from the ion trap is directly proportional to the rf voltage (for a given ro and S2) an upper limit to the massto-charge range of the ion trap is imposed by the magnitude of the rf voltage that can be applied to the electrodes.  1.3.2 Linear Ion Traps  In 1969 Church described "ring" ion trap and "racetrack" ion trap geometries [19]. Bending the two-dimensional quadrupole rod electrodes into a circle formed the ring ion trap. He was able to trap and measure the presence of El + ( m / z =1) and 3 He + ( m / z = 3). If a linear (two — dimensional) quadrupole is operated with rf-only voltages, and if stopping potentials are applied to electrodes at the ends of the quadrupole, ions of a broad range of m /z can be trapped in the quadrupole. Ions are confined in the radial ( x, y) direction by the quadrupolar potential and in the axial (z ) direction by the electrostatic potentials at the ends of the quadrupole. There are several advantages associated with the trapping of ions in linear ion traps [20]. Since there is no quadrupole field along the z -axis, linear traps have higher injection efficiencies than 3-D traps. The larger volume of the linear trap compared to a 3-D trap enables storage of more ions without space charge effects. This can be attributed to strong focusing of ions along the centerline of the linear ion trap, increasing the volume occupied by ions. 11  Linear ion traps first were used purely as traps. In 1988 Dolonikowski and coworkers [21] trapped ions in an rf — only quadrupole to study ion/molecule reactions. After reactions occurred in the linear ion trap, these ions were pulsed into a quadrupole mass filter for mass analysis. Beaugrand et al. [22] also studied the chemical equilibria and kinetic and thermodynamic parameters of selected ion/molecule reactions in a triple quadrupole instrument where the central quadrupole served as a linear ion trap and collision cell. This technique has subsequently been used by others to study ion/molecule chemistry [23]. At about the same time, Prestage et al. [24] presented a novel linear ion trap, which increased the number of laser cooled atomic ions that could be trapped in a fixed volume with minimal effects from Doppler shifting caused by the rf confining fields. The success of this instrument has led to the application of linear ion traps in frequency standards experiments [25]. Linear ion traps have been used in combination with other mass analyzers. The external accumulation of ions in multipole traps allows higher trapping efficiency and space charge capacity. Thus they can be used as storage devices with ion manipulation capabilities. Douglas [26] described coupling a linear trap to a 3-D ion trap. In this instrument the linear trap can be used to pre-concentrate analyte ions and remove unwanted ions prior to mass analysis in the 3-D trap [27, 28]. This improves the duty cycle significantly and allows detection of trace analyte ions in a large excess of other ions. The storage capabilities of multipole and linear ion traps provide a convenient method for interfacing a continuous ion source like electrospray ionization (ESI) to Time of Flight (TOF) [29] and Fourier Transform Ion Cyclotron Resonance (FTICR) mass  12  spectrometers. The ion trap acts as a front-end storage device for these instruments. Ions are continuously stored as they are injected into the trap, and are subsequently pulsed out into these mass analyzers for detection. Hardman et al. [30] showed that an "electrostatic" trap mass analyzer (Orbitrap) can be coupled to a continuous electrospray ion source by accumulating ions in an rf — only quadrupole prior to their injection into the "electrostatic" trap. Liquid Chromatography/ Mass Spectrometry (LC/MS) analysis with FTICR instruments become more practical with the increase in sensitivity made possible by accumulation of electrosprayed ions in a linear octopole ion trap, prior to their transfer to the FTICR cell [31]. In some instruments linear hexapole or segmented linear quadrupole ion traps are used for the same purpose. A linear trap can be used for dissociation or hydrogen exchange of ions prior to ion detection by FTICR [20, 32]. By coupling linear ion traps to TOF mass spectrometers, different research groups also used traps for ion isolation and fragmentation through ion excitation [33-35]. This adds tandem mass spectrometry capability to TOF mass spectrometers.  1.3.3 The Secular Frequency and Resonant Excitation  Ions in a linear quadrupole ion trap can be resonantly excited when an auxiliary ac voltage at a frequency Oex is added to the drive rf frequency f2. The amplitude of the excitation voltage is several orders of magnitude lower than the amplitude of the drive rf voltage. Dipole and quadrupole excitation are possible. For dipole excitation, the auxiliary ac is applied between two opposite poles of the quadrupole rod set and the electric field of the excitation is constant (independent of position). Resonance takes  13  place when the frequency hex coincides with one of the secular frequencies given by equation (1.11). Quadrupole excitation occurs when the auxiliary ac is applied to all four poles of a quadrupole rod set. In this case the magnitude of the electric field is linearly proportional to the coordinates x and y . Sudakov et al. [36] calculated the excitation frequencies of ions with quadrupole excitation and showed ions are excited when coex^+ xj K n^(1.14) where K =1,2,3,..., / = 0,±,1 f 2,... and )6. =!''x or fly . When ions are resonantly excited, the amplitude of their oscillation begins to increase. If the amplitude of the supplemental ac voltage is sufficient, ions can be ejected from the ion trap. This process is referred to as resonant ejection. Resonant excitation of ions has been effectively used for isolating, fragmenting and mass-selectively ejecting ions at different q values in quadrupole ion traps.  1.4 Quadrupoles with Added Multipoles  1.4.1 Multipole Potentials A potential, (I), within a region free of charge, must satisfy Laplace's equation V 2 cI) = 0 (1.15) Multiple solutions to the Laplace equation that satisfy the above condition exist. If each individual solution is considered to be a component (or fraction) of the overall potential, one additional solution is the linear combination of the component potentials. The  14  component potentials may be expressed in terms of a multipole expansion. In Cartesian coordinates a two-dimensional electric potential 131)(x, y, t) can be expanded in multipoles, ON (x, y), as [20] : y, t) = V(t)E A N ON (x, y)^(1.16) N=0  where V(t) is a time dependent amplitude of the potential, and AN is the dimensionless amplitude of the multipole ON (x, y). The term ON (x, y) can be derived from: ON (X,  iyi N 3)) = Re [x + rnorm  (1.17)  where rnorm is a normalization radius and Re[f (4")] means the real part of the complex function f (C) , (C = x + iy) and i 2 = —1 [37]. Analytical expressions for the multipoles in Cartesian coordinates are given by Szilagyi [38]. The term 00 (x, y) =1 represents a constant potential that is independent of x and y , 0 (x, y) corresponds to a linear dipole ,  potential, 02 (x, y) is a quadrupole potential, 0 3 (x, y) is a hexapole potential, 0 4 (x, y) is an octopole potential, etc. The values of the coefficients A N depend on boundary conditions. For a system of four parallel rods, these can be calculated with the method of effective charges [39]. Even order multipoles (N=2, 4, 6 ...) are symmetric with respect to reflection in the x and y axes and odd order multipoles (N=1, 3, 5 ...) are antisymmetric with respect to reflection in the x axis and symmetric with respect to reflection in the y axis. In quadrupoles, electric field components higher than those from 02 are non-linear and are termed higher order fields. A summary of the multipoles is given in Table 1.1.  15  Table 1.1 Summary of the potential for each multipole.  Multipole^Potential Dipole (N=1)^= xlrnorm Quadrupole (N=2)^02 =  x 2 y  2 ) norm  Hexapole (N=3)  03 (X3 — 3XY 2 ) rn3orm  Octopole (N=4)  04 = (X 4  Decapole (N=5)  05 = (X 5 — 10x 3 y 2 5Xy 4 )1rn5orm  Dodecapole (N -6)  06  -  = (x6  + 4 ) rn4orm —6x2y2y  —15x4y2 +  15 x 2 y 4 y 6)/ rnorm  1.4.2 Higher Order Fields in 3-D and Linear Ion Traps Non-idealities in the electrode geometry of the quadrupole mass analyzer and the 3D quadrupole ion trap result in the presence of higher order fields. These non-idealities result from the necessary truncation of the electrodes in the quadrupole mass filter and the quadrupole ion trap, using round rods for the quadrupole mass filter, holes in the end caps of ion traps for ion injection or ejection, and imperfections in the machining and manufacturing of electrodes [40]. Several groups have studied the effects of mechanical errors on quadrupole mass filter performance and recommended that quadrupole mass filters be manufactured to very high precision to avoid field distortions [10, 13, 41]. Other studies showed that it is  16  possible to adjust the contributions of higher multipoles in a round rod quadrupole mass filter by changing the ratio of rod radius, r , to field radius, rc, , to optimize the peak shape and resolution [9, 42-44]. In all these studies the amplitudes of the higher multipole fields were about 10 or less of the quadrupole term. The presence of higher order fields in the 3-D quadrupole ion trap has both advantages and disadvantages. In the early years of research, ion losses, shifts in the observed mass-to charge-ratio of ions and some "ghost" peaks (peaks observed at spurious mass-to-charge values) were attributed to the effects of higher order fields [8]. Later work showed methods to minimize all of these phenomena by intentionally introducing weak higher order multipole fields [45-47]. Franzen [48, 49] described the distortions caused by these fields mathematically. Addition of a positive even-order higher multipole to the field in the z direction of a 3-D trap introduces non-linear effects; the most important is a shift of the frequency of ion oscillation with the amplitude of oscillation [49]. Later it was recognized that higher order fields could be beneficial to ion trap performance because they increase the ion fragmentation efficiency in mass spectrometry/mass spectrometry (MS/MS) experiments, and give higher resolution in ion ejection or isolation [48, 50, 51]. These benefits might also be expected to apply to linear quadrupole traps. Douglas and coworkers have investigated methods to add higher order multipole fields to linear quadrupoles [52-54]. They have shown that higher order multipole fields can be added to linear round rod quadrupoles by modifications to the electrode dimensions. These modifications to the quadrupole rod structures were calculated to produce 2 — 12% octopole or hexapole fields while the amplitudes of other higher  17  multipoles remained relatively small. The percentage of added multipole field is calculated from  A AN A2  x 100 = % Added multipole  (1.17)  where N is the order of the multipole. Therefore with a 2.0% added octopole field A A2  = 0.02. Octopole fields of 2 — 4% were added to linear quadrupoles by making one  pair of rods greater in diameter than the other pair [52, 53] and 2 — 12% hexapole fields were added by rotating two rods (the y rods) towards an x rod [54, 55]. In both cases all rods are equally spaced from the central axis. Figure 1.4 shows a photograph of a round rod quadrupole with a 2.0% added octopole field. The ratio  Ry  Rx  s Surprisingly it i1.22.  was also found that conventional mass analysis with applied dc and rf fields is possible with this rod set, despite the large field distortions, provided the dc is applied with the correct polarity, i.e. the positive dc applied to the smaller rods [56]. The positive dc on the smaller rods is for positive ions but is reversed for negative ions. Experiments where trapped ions were resonantly excited to induce fragmentation showed that a rod set with a 4% added octopole field can give higher efficiency in dissociating ions than a conventional rod set [57], especially at pressures of 1x10 4 Torr or less.  18  Figure 1.4 A round rod quadrupole with a 2.0% added octopole field.  1.5 Linear Ion Traps as Mass Analyzers Despite the previously described advantages of 2-D ion traps in hybrid instruments, only recently have they been commercialized as stand-alone mass analyzers. Some earlier examples of 2-D ion traps used as mass spectrometers are presented here briefly. Senko et al. demonstrated image current detection with Fourier transform (FT) analysis with a 2-D trap, which utilized independent detection electrodes between the quadrupole rods [58]. Although the results were promising, space charge effects were found to limit the sensitivity. Welling et al. demonstrated two alternative methods for mass selective instability scans in a linear quadrupole ion trap [59]. The first relied on the manipulation of the q-value of the trapped ions and provided fast scans of about 1000  19  Th/s with low resolution (m / Am Pz 6) that was relatively mass independent over large mass ranges of 20-1000 Th. The second used frequency swept parametric excitation to eject ions between the quadrupole rods. With lower scan rates of 15-30 Th/s, resolution of 800 at m / z 130 was obtained.  1.5.1 Linear Quadrupole Ion Trap with Radial Ejection  Bier and Syka described several forms of linear and circular 2-D ion traps that can be used as mass spectrometers [60]. They suggested using the mass selective instability scan mode of operation (with resonance excitation) for scanning these 2-D ion traps. Schwartz and co-workers [61] described a working instrument based on this. They used hyperbolic rods cut in three sections as their quadrupole linear ion trap. Ions are confined radially in the central section by the rf voltage and axially by dc potentials on the end sections. The ion trap section has slots cut into the x -rods through which ions are ejected. These slots cause imperfections in the fields. To improve performance, the x-rods were moved 0.75 mm beyond their normal spacing. Dipole excitation with auxiliary ac voltages on the x rods is used to isolate, excite, and eject ions. Ions are isolated by a broadband waveform with frequencies 5-500 kHz, with a notch at the frequency of the target ions usually at q = 0.83. For MS/MS, ions are activated by resonant excitation at a q of 0.25 — 0.35. The detection efficiency can be doubled because a detector can be put on either side of the 2D ion trap to detect ions that are ejected through either x -rod. A mass resolution of greater than 30,000 at a scan rate of 27 Th/s was obtained and MS 4 was demonstrated [61].  20  In 2004 Cooks and co-workers introduced a miniaturized linear ion trap called a rectilinear ion trap (RIT) [62]. The RIT has two pairs (x, y) of rectangular electrodes, where the x-rectangles have slots in them for ion ejection. The RIT uses two flat electrodes at either end of the ion trap to confine ions. The rf signal is applied between the x, y electrode pairs and this field is approximately quadrupolar, at least near the trap center. The basics of operation of the RIT are very similar to the linear quadrupole ion trap described by Schwartz and co-workers [61]. The demonstrated capabilities of the RIT include tandem mass spectrometry, a mass resolution of around 1000, and a m / z range of 650 Th.  1.5.2 Linear Quadrupole Ion Trap with Axial Ejection  In 1970's and 1980's research was focused on developing an rf-only mass spectrometer, which would overcome some of the shortcomings of rf/dc mass filters. Among these, the important inherent problem of conventional rf/dc mass filters was considered the dependence of achievable resolution and good peak shape on the precision of the quadrupole field [63]. Another limitation of the mass filter is the discrimination by the fringing fields against slow ions (high mass or low energy) [13] and also the loss of transmission, which occurs at high resolution. The rf-only quadrupoles offer some promise with regard to the above limitations. Without the dc component of the fringing fields at the entrance of the quadrupole there is no discrimination against high mass ions. This means that the transmission efficiency is independent of mass for any particular instrument. Its exact geometry should be less important since ions spend less time near the outer limits of the field [64].  21  Brinkmann reported the first rf-only operation of a linear quadrupole as a mass spectrometer [17]. Brinkmann made the fundamental point that ions leaving the quadrupole rods could gain considerable energy from the fringing fields. This is possible when the ions travel through the exit region with considerable radial amplitude where the fringing fields are close to their maximum. This condition applies when the rf-only quadrupole rod set operates with ions at the edge of the stability diagram. Ions on the verge of instability near q = 0.908 acquire large axial energies from the exit fringing fields; therefore they can be distinguished from stable ions with lower q-values, which oscillate near the field axis. An energy filtering technique based on a variable spherical retarding field was used for mass separation. Brinkmann obtained a resolution in excess of 1000 at m/z = 500, demonstrating ten times higher transmission than that obtained with the same instrument with rf/dc operation mode [17]. Others expanded Brinkmann's work in developing rf-only mass spectrometers by changing the geometry of the retarding field and accelerating ions at the ion exit [65-69] All reported the advantages of high tolerances for mechanical imperfections in the quadrupole rod assembly, higher sensitivity and higher resolution compared to conventional rf/dc mass analyzers. However there were some differences in the results presented by two groups of researchers regarding the dependence of resolution on the number of rf cycles ions spend in the quadrupole rod sets [64, 70]. It was clear that the rfonly mode operation was not well understood and further research was needed for its complete characterization. In 1999 Hager [71] reported a new method of mass scanning with linear quadrupoles, called mass selective axial ejection (MSAE). This method is a further  22  development of Brinkmann's idea of using fringing fields at the exit of the quadrupole rod set. In the fringing field, the otherwise independent ion motions in x, y and z are coupled. The quadrupole is operated in if-only mode with ions flowing continuously into the quadrupole. The end plate or exit lens is set at a stopping potential relative to the quadrupole rod offset. Within the fringing field, radial energy of the ions is converted into axial energy and ions can surmount the exit lens barrier to reach a detector. Ions with larger radial displacements in the fringing field receive greater axial kinetic energy increases than ions with smaller radial displacements. Thus some form of radial excitation of ions is required for ion ejection. The same concept was then used for axial ejection of ions trapped in a linear quadrupole [72]. Experiments were done with a triple quadrupole mass spectrometer like that shown in Figure 1.5. Fragment ions produced in tandem mass spectrometry were trapped in the collision cell (Q2) or the last mass analyzing quadrupole (Q3), by applying stopping potentials to lenses at the ends of the quadrupoles. For axial ejection, ions were excited at their resonant frequencies by applying fixed-frequency auxiliary ac voltages to two or all four rods of a quadrupole or to the exit lens. By scanning the trapping if amplitude, ions of different m / z ratios came into resonance and were ejected to produce a mass spectrum.  23  N2 SK QO  Q1  Q2  Q3  Exit lens  ■ 0  1)  I^I  Rotary Turbo pump pump  II—  I I YD  I Turbo pump  Figure 1.5 Schematic of the ESI-triple quadrupole mass spectrometer system: N2, nitrogen curtain gas; C, curtain plate; 0, sampling orifice; SK, skimmer; QO, rf only quadrupole; Ql, mass-analyzing quadrupole; Q2, collision cell; Q3, mass-analyzing quadrupole; D, detector.  The resolution at half height (R 112 ) with axial ejection from Q2 (4x10 -4 Ton) was typically about 1000 at m/z 609 with a scan rate of 1000 Th/s. Slower scans, 5 Th/s, resulted in much higher resolution, R112= 6000 at m/z 609. It was found that, because of the lower pressure in Q3 (3x10 -5 TO/T), R172= 6000 could be obtained at the higher scan speed of 100 Th/s. Experiments with fragment ions formed in Q2 and then trapped and axially ejected from Q3 showed 16 times greater sensitivity than a conventional triple quadrupole MS/MS scan [72]. Hopfgartner and co-workers [73] were first to employ this method in the drug discovery field. They described an increase in the sensitivity of MS/MS by a factor of 60 compared to running MS/MS in the normal triple quadrupole mode on the same instrument. Leblanc et al. [74] described applications of MSAE to proteomics. They showed that the combination of the triple quadrupole based MS/MS scans with the very sensitive ion trap product MSAE scans allows rapid identification of peptides at low concentrations. It was demonstrated that with this instrument it was possible to conduct a  24  variety of ion processing steps prior to performing a mass scan. Thus with a triple quadrupole system, trapping in Q2 or Q3 with MSAE allows higher sensitivity in MS/MS, but at the same time, all the scan modes of a triple quadrupole system such as single reaction monitoring, multiple reaction monitoring and neutral loss scans are still possible. These latter scan modes are not possible with other 2D or 3D trap systems. Higher energy fragmentation patterns are generated with this instrument, leading to a richer product ion spectrum without an inherent low mass cut off.  1.5.3 Islands of Stability Sudakov et al. [36] derived the first and higher order resonance conditions for ions confined in a quadrupole ion trap with auxiliary quadrupole excitation (equation (1.14)). They also showed that auxiliary quadrupole excitation changes the stability conditions of an ion in the quadrupole field. Collings and Douglas [75] demonstrated excitation of ions in a pressurized linear ion trap (1.8-7.3 mTorr) using higher order resonances (up to K=6). With quadrupole excitation in a linear ion trap, multiple bands of instability appear on the stability diagram due to the first and higher order resonances. Thus multiple ejection conditions can occur for the same ion at a single excitation frequency [36]. Konenkov and co workers [76] showed that if the quadrupole excitation is applied to an rf/dc mass filter, where the quadrupole field is characterized by the two different values of^and fly , then ions can be excited in two different directions (x, y) with the same excitation frequency. As the excitation amplitude increases, the stability diagram splits into a number of stable areas or islands, each with its own operating point and mass  25  resolving abilities. They investigated this phenomena theoretically and experimentally [76]. Using an inductively coupled plasma mass spectrometer, experimental mapping of the stability diagram confirmed the theory. Peak shape enhancements (i.e. low mass tail suppression) were demonstrated by measuring Ar ion isotope abundances. An operating point was found that gave almost a 1000 times increase in abundance sensitivity for m / z = 39 in the presence of 4°Ar+ . In principle using islands of stability for mass analysis in a quadrupole mass filter may be considered as a new method of mass analysis. Recently this method of mass analysis was investigated theoretically [77] and experimentally [78] for a quadrupole with an added octopole field. Details will be given in Chapter 6 of this thesis.  1.6 Outline of This Thesis The results from the MS/MS performance and operation of quadrupoles with added octopole fields as mass filters are of interest for the following reasons. First, despite the added octopole field, the quadrupole rod sets can give resolution comparable to that of a conventional rod set, provided the dc voltage is applied with the correct polarity [56]. Second, the rod sets show increased fragmentation efficiency compared to conventional rod sets [57], especially at pressures of 1x10 -4 Ton or less. Some triple quadrupole instruments operate both as a conventional triple quadrupole MS/MS system and with trapping of ions in Q3. Therefore the last quadrupole, Q3, when operated as mass filter must be capable of at least unit mass resolution. When the same Q3 rod set is used for trapping and resonant excitation, the mass scanning method is axial ejection. Therefore if a quadrupole rod set with added octopole field that provides higher MS/MS efficiencies  26  can also operate as a mass filter with axial ejection, then in principle it can replace the Q3 conventional rod set in such instruments. Investigation of this hypothesis is a major focus of this thesis. Chapter 2 describes the instrumentation, experimental apparatus, sample preparation and methods of data acquisition and analysis used in this study. Chapter 3 describes the results obtained with MSAE of ions from a conventional linear quadrupole, and a quadrupole with 2.6% added octopole field without trapping. The focus of Chapter 4 is the MSAE of ions from a conventional linear quadrupole ion trap operating with different excitation modes. Chapter 5 describes, the results of the MSAE of ions from a linear quadrupole ion trap with 2.0 % added octopole field operating with different excitation modes. Some of the work described in this chapter is submitted to the Journal of the American Society for Mass Spectrometry for publication. Chapter 6 describes experimental investigation of mass analysis with islands of stability with a quadrupole mass filter with a 2.0% added octopole field. Most of Chapter 6 has been published in reference 78. Chapter 7 is a summary with suggestions for future work.  27  Chapter 2 Experimental Methods 2.1 Instrument Experiments were done with the system shown in Figure 2.1. Details are given in Table 2.1. Ions formed by pneumatically assisted electrospray ionization pass through a 1 5 mm diameter aperture in a curtain plate, through a dry N2 curtain gas, and enter the vacuum system through a 0.125 mm diameter orifice in the tip of a cone. Ions then travel through a quadrupole ion guide, Qo where they are collisionally cooled. The 20 cm long QO rods are capacitively coupled through two 25 pF capacitors to the Q1 drive rf voltage. The mass filter quadrupole, Ql, is separated from the ion guide by the entrance lens plate with a 1 0 mm diameter aperture. Ions leave Q1 and pass through two additional lenses, the first with a mesh covered 9 mm aperture, and the second with an open 9 mm aperture. The mesh-covered lens is referred to as exit lens 1 and the open aperture lens as exit lens 2. Exit lens 1 is located 3 5 mm from the end of the Q1 and exit lens 2 is separated from exit lens 1 by a 5 mm spacer. The pumping system consists of two turbo pumps and two rotary pumps. A Pirani gauge and an ion gauge are used to measure the pressures in the first and second chambers. Rotary pump 1 and turbo pump 1 for the first vacuum stage have speeds of 7.14 and 360 L/s respectively. Rotary pump 2 and turbo pump 2 for the second vacuum stage have speeds of 6.67 and 50 L/s respectively. With these arrangements the first vacuum stage pressure was measured as 10 x 10 -3 Torr and the second vacuum stage 3.2 x 10 -5 Ton. This experimental set up was used for non-trapping experiments.  28  d3 I  o. EO  0  r o a.  2  (I)  0 "CU CD  -  a0 a_  0-  E  =  a.  2 ts  - --->  13-  co  I-  I^/^\ IP, 0^ O/  0  0. E =  .  -71 cqg  • -..,  7'4^• •  a)  (.5  )^'_ _)  \ \ as  ^\  (7) \ cT-  F^Luc 0^ -t D (..)  29  Table 2.1 Instrumentation.  Syringe pump  Harvard Apparatus, model 22, (South Natick, MA)  Quadrupole rod set  MDS SCIEX (Concord ON)  Quadrupole power supply  MDS SCIEX (Concord ON) API 3+  Pumping system  Rotary pump 1, Leybold (Germany) Trivac 25B Rotary pump 2, Leybold (Germany) Trivac 16A Turbo pump 1, Leybold (Germany) Turbovac 361 Turbo pump 2, Leybold (Germany) Turbovac 50  Detector  Burle Electro-Optics channeltron electron multiplier, model 4822B, (Sturbridge, MA)  Computer  Power Macintosh 7100/80  Ion gauge  Kurt J. Lesker (Clairton, PA.), model GlOOF  Pirani gauge  Leybold (Germany), Thermovac TM230  Preamplifier  Ortec/Ametek (Oakridge, TN) 9302 fast amplifier  Discriminator  Tennelec TC453 constant fraction discriminator (leading edge mode)  30  For trapping experiments the entrance aperture diameter was changed to 3 0 mm to mimic the conditions used by Hager [72]. With this it was necessary to change the turbo pump 2 to a 360 L/s pump in order to maintain the second chamber pressure around 1.6 x 10 -5 Torr. At the same time the cone orifice diameter was also changed to 0.0875 mm, which decreased the pressure in the QO chamber to 8 x 10 -3 Ton- . The quadrupole power supply operates at 1.20 MHz. It has a maximum rf output voltage Vmax (the zero to peak voltage between each rod and ground) of 5000 V and a maximum dc  output voltage U (the voltage between each rod and ground) of ± 840 V. When operating the quadrupole as a mass filter, the quadrupole power supply was controlled by software (Tune 2.2, SCIEX, Concord, ON). The quadrupole power supply was connected to a Macintosh computer (PowerMac 7100/80) through a digital-to-analog converter (DAC). The mass ranges set in the software are converted to mass command voltages by the DAC. These mass command voltages set the required rf voltage levels to scan the quadrupole power supply. This method of scanning was used when the instrument was operated as an rf/dc mass filter and as an rf only quadrupole for MSAE experiments without trapping. To perform MSAE experiments in trapping mode the quadrupole power supply was modified to have an external scanning option and also modified so that low-level resolving dc (< ± 15) could be added between the rod pairs of the quadrupole. For external scanning, the drive rf voltages were set by an external analog voltage ramp provided by a multichannel scaler (MCS-pci, OrtecAmetek, Oak Ridge, TN, USA). The ramp output voltage range is computer adjustable within the range of 0 to +10 V. The MCS was also used to collect spectra and is plugged into the pci-bus of an Intel Pentium III computer.  31  A channel electron multiplier (CEM) is used as the ion detector. The CEM is a continuous dynode device, which can detect either positive or negative ions. For positive ion detection the input is generally at a high negative potential and the output is at ground. An ion striking the input face of the CEM starts an electron cascade, resulting in a current pulse (30 ns, —10 -6 A), which is amplified by a preamplifier. A discriminator is used to distinguish pulses caused by ions from background noise. The ion signal is recorded in ion counting mode. The recorded data are the total number of ions detected at different  m/ z ratios. The  computer calculates the count rate (ions/s) for each scan and these data are used to construct a mass spectrum over a certain  m/z  range. To reduce the pick up of rf voltage by the  detector circuit, two 1830 pF capacitors were added to the detector circuit as shown in Figure 2.2. CEM  signal 10M0^20MQ^1MC2 1830 pF ^ 1830 pF -  HV  Figure 2.2 Circuit diagram of the detector circuit for detection of positive ions.  Experiments were done with a conventional quadrupole rod array with a field radius ro = 4.17 mm, and ratio of rod radius to field radius R/ro = 1.126 , and with quadrupoles with  32  2.0 or 2.6 % added octopole fields with field radii ro = 4 5 mm (Figure 2.3). The octopole fields are added by making the radius of the y rods, R y , greater than the radius of the x rods, R x (Rx = r0 ). For the quadrupole with a 2.0% added octopole field, Ry R x = 1.220 , and for  the 2.6% added octopole R y 1 R x = 1.300 . Table 2.2 shows the dimensionless amplitudes of the even multipoles up to N = 10 calculated as described in Ref [35]. Table 2.2 Multipole amplitudes.  Rod set  AO  A2  A4  A6  A8  A10  Conventional  0.0000  1.00149  0.0000  0.001267  0.0000  -0.002431  2% Octopole  -0.02029  0.9994  0.01961  0.003281  0.0008604 - 0.002345  2.6% Octopole  -0.02638  1.0014  0.02567  0.001286  0.0009514 -0.002358  33  Figure 2.3 Cross sections of the electrodes of a quadrupole with an added octopole field.  2.2 Linear Ion Trap Experimental Set Up The single-quadrupole instrument shown in Figure 2.1 was modified to operate as a linear ion trap. A block diagram of the apparatus as used for trapping experiments is provided in Figure 2.4. The entrance and exit lenses were connected to a two-channel arbitrary waveform generator, (PC Instruments AWG-344, Twinsburg, OH, USA). Each channel provides a maximum amplitude output (0 to peak) of 12 V, which is increased by homemade amplifiers to the desired voltages. The master clock is provided by the arbitrary waveform generator. First it was necessary to estimate the number of ions trapped in the linear ion trap in each injection period. The timing parameters for this are shown in Figure 2.5. The  34  quadrupole power supply was operated in rf-only mode and the rf voltage was manually set to a voltage corresponding to the desired q value of ion injection. Ions were injected in the trap by lowering the entrance lens to -15 V in first experiments. During the injection period, the exit lens was held at a stopping potential (+120 V). Then the entrance lens was increased to the same stopping potential of (+120 V) and ions were cooled for 50-100 ms. Ions were detected by lowering the exit lens to (-15 V) to transmit ions. Ions were then detected by triggering the MCS to collect data. For this experiment it was expected that the injection time and number of detected ions should be linearly related until a plateau is reached. With this experimental set up the number of ions trapped in the LIT was found to decrease with injection time as shown in Figure 2.6. This strange result could be explained by following the ion path with the respective potentials step by step. Ions enter the LIT, travel towards the exit lens, approach the barrier of (+120 V), reflect back and proceed towards the entrance lens.  35  0 G.)  a)  s  rn (13  CO -a  r)  0) Q.  0  ca  2  0  0  .  0  E  0  4 .  0  0  C) C)  c  0  36  Inject  Scan  Drain  100 ms  10-50 ms  Cool  Trap Entrance  Trap Exit  rf voltage corresp onding to q =0.4  Drive rf 10-50 ms  50 ms  Figure 2.5 Pulse sequence for counting injected ions.  12000  10000  8000  6000  4000  2000  0  ^  10^20^30^40^50  Injection Time (ms) Figure 2.6 Injected ion count vs. injection time.  37  For the reflected ions, the entrance lens must also provide a potential barrier; otherwise ions can leave the trap. The entrance lens initially was held at (-15 V) during the injection time, which allowed ions to leave the trap. Only for the very shortest injection period was it possible to detect increasing numbers of ions with longer injection times. When the offset of the entrance lens was increased to a value that simultaneously allowed the passage of ions into the LIT and enabled trapping of reflected ions, the ion count increased with longer injection times as shown in Figure 2.7. This required that the lens voltage be one or two volts higher than the rod offset voltage of the Q1 rod set. The trapping efficiency is low for these experiments because of the low pressure in the linear ion trap. The kinetic energy losses of ions in the ion trap can be estimated from [23]: E^CD Anm 2 1 " — = exp m 1^I Eo  (2.1)  where E0 is the initial ion kinetic energy at the trap entrance, E is the energy after collisions with background gas, CD is a drag coefficient, A is the collision cross section, n is the gas number density, m 1 is the ion mass, m 2 is the collision gas mass and 1 is the  length that ions travel. For these experiments, CD = 2.2, n = 5.28 x 10 11 cm-3 , A = 280 A, 1= 40 cm, m 2 = 28 amu, m 1 = 609 amu, so that E = 0.94E0 , after ions pass through the  quadrupole and then back to the entrance. Ions lose only about 6% of their initial energy. With a QO rod offset of +2.0 V and a Q1 rod offset of –1.0 V, the initial energy of the ions is about 3 eV, and after one round trip the energy will be reduced to 2.82 eV. Therefore the entrance lens voltage of 0.0 or +1.0 volt is not sufficient to stop the ions from leaving Q1 and entering the QO chamber, where they are lost.  38  4400 4200 4000 3800 +E.  0 0 0  3600 3400 3200 3000 2800 2600 0  ^  20^40^60^80  ^  100  ^  120  Injection Time (ms)  Figure 2.7 Injected ion count vs. injection time for injection at q = 0.4.  A schematic of the timing parameters for a typical MSAE scan with trapped ions is shown in Figure 2.8. First a variable length (10-50 ms) pulse, 1 volt higher than the Q1 rod offset but below the QO rod offset (+2 V), is applied to the entrance lens to allow ions to enter Ql, (Q1 offset —1 to -5 V). During this injection step the exit lens is held at +120 V. At the end of the injection pulse the entrance lens is raised to +120 V. Next, the trapped ions are cooled for 50 ms. Just prior to the mass scan the dc voltage applied to the exit lens is reduced to a scan value. For lower scan speeds this was 2-3 volts above the dc rod offset of Q1 and for higher scan speeds 10-25 volts above the Q1 rod offset. Auxiliary dipole or quadrupole excitation is applied at a fixed frequency, and the drive rf is ramped either up or down, over the chosen mass-to-charge range to eject ions from the  39  linear ion trap. Finally, the dc voltages applied to the entrance lens and the exit lens are lowered to -15 V for 10-50 ms to drain any residual ions from the linear ion trap and QO. Operating voltages are shown in Table 2.3.  Inject^Cool^Scan^Drain  Trap Entrance  Trap Exit •  Drive rf  Auxiliary ac 10-50 ms  50 ms^0.2-500 ms^10-50 ms  Figure 2.8 Schematic of the timing parameters for MSAE experiments.  40  Table 2.3 Operating voltages.  Sprayer  +3500  Curtain plate  +500  Orifice  +50; +30  QO rod offset  +2  Entrance lens  +1, 0, -1, -2 or +120  Q1 rod offset  0, -1, -2, -3, -4, -5  Exit lens 1  -15 or +120  Exit lens 2  -300  Auxiliary ac from an arbitrary waveform generator (SRS DS345, Stanford Instruments, Sunnyvale, CA) was applied between one pair of rods (x or y) as dipole excitation [33] or simultaneously between two pairs of rods as dipole-dipole excitation, or to all four rods as quadrupole excitation. For dipole excitation the electrical connection between the (x or y) pair of the rods was disconnected and the output from the main drive was connected to the center tap of the secondary winding of a bipolar transformer (1:1 turns ratio). The primary winding of the transformer was connected to the SRS arbitrary waveform generator and the two ends of the secondary were connected to a rod pair. Quadrupole excitation was applied through the quadrupole power supply through a circuit supplied by MDS-SCIEX. For all the experiments with trapped ions reported here, approximately 23% of the drive rf (in phase with the pair of poles that has the auxiliary excitation) was added to the  41  exit lens by connecting the lens to the rf output of the quadrupole supply through a 15 pf capacitor [79] as shown in the scale diagram in Figure 2.9.  co 3  35  • mm  cc,  3 3  mm  111,  m^co 3^3 3 3  3 pF  15 pF  50 pF stray capacitance  • dc input  Figure 2.9 Cross section view of the two exit lenses and the pair of the quadrupole rods that are capacitively coupled to exit lens 1.  42  2.2.1 Sample preparation  Reserpine (C33H 40N20 9 ) (m.w. 609.7) and renin substrate tetradecapeptide (DRVYIHPFHLLVYS) (m.w. 1759.0), were from Sigma (St. Louis, MO, USA). Agilent tune mix was from Agilent technologies (Santa Clara, CA, USA). Methanol and acetic acid were from Fisher Scientific (Nepean, ON, Canada). UHP grade nitrogen was from Praxair (Vancouver, BC, Canada). Solutions were as follows: reserpine, 1-10 ptM, renin substrate 10 —5011M, all in 70% (V/V) methanol, 29.5% (V/V) water, 0.5% (V/V) acetic acid; Agilent tune mix as supplied. The solution flow rate for all experiments was 1 µL/min.  2.2.2 Data Analysis  Data analysis used in-house developed software. The software is designed to read MCS produced spectra with the corresponding parameters (e.g. rf voltage specifications) and save spectra in a database for later analysis and graphing. In a few steps a user can graph spectra as intensity vs. mass-to-charge ratio, find peaks and calculate resolution. The software is capable of storing and sorting thousands of spectra based on their collection date. Using this software it was possible to organize and quickly browse data from a large number of experiments. Figure 2.10 and 2.11 show the Graphic User Interface (GUI) of the MSAE data analysis software.  43  klAnial Ejection Data Analysis Tools (MES Tile A  MCS Tassel  CS Ready About MCS liesr.mcs)  Trap Calculation  e, Annie Exp. 2006 Annie  Axial Ejection (2006107117)  350  TrapOttacs Trap02.Mcs Trap03.Mcs Trap04.Mcs Trap05.Mcs TrapAE01.Mcs Tr.. CO2Mcs T^ EI  la, My Documents la, Annie  -4.0F8241/12.5E16.2,13.8qa0.80KInMEDC. PassCounta2000 Dwe8AmemS0 us 1.C..2143  260-  210-  140 -  -_- Read Selected MCS Fie(*) I ^ICAMy OccumenteArne1T1apC,Soulaoon4Arne Exp. ZOOSNA  e^  eau& Values  FieNeme Id  rapAE03  00  10: n-7  200E07171E16:5G  TimeSternpr. 13/22/2006 123057PM Vots;e Start Mkt^End  Owel^0  33.2  66.3^99.5^132.7^165.8^199.0 Apparent Mass (mh)^TmoisEcuvos  OAS Glialml400144011  an0384 7.57079  0,4104i AcciMode^1  ,  Range [0..1[ 193814 2  F913ForrnetDwel^50 Passiength^200 PassCount^2000  Range (1.,z 16563  Range R.XPc 121  -  PassCouniPresel^2000  8,170570 , OF.TiW3  0575 8,1702.756 3-  P43.0 7675 9 : 706651  Time^16:0056 Date^07172006  1  M aAmrChannel MCSNumbel^1  xis es sit en  •••  1ST  1 .- 11'4 1 + 1  CalibrationType^0 CalibrationUnits Caihratiudaefficienl0 0 CakbrationCoefficientl 0 Estemall) miff Meshold 1068713483 ReplaceThenSumMode 1  Add 'his MCS to Database  !scan  _-_J  MI W.^itell ■■••■11..  Figure 2.10 MSAE data analysis software GUI.  44  klApial Election Data Analysis Cosh (MCS Fee Analysis) [Version 0.11- Sep 20051  MCS Bias.. 1 MCS Reader Abort ID: 120070010123029  Axial Ejection (2007/08110)  350000  I OF414A01E1 04,-0.413q-OMM3 PeasCour9e100 Dweiline-5 1.0,1617699  Des.: 1.0F41440.1/18.92768.3348E1.04.9  .—'- Alickl 297823 End: Voltage Slot 709E7  0M  R8nge10. 11 A 1230.35034 9-1 0.0742  687 33  Range ri 2[A.Range R. 31k 123(0496 Id 0.06333 pl ango3 4psz r171.18 23 361 A:FROT563  41101-1.1+1 I lel sodbo.(Asci  I  210000-  111Z!MOICE311.1 2007O01012 ;: r+  io 2007081012.41.37 I 200706101252:63  140000-  20070810123426 i 2007081012582 2037081013736:0-677^1  688.70  200708101311:06  g  70810131E33  70000-  scAttial Eection (2007/08/10) 30300  689.94  11,111.13M134.-0.13,-311610 1411.1.1111 1.1111w-Semt  686.2  ^  689.8  Iaph  70000  SelecA Peak r 9618.31 Resolution  0 0 033.3E6.399.1 33.785.1399.0  Mime•ai 018778saiiei  RAW MCS Data  Ed  ^  Apparent Mass (min)  40000  ^ Add For Pink  f  r sd.etwx C'  690.9  ^  ^  692.1  ^  693.3  Trap. 5  SeieciMes3C  1808r8 Election Pint to W31F Fie  Delete Lot - , ^Deke Buffer  Figure 2.11 MSAE data analysis software GUI.  45  Chapter 3 Mass Selective Axial Ejection of Ions Without Trapping 3.1 Introduction This chapter describes the experimental set up and methods for performing MSAE of ions from a conventional rod set and a 2.6% added octopole field quadrupole rod set without trapping the ions. The purpose of this work was to reproduce Hager's results with a conventional round-rod quadrupole for comparison to MSAE results from the quadrupole rod set with a 2.6% added octopole field.  3.2 Experimental The experimental apparatus is shown in Figure 2.1. The operating voltages are summarized in Table 3.1. First, the quadrupole power supply was operated in rf/dc mass filter mode and a spectrum of reserpine isotopic peaks was recorded. Then, in single ion monitoring mode, the monoisotopic peak (609.3) was monitored while increasing the exit lens voltage to stop the ions. With the operating voltages shown in Table 3.1 the exit lens barrier to stop the ions was +300 volts. In order to decrease the required voltage, all the dc voltages of the system were lowered such that +100 volts on the exit lens stopped the ions. The final operating voltages are summarized in Table 3.2. Once the stopping potential for the monoisotopic peak (609.3) of reserpine was determined, the instrument was operated in rf-only mode with the stopping potential applied to the exit lens. The  46  amplitude of the drive rf was scanned to bring ions of different m / z ratios to the stability boundary (a = 0, q = 0.908). Ions near the boundary gain large amplitudes of oscillation.  Table 3.1 Initial operating voltages (V).  sprayer  +3700  curtain plate  +550  orifice  +200  QO rod offset  +110  interquad lens  +70  Q1 rod offset  +109  Exit lens 1  -10, +300  Exit lens 2  -10, +300  Table 3.2 Final operating voltages.  sprayer  +3700  curtain plate  +441  orifice  +91  QO rod offset  +1  interquad lens  -39  Q1 rod offset  0  Exit lens 1  -119, +100  Exit lens 2  -119, +100  47  These excited ions overcome the exit lens barrier and are ejected to produce a mass spectrum [71]. Initially experiments were done with a conventional quadrupole rod set using balanced and unbalanced (up to 15%) rf, with 7 V dc applied between the rods and with 50-110 Vp-p auxiliary rf (at the frequency of quadrupole power supply) applied to the exit lens. This rf was 1.8 to 3.9 % of the main rf and was in phase and phase locked with the drive if. Figure 3.1 shows a block diagram of the experimental set up for applying rf to exit lens in this configuration. The software (Tune 2.2, Sciex) used to count ions, indicates the number of counts per second of the most intense peak times the number of scans. To report the intensity as counts per second, the number taken from the software was divided by the number of scans. rf out  5.6mH pulse amplifier  QPS  pulse generator  To Exit Lens  Figure 3.1 Block diagram of the experimental set up to add rf to the exit lens.  The stability boundaries for a quadrupole with a 2.6% added octopole field were calculated as in [13]. The transmission of the quadrupole for given a, q values was calculated from 6000 ion trajectories. The initial spatial distributions were Gaussian with standard deviations a x = 6 y = 0.0020ro . Initial velocity distributions were thermal for an ion of mass 390. Multipoles up to the 20 pole term (N =10) were included in the  48  calculation. No fringing fields were included. Points with a transmission of 1% were taken as the stability boundaries.  3.3 Results and Discussion  3.3.1 Experiments with a Conventional Quadrupole Rod Set  Figure 3.2 shows a spectrum of reserpine isotopic peaks obtained by operating the quadrupole as a conventional rf/dc mass filter. The resolution (R112) is about 2900 and the scan speed is 5 Th/s. Figure 3.3 shows a spectrum of the isotopic peaks of reserpine with MSAE, obtained with balanced rf and ejection at the stability boundary q 0.908 with a scan speed of 0.8 Th/s. With MSAE scans, adjusting the rod offset and the exit lens voltages can optimize the resolution. For Figure 3.3 the exit lens voltage was 108 volts repulsive with respect to the dc rod offset of the quadrupole (-8.0 volts). This value yielded optimum signal-to-background levels. The resolution (R112) is about 1900, more than sufficient to separate the isotopic peaks. The background level was 10 counts/sec on average and it was not possible to improve the signal-to-background ratio beyond what is shown in Figure 3.3.  49  Resolution = 2900 1000 -  608^610^612^614 m/z  Figure 3.2 Mass analysis of reserpine ions with operation at the tip of the stability region with a conventional quadrupole rod set and a scan speed of 5 Th/s.  50  250 Resolution = 1900 200 -  50 -  608^610 ril/Z  ^612^614  Figure 3.3 MSAE of reserpine ions at q = 0.908 obtained with balanced rf and a scan speed of 0.8 Th/s.  As in Hager's experiments [71], unbalancing the drive rf by approximately ±15% has a dramatic effect on MSAE performance. Both sensitivity and resolution increase. The effect of an unbalanced rf is shown in Figure 3.4. A lower rf voltage (-15%) was applied to the A-poles (the poles with positive dc, x -poles). The sensitivity is ca. 5 times greater than with balanced rf (Figure 3.3). The resolution (R1/2) is 2095. Figure 3.5 shows the MSAE of reserpine ions when the A-poles have +15% rf unbalance and the resolution (R1/2) is 2386. With unbalanced rf slightly better resolution is obtained when the A-pole has the higher (+15%) rf voltage. When the ions enter the exit fringing field the ion motions in the xz and yz planes are coupled and become very complex and there is no  51  theoretical treatment available. However, Hager argued [79] that when the rf is unbalanced the field gradient will be different in the xz and yz planes. If the rf is unbalanced such that the higher rf is on the x -pole ( the positive dc pole) pair, then ions aligned with the y -pole (the negative dc pole) pair are slowed down and spend more time in the exit fringing field which improves the radial to axial coupling. Therefore for a given exit lens barrier voltage this results in significantly higher ion ejection energies and improved ejection efficiency.  1400 k  Resolution = 2095  1200  1000  400  200  0 608  ^  610  ^  612  ^  614  rrl/Z  Figure 3.4 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the A-pole pair has 15% lower rf voltage than with balanced if  52  1400  1200 -  Resolution = 2386  1000 >, 800 v) N 4E' 600-  400 -  200 -  608^610^612^614 m/z  Figure 3.5 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the A-pole pair has 15% higher rf voltage than with balanced rf.  Hager found that it was necessary to apply the higher voltage unbalanced rf to the pole pair with the negative resolving dc in order to obtain higher resolution and sensitivity. He argued that small amounts of resolving dc are needed to align the ion beam (positive ions in this case) with the pole pair that has the lower unbalanced rf voltage. Under these conditions ions aligned with this pole pair spend more time in the fringing field and receive higher axial kinetic energies [79]. Adding small amounts of resolving dc ±3 -5 V) in conjunction with the unbalanced drive rf, which gave the best performance for Hager's experiments, did not prove to be as effective with our experimental set up for MSAE at q = 0.908. Figure 3.6 shows a spectrum from MSAE of 53  reserpine ions with +15% unbalanced rf applied to the B-pole pair ( y rods) which has —3 V resolving dc.  700 Resolution = 1335  600 -  500 U)  o_ o 400  N  -  300 -  c  200 -  100 -  608^610^612^614 Mk  Figure 3.6 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf is unbalanced so that the B-pole pair has 15% higher rf voltage and —3V dc.  The resolution (R112) is 1335. Adding the ± 3 V resolving dc decreases both peak  .  intensity and resolution. The reason for this difference from Hager's observations is believed to be the differences in the experimental set up, including the exit lens aperture size, distance from the rods, and the detector mounting. Figure 3.7 shows the spectrum of reserpine ions axially ejected at q=0.908 when the higher unbalanced rf voltage was applied to the A-pole pair which had +3V resolving dc.  54  As expected from Hager's results this mode of operation results in considerably poorer peak shapes and lower ion intensity.  700 Resolution = 650  600 500 J) o_ .S. 400 .>, w a) 300 a )  4 .  608^610^612^614 m/z  Figure 3.7 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 This. The rf is unbalanced so that the A-pole pair has 15% higher rf voltage and +3V dc.  Figure 3.8 is a plot of ion intensity vs. the exit lens voltage for MSAE of reserpine ions with a series of combinations of unbalanced rf and resolving dc conditions. It shows that high exit energies are only observed when unbalanced rf is applied and a higher rf voltage is applied to the A-pole pair (x rods).  55  1.0e+5  A-pole pair +15% rf A-pole pair +15% rf, +3 V dc A-pole pair -15% rf, +3 V dc A-pole pair -15% rf  o_ >,  1.0e+4  a) E C  .  1.0e+3  1.0e+2  80  ^  100^120^140  ^  160  ^  180  ^  200  Exit Lens Voltage  Figure 3.8 Intensity vs. the exit lens voltage for reserpine ions obtained using different combinations of unbalanced rf and added dc.  Hager found that the effect achieved by unbalancing the rf applied to the rods can also be achieved by applying a certain percentage of the drive rf with proper phase to the exit lens [80]. An unbalanced rf is equivalent to a balanced rf with an added axis potential between the quadrupole and exit lens [39]. This potential difference between the quadrupole and exit lens can be produced by applying some of the quadrupole rf to the exit lens without the need to unbalance the rf. MSAE experiments were also performed with balanced rf and 1.8-3.9 % of the drive rf applied to the exit lens. The resolution obtained with 50 Vp-p rf applied to the exit lens was R172 = 1800. Figure 3.9 shows MSAE of reserpine ions obtained by applying 110  Vp-p  rf to the exit lens. The resolution (R112) is 56  1881. The resolution increases slightly with higher rf voltages on the exit lens. With the set up at that time, it was not possible to add more than 110 Vp-p rf to the exit lens.  700 600 -  Resolution = 1881  500 U)  o_ c.) 400  N 300 200 100 -  608^610^612^614 111/Z  Figure 3.9 MSAE of reserpine ions at q = 0.908 with a scan speed of 0.8 Th/s. The rf was balanced and 110 Vp-p rf applied to the exit lens.  57  3.3.2 Experiments with a Quadrupole Rod Set with a 2.6% Added Octopole Field 3.3.2.1 MSAE of ions at the stability boundary q = 0.908 Conventional rf/dc mass analysis- is possible with a quadrupole with 2.6% added octopole field when the positive dc voltage is applied to the smaller rods (for positive ions) [56]. Figure 3.10 shows a spectrum of reserpine ions obtained with this mode. The resolution (R 1 12) is 2500. MSAE experiments without trapping and ejection at q = 0.908 were then tried with this quadrupole. With balanced rf and no dc between the rods, a very broad peak with poor resolution (nominal R112=76) was produced at about m /z =607, Figure 3.11.  58  100 Resolution = 2500 80 -  U)  0-  60  c 40-  20 -  ^ 0  608  I  ^  610  ^  612  ^  614  Mk  Figure 3.10 Conventional rf/dc mass analysis with a quadrupole with a 2.6% octopole field and a scan speed of 5 Th/s.  Combinations of unbalanced rf, dc between the rod pairs, and rf on the exit lens were tried, but the resolution could not be improved. Evidently with axial ejection at q = 0.908 and with excitation at the stability boundary, the quadrupole with 2.6% added octopole field produces much lower resolution than a conventional quadrupole.  59  2.2e+5 ^ 2.0e+5 1.8e+5 1.6e+5 U)  o.  1.4e+5  -  N c 1.2e+5 -  a)  1.0e+5 8.0e+4 6.0e+4 4.0e+4 595  600  605  610  615  rniz  Figure 3.11 MSAE of reserpine ions from a quadrupole rod set with a 2.6% added octopole field at q = 0.908 and a scan speed of 0.8 Th/s.  The lower resolution may be a result of changes to the stability boundaries caused by the octopole field. With a conventional rod set, at the a = 0 , q = 0.908 boundary, ion motion becomes unstable in the x and y directions simultaneously. The stability boundaries of a quadrupole with 2.6% octopole field are shown in Figure 3.12. The x and y motions have separate stability boundaries on the a = 0 axis. The x boundary is at q = 0.908, but the y boundary is at about q = 0.931. The y boundary is diffuse [56]. The octopole field couples the x and y motions. Excitation of ions in x near q = 0.908  60  may lead to excitation in the y direction where motion is stable, resulting in delayed ejection and low resolution.  0.08  0.04 x stability boundary  al 0.00  -0.04  -0.08 0.87  y stability boundary  0.88^0.89^0.90^0.91^0.92^0.93  ^  0.94  q Figure 3.12 Calculated stability boundaries of a quadrupole with a 2.6% added octopole field (calculated by W. Xiao).  61  3.3.2.2 MSAE of ions with dipole excitation at q = 0.8765 When dipole excitation (4.0 V p _p) at 500 kHz is applied between the larger rods, substantially better resolution is obtained. The isotopic peaks of reserpine could be resolved although not to baseline (R112=758) (Figure 3.13). The same result could not be reproduced with dipole excitation between the smaller rods (R112=200) (Figure 3.14). The scan speed with dipole excitation applied to the larger or the smaller rods was 0.8 This and forward scans were used.  70000 ^ Resolution = 758  60000 50000 U)  40000 -  a) 30000 20000 10000 -  608^610^612^614 m/z  Figure 3.13 MSAE of reserpine ions at q 0.8765 with 4.0 Vp-p dipole excitation applied to the larger rods.  62  40000 35000 30000  Cn 25000 a 0  --  u)  20000  C  a)  E  15000 10000 5000 0 600  ^  605  ^  610  ^  615  ^  620  rrilz Figure 3.14 MSAE of reserpine ions at q = 0.8765 with 4.0 Vp-p dipole excitation applied to the smaller rods.  63  3.4 Summary Resolution and peak shapes with MSAE of ions at the stability boundary q = 0.908 with a conventional round rod set were similar to those obtained by Hager, with some differences that were discussed in this chapter. MSAE of ions with a quadrupole with 2.6% added octopole field produced only a low-resolution spectrum with ejection at the stability boundary. Calculation of the stability diagram showed that the x and y motions have separate stability boundaries on the a = 0 axis. Results obtained when dipole excitation was applied between the larger rods and ions were ejected at q = 0.8765 were promising. Resolution was improved by an order of magnitude and isotopic peaks were resolved (not to baseline).  64  Chapter 4 Mass Selective Axial Ejection of Trapped Ions from a Linear Quadrupole 4.1 Introduction In this chapter the MSAE of trapped ions from a conventional quadrupole rod set will be described. Different modes of excitation will be demonstrated. For each mode of excitation the optimum values of excitation amplitude and exit lens voltages were investigated. The effects of scan direction and scan speed on axial ejection of ions with each mode of excitation were explored.  4.1.1 Review of the Theoretical Treatment of MSAE of Ions from Linear Ion Traps Londry and Hager [81] studied the electric fields responsible for MSAE of ions trapped in a linear ion trap using a combination of analytic theory and computer simulations. The decay of the two dimensional quadrupole potential in the fringing region near the ends of the rods was described by a function f (z) so that the potential in the fringing regions, O FF can be written as FF  (1)(X, y)  f (z)  (4.1)  where Vx, y) is the quadrupole potential described in equation (1.1). The axial component of the electric field due to the decay of the quadrupole field is E  af  z  (x, y) az ^- -4D^ (  )  (4.2) 65  In trapping mode there is no dc component to the quadrupole potential. Therefore the Dehmelt [82] approximation for ion motion can be adapted and 01)(x, y) and consequently Ezquad can be approximated by a pseudo or effective potential. The effective potential for  the time dependent potential of equation (1.1) is given by -.2  Veff  eE  (4.3)  4mQ 2  For the potential of equation (1.1) the effective potential can be calculated using equation (4.3) qA22 V .X 2 + y 2 Veff(x,Y)= ^ (^ 2 )  4^ro  (4.4)  which gives Ez,quad  af (z) MC22 q 2 2 (x + y ) az 16e  (4.5)  where m is the mass of a singly charged ion, e is the electronic charge and C2 is the angular frequency of the drive rf. Equation (4.5) shows that as a result of a decreasing quadrupole potential in the fringing region ( f (z) decreasing with z), ions will experience a net positive axial electric field. To a first approximation, this field is proportional to the square of the radial displacement, the square of the q value and the mass to charge ratio of the ion. In order to eject ions in a mass selective fashion the positive electric field described by equation (4.5) must be balanced by a negative electric field, which decreases in strength with increasing ion radial displacement. This can be achieved by applying a static potential to the exit lens. Londry and Hager [81] obtained the electric field  66  E z lens arising from the exit lens potential, by differentiating a numerical solution to the  Laplace equation. Plotting the contribution of E zjens to the total electric field in the x — z plane, for a specific exit lens potential showed that the lEzaens decreases with increasing x . The two contributions to the axial component of the electric field, Ez ,2,„ and Eziens were summed to obtain the total axial field experienced by an ion, ^. When the  resulting Ez ,f was plotted as a function of axial position for most values of radial displacement x , there was a value of z for which Ez ,f = 0. The locations of these zero crossings were marked in the x — z plane. These points defined a surface on which the net axial force acting on an ion is zero. The shape of this surface is similar to a cone and for this reason it was called the "cone of reflection". Only ions with sufficient radial amplitude are able to penetrate this surface and be ejected axially, while others are reflected. Londry and Hager [81] discussed the impacts of different parameters like the q value and exit lens potential on the cone of the reflection. The calculations were consistent with their experimental results. The effects of the exit lens potential are discussed below. For MSAE to be effective, the exit lens potential must be chosen carefully. When it is reduced below optimum, resolution is degraded. If increased above optimum, sensitivity is reduced. The mapping of cones of reflection for different exit lens potentials confirmed this. When the exit lens potential is too low, the cone of reflection is further from the exit lens. As a result, the cone can be penetrated by ions with only moderate  67  radial amplitude and the resolution is degraded. With increasing exit lens potential, the cone moves toward the ends of the rods, and ions require higher radial amplitudes to penetrate the cone and be detected. In this thesis a theoretical treatment of this kind is not attempted. Nevertheless the experimental results are consistent with Londry and Hager's theoretical results, both for MSAE of ions from a conventional linear quadrupole, and a linear quadrupole with a 2.0% added octopole field.  4.2 Experimental The single quadrupole instrument described in chapter 2 was used to perform MSAE experiments with a conventional linear quadrupole. The instrument was operated in trapping mode as described in chapter 2. Briefly, as shown in the schematic of the scan function provided in Figure 2.8, ions are injected into the linear ion trap and cooled. These ions can be ejected axially in a mass selective way by ramping the amplitude of the rf drive, to bring ions into resonance with a single frequency dipole, dipole-dipole or quadrupole auxiliary signal. The ions gain radial amplitude until they are ejected axially or neutralized on the rods.  4.3 Results and discussion  4.3.1 Dipole Excitation  Dipole excitation was used to excite ions in a conventional rod set at q = 0.80 (excitation frequency 413.14 kHz, amplitude 0.03 VP-p). For the experiments described  68  here for scan speeds of 15 This there was no resolving dc added to the rods. For all the other reported scan speeds there was 7 V dc added between the rods to eliminate the background and to increase sensitivity with faster scans. As Hager [83] argued, the problem of an underlying continuum background could be significant for MSAE experiments with ions introduced from atmospheric pressure ion sources like ESI. These devices can produce ionic clusters of varying sizes and energies. Higher mass ions with q -values lower than the ejection q -value can also pass the exit lens barrier if their  kinetic energies are sufficient. These ions do not gain significant energy in the fringing field and they will be observed as a background contribution to the mass spectrum. It was found that the application of a low level of resolving dc to the quadrupole rod set could significantly reduce this background by allowing the quadrupole to act as a low pass filter [83]. Hager and Londry showed that applying some of the trapping rf to the exit lens can improve the resolution, with no loss of ion signals [79]. Thus in all experiments with trapped ions the drive rf was balanced and, as shown in chapter 2, approximately 23% of the rf was added to the exit lens. With dipole excitation applied to either pair of rods, MSAE of reserpine ions with forward and reverse scans at low scan speed (15 This) and an excitation amplitude of 0.03 Vp_p gave similar spectra, with resolutions of up to 4900 (Figure 4.1).  69  (a)  Resolution = 4980  (b)  Resolution = 4980  1.0 -  0 a)  0.0  1.0 -  0.0 608  610  614  Mass (m/z)  Figure 4.1 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation. a) forward scan, ejection at q = 0.80 , 15 Th/s b) reverse scan, ejection at  q = 0.80 , 15 Th/s.  70  As expected forward and reverse scans with a conventional quadrupole linear ion trap produced similar resolution spectra. With forward and reverse scans, at 1500 Th/s (excitation amplitude 0.6 V p_p) spectra with a resolution of about 3000 were obtained. With forward scans, at 3300 Th/s (excitation amplitude1.0  Vp-p),  the resolution was  2350. For the same scan speed and excitation amplitude and with a reverse scan, resolution of 2400 was obtained. With forward scans at 5000 Th/s (excitation amplitude 2.0 Vp-p), peaks showed mass shifts and unequal spacings. To calculate the resolution in this case, the peak width of the most abundant peak (the monoisotopic peak) was compared to the spacing between the two most abundant isotopic peaks, taken as 1 mass unit. The resolution, calculated as described above, was 1970. With reverse scans at 5000 Th/s a similar resolution, 2000, (same method of calculation) was achieved. Spectra are shown in Figure 4.2. The unequal peak widths and spacings are likely a result of a limitation of the quadrupole power supply, which was designed for scan speeds of ca. 100 Th/s with step sizes of 0.1 Th.  71  (a)  Resolution = 1971  (b)  Resolution = 2057  1.0 -  0.0  1.0 -  0.0 608^610^612^614  Mass (m/z)  Figure 4.2 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation. a) forward scan, ejection at q = 0.80 , 5000 Th/s b) reverse scan, ejection at q = 0.80 , 5000 Th/s.  72  4.3.2 Quadrupole Excitation  Auxiliary quadrupole excitation was applied to the conventional quadrupole rods to give parametric excitation at twice the fundamental frequency of ion oscillation. Due to an electronics limitation, the higher auxiliary voltages at the higher frequencies needed for quadrupole excitation at q = 0.80 could not be applied, so experiments were performed with ions trapped at q = 0.7002 (excitation frequency 676.00 kHz ).With quadrupole excitation (0.90 V p _p ) and with a scan speed of 15 Th/s, both forward and reverse scans gave a resolution of 4300-4700. High scan speed was also possible with both forward and reverse scanning. With 7 V dc added between the rods, forward scanning (3.76 Vp_p) and a scan speed of 3800 Th/s, the resolution was 1580, and with reverse scanning (3.65 V p _p ) and a scan speed of 3300 Th/s, resolution of 1500 was possible. Scan speeds higher than 3300 - 3800 Th/s in each scanning direction resulted in poor peak shapes. Reverse scanning gave somewhat better peak shapes and slightly higher resolution. Figure 4.3 shows MSAE of Agilent tune mix m / z =622 with reverse scanning at two different scan speeds.  73  (a)  Resolution = 3600  1.0 -  0.0  Resolution = 1600  (b) 1.0 -  0.0 621  ^  623  ^  625^627  Mass (m/z)  Figure 4.3 Peak shapes and resolution with axial ejection of trapped ions, and quadrupole excitation. a) reverse scan, ejection at q = 0.7002 , 15 Th/s b) reverse scan, ejection at q=  0.7002 , 3300 Th/s.  74  4.3.3 Dipole-Dipole Excitation  Experiments were done with dipole excitation applied simultaneously to both pairs of rods. The optimal excitation amplitudes for different scan speeds ranged from 0.05 Vp . p at 15 Th/s to 3.5 vp_p at 5000 Th/s. With forward scans, low scan speeds (15 Th/s) gave a resolution of around 4600. With increasing scan speed, about 3000 Th/s, a resolution of 2100 was possible, and with a scan speed at 5000 Th/s, the resolution was 1500. Dipole-dipole excitation resulted in lower resolution at higher scan speeds than single dipole excitation. No improvements in scan speed or resolution were found with dipole-dipole excitation.  4.4 Summary High resolution and high scan speeds were possible with MSAE experiments with a conventional round rod quadrupole ion trap. Different excitation modes with different scan direction and scan speeds were tested. With dipole excitation with either forward or reverse scanning directions at scan speeds of 5000 Th/s resolution of 2000 is possible. With quadrupole excitation maximum achievable scan speed was about 3300 — 3800 for forward and reverse scanning respectively. In this case resolution was 1500 Th/s. With dipole-dipole excitation resolution of 1500 was possible with a scan speed of 5000 Th/s. Dipole excitation yields higher resolution than quadrupole or dipole-dipole excitation.  75  Chapter 5 Mass Selective Axial Ejection of Trapped Ions from a Quadrupole with a 2.0% Added Octopole Field 5.1 Introduction In this chapter the MSAE of trapped ions from a quadrupole with 2.0% added octopole field will be described. Different modes of excitation will be discussed. For each mode of excitation the optimum values of excitation amplitude and exit lens voltage were investigated. The effects of scan direction and scan speed on axial ejection of ions with each mode of excitation were explored.  5.1.1 Octopole Potential and Frequency Shifts The electric potential within the rod sets with a 2.0% octopole field is given to a good approximation by 2 2^4 2^2^4 +y - y^y ^x —ux^ (1)(x, y, t) =(^ A 0 + A2^+ A 4^ (U - V cos Sgt)) 4 r00^r0  ^x  (5.1)  where xis the distance from the centre towards a smaller rod, y is the distance from the centre towards a larger rod, U and V are the amplitudes of dc and if voltages applied from pole to ground, A o , A2 and A 4 are the dimensionless amplitudes of a constant potential, the quadrupole potential and the octopole potential respectively. For these rod  76  sets A 2 r-t1 1.00 and A o —A 4 . Use of round rods adds other multipoles to the potential (Table 2.2) [53, 56]. For the potential of equation (5.1) the effective potential can be calculated using equation (4.3) as [57] V  =  eff  qA22 V (x 2 + y 2^qA2 A4 V X 4 - y 4  ^4^r:^1  ro4  (5.3)  ±•••  where q is given by equation (1.6). The first term in equation (5.3) is the effective potential for a linear rf-only quadrupole, and the second term describes the modifications caused by the octopole field. Terms in xm yn have not been included in equation (5.3) since only the excitation of the x motion when y = 0 is considered and the y motion when x = 0 . In the direction of the x rods the effective potential increases more rapidly with distance from the center than that of a pure quadrupole potential, and in the  y  direction increases less rapidly than that of a pure quadrupole potential. Motion of a singly charged ion in the x direction in the effective potential of equation (5.3) is described by m  = eqA22 V2x 4eqA 2 A4 VX 3 dt 2^OX^41-02^ro4  d 2 X F _e  avo.  (5.4)  Equation (5.4) can be written  d 2 X^2^4eqA2 A4 VX 3 x= ^ ^C°0 dt 2^Mr°4  (5.5)  where 2 eqA 22 V2 coo = 4mr02  (5.6)  which can be written as 77  coo =  qA2C^  (5.7)  ^  Equation (5.7) is the secular frequency of the ion which can be calculated using equations (1.10) and (1.11). Equation (5.5) resembles the equation of motion for an anharmonic oscillator described by Landau and Lifshitz [84] d2X  2 + CO 0 X =  dt2^  —ax 2 — fix'  (5.8)  4eqA2A4V  where a =0 and 18 =^anharmonic The terms on the right of equation (5.8) 4 mr0  cause shifts in the resonant frequency from co o , given by [84] Ow =  3/3  5a2  8coo^12co (3)  b2^  (5.9)  where b is the amplitude of oscillation. Therefore the frequency shift caused by the octopole field is 0w =  3eqA 2 AA V b2  2 mr04 coo  (5.10)  Equation (5.10) can be rewritten substituting V from equation (5.6) Aco=  A^( b 2.\  3=.1 — 0)0 A^ 2 \, r 02  (5.11)  5.1.2 Mass Resolution and Frequency Resolution  Mass resolution and frequency resolution in the ion trap can be related by proceeding from the fundamental equation [85],  78  12-eV m= ^ coo ro2 — n  q. < 0.4^(5.12)  Differentiating equation (5.12) gives \^( rdV ^ do0 dm =^ woro2 n j,,, n^cpo2 ro2 cl v 3-1^  ^[NrieV^-,f2eV^..lieV )^An^ (  2  2^"4 4  co0 r0^ Q  (5.13)  coo , V  Equation (5.13) indicates that a small change in the amplitude of the drive rf or in the secular frequency or the drive frequency is linearly related to a small deviation in mass. Consequently, mass analysis by resonance ejection can be achieved by ramping the rf voltage level, by varying the frequency of the supplementary excitation, or by sweeping the drive rf frequency. Setting dV and dC2 to zero in equation (5.13), dividing by equation (5.12), and making the assumption that do ° ,.=:,' Aco o and dm r.::, Am yields  coo^m AN ° Am  (5.14)  This indicates that mass resolution is numerically equal to the frequency resolution for q u < 0.4. Substituting the expression coo = qu n ,— into equation (5.14) gives 2-V2 m = qu 0 Am 2JAcoo  (5.15)  Equation (5.15) shows the relation of mass resolution to the fundamental operating parameters and the frequency resolution. For a given Aco o , the mass resolution increases with q .  79  5.2 Experimental The single quadrupole instrument operated in trapping mode as described in chapter 2 was used to perform MSAE experiments with the quadrupole with a 2.0% added octopole field. Different modes of applied rf, excitation and applied dc are possible and are summarized in Table 5.1. In principle, any of the three rf modes can be combined with any of the excitation modes and with any of the methods of applying dc (36 combinations). Table 5.1 Modes of applied rf, excitation and dc.  rf  balanced unbalanced 20% on exit lens  Excitation Mode  none dipole (smaller or larger rods) dipole-dipole  dc between Rods  none + smaller rods  + larger rods  quadrupole  5.2.1 Mass Calibration The rf and dc levels of the voltages applied to the quadrupole rods with conventional analysis are set by and are linearly proportional to a mass command voltage between 0 and 10.0 V. To mass calibrate the spectra shown here, the quadrupole was first run 80  conventionally with rf/dc and calibrated so that the monoisotopic reserpine peak appeared at m/z 609.3. In this case the rf level corresponds to the tip of the stability diagram where q = 0.70600 [7]. Ions were then mass selectively ejected at various q values, and the voltage at which they were ejected was determined from the MCS ramp parameters. The apparent mass was calculated from apparent mass= (ejection voltage) * 609.3/ (voltage with conventional analysis). The apparent mass did not correspond exactly to that expected from the q value selected for ejection (see below). For the spectra of Figures 2-6, the masses were recalculated so that the monoisotopic peak appeared at the correct mass (e.g. 609.3 for reserpine).  5.3 Results and Discussion  5.3.1 Dipole Excitation with a Quadrupole with a 2.0% Added Octopole Field Initial experiments with trapped ions and a quadrupole with a 2.0% added octopole field were tried with ejection at the stability boundary near q = 0.908. As with experiments without trapping, only very low resolution was found. Therefore all subsequent experiments with trapped ions used auxiliary ac voltages to excite ions for axial ejection. Axial ejection experiments with dipole excitation between the larger or smaller rods were done with a quadrupole with a 2.0% added octopole field. When the quadrupole is used as either a mass filter or a linear trap in a triple quadrupole system [72], it is necessary to operate the rod set as both a conventional rf/dc mass analyzer and a linear  81  ion trap with axial ejection. Operation as a mass filter requires that the positive dc be applied to the smaller rods [56]. As mentioned in section 3.3.1 applying some of the trapping rf (balanced) to the exit lens can improve the resolution, with no loss of ion signals [79]. Thus in all experiments with trapped ions the drive rf was balanced (23% applied to the exit lens) and the positive dc was applied to the smaller rods. The polarity of the dc applied between the rods was reversed and it was found that this gave no improvements in resolution. With low scan speeds (10-15 Th/s), no resolving dc was added to the rods. Adding dc did not improve the resolution. With high scan speeds (>300 Th/s) adding the low and optimum levels of dc that are indicated below helped to improve the ejection efficiency and resolution.  5.3.1.1 Comparison of Ejection at Different q Values Initially, ejection with excitation frequencies corresponding to q values of 0.4, 0.5, 0.6, 0.7 and 0.8 was tested. Figures 5.1 and 5.2 show results of ejection at q = 0.40 and q = 0.80 respectively, with excitation between the larger rods (reverse scans) and smaller rods (forward scans) respectively. No resolving dc was added. Higher q values result in higher resolution. With dipole excitation applied to the larger rods and reverse scanning, excitation amplitudes of 0.03 - 0.1 vp_p at scan speeds of 10-15 Th/s gave the best peak shape and resolution. With dipole excitation applied to the smaller rods and forward scanning, an excitation amplitude of 0.30 Vp_p at scan speeds of 10-15 Th/s, was optimal.  82  (a)  Resolution = 1720  (b)^  Resolution = 3500  1.0 -  0  a) 0.5 a)  0.0  1.0 -  0.5 -  A  0.0 608^610  612  614  Mass (m/z)  Figure 5.1 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation between the larger (y) rods. a) reverse scan, ejection at q = 0.40 , 10 Th/s b) reverse scan, ejection at q = 0.80 , 10 Th/s.  83  (a)  Resolution =1679  (b)  Resolution = 2475  1.0 -  0.0  1.0 -  0.0 608^610^612^614 Mass (m/z)  Figure 5.2 Peak shapes and resolution with axial ejection and dipole excitation between the smaller (x) rods. a) forward scan, ejection at q = 0.40 , 10 Th/s b) forward scan, ejection at q = 0.80 , 15 This.  84  Three factors may contribute to the higher resolution at higher q values. First, ions have higher oscillation frequencies at higher q . According to equations (5.14) and (5.15) for a given Aco o , the frequency resolution coo / Acoo and hence mass resolution, m I Am increases with q . Second 10 , and hence the resonant frequency of an ion, is a nonlinear function of q and increases more rapidly with q at higher q values. This increases the rate of change of frequency with mass, (  df df dq q df = ) which may also increase dm dq dm m dq  —=  — —  — — —  mass resolution. Third, the strength of^increases with the square of q (equation (4.5)). Higher values of E zquad mean that higher stopping potentials can be used on the exit lens and these higher potentials give higher resolution. 5.3.1.2 Comparison of Forward and Reverse Scans  Figure 5.3 shows a comparison between forward and reverse scans with excitation between the larger rods (15 Th/s). No dc was added between the rods. Higher resolution is possible with reverse scans. Figure 5.4 compares forward and reverse scans with excitation between the smaller rods (15 Th/s). No dc between the rods was added. In this case forward scans give higher resolution. These results are as expected from the frequency shifts caused by the added octopole field [86]. The shift of oscillation frequency, A co , in a quadrupole with an added octopole is given by equation (5.11). When A 4 > 0, the x motion shifts to higher frequencies. The shift is proportional to A 4 and to the square of the amplitude of ion oscillation. For they motion there is a shift  to lower frequency of the same magnitude for the same amplitude of oscillation. With excitation between the smaller rods and forward scanning, as the rf amplitude increases,  85  the oscillation frequencies of the ions increase. As the ions come into resonance their frequencies are further increased by the octopole component. These frequency shifts drive the ions faster toward the frequency of the auxiliary ac, which in turn causes the ion oscillation amplitudes to grow more rapidly until ions are ejected from the trap. With excitation between the smaller rods and reverse scanning, as the rf amplitude decreases the oscillation frequencies of the ions decrease. As the ions come into resonance their frequencies are increased by octopole component. These frequency shifts causes the ions to move away from the frequency of the auxiliary ac, which in turn causes the oscillation amplitudes to grow more slowly, and this degrades mass resolution. For similar reasons, reverse scans give higher resolution with excitation between the larger rods. The apparent masses at which ions of in/z 609.3 are ejected are consistent with this explanation and are shown in Table 5.2. With forward scans, and excitation between the smaller rods, ions are ejected at an apparent mass of 685.56. With the ejection between the larger rods, the ions are ejected at 686.15, showing that ejection is delayed and the quadrupole must scan up to a somewhat higher rf voltage before the ions are ejected. With a reverse scan and excitation between the larger rods, ions are ejected 689.32. With excitation between the smaller rods, the ions are ejected at 688.53, showing again that ejection is delayed and the quadrupole must scan down to a lower rf voltage before the ions are ejected.  86  (a)  ^Resolution = 2490  1.0 -  0.0  (b)  ^  Resolution = 4230  1.0 -  0 a)  0.0 608  ^  610  ^  612  ^  614  Mass (m/z)  Figure 5.3 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation between the larger (y) rods. a) forward scan, ejection at q = 0.80 , 15 Th/s b) reverse scan, ejection at q = 0.80 , 15 Th/s.  87  Resolution = 3000  (a) 1.0 -  0.5 -  0.0  )  \  (b)  Resolution = 1400  1.0 -  0.5 -  0.0 608  ^  610  ^  612^614  Mass (m/z)  Figure 5.4 Peak shapes and resolution with axial ejection and dipole excitation between the smaller (x) rods. a) forward scan, ejection at q = 0.80 , 15 Th/s b) reverse scan, ejection at q = 0.80 , 15 Th/s.  88  Table 5.2 Apparent mass of reserpine with different scan directions with trapped ions excited between the smaller and larger rods at q 0.8 and a scan speed of 10 'Th/s.  Scan direction  rod pair with  Apparent mass  applied excitation  of m/z 609.28  forward  smaller  685.56  forward  larger  686.15  reverse  larger  689.32  reverse  smaller  688.53  5.3.1.3 Comparison of Different Scan Speeds The effects of higher scan speeds were investigated. Figure 5.5 shows spectra of reserpine ions with excitation between the larger rods and scan speeds of 1570 and 5000 This respectively (reverse scans). There was 10 V dc added between the rods. At higher scan speeds, with dipole excitation applied to the larger rods and reverse scanning, an excitation amplitude of 0.55 — 1.0  Vp-p  at scan speeds of 3000-5000 This gave the best  peak shape and resolution. Figure 5.6 shows spectra of reserpine ions with excitation between the smaller rods at scan speeds of 1500 This (with 7 V dc) and 5000 Th/s (with 10 V dc) respectively (forward scans). With dipole excitation applied to the smaller rods and forward scanning, an excitation amplitude of 10 Vp-p at scan speeds of 3000-5000 This was optimal. At scans speeds of ca.1500 This (Figures 5.5a and 5.6a) the resolution is about 1500. At 5000 This (Figures 5.5b and 5.6b) the peak widths and spacing are not constant, particularly with reverse scans, Figure 5.5b. The resolution in this case, was 89  calculated as described in section 4.3.1. Resolutions of ca. 1000 (Figure 5.5b) and 1600 (Figure 5.6b) are calculated.  (a)  Resolution = 1400  1.0  0.0  1.0  (b)  Resolution = 1000  0.5  0.0 620  ^  622  ^  624  ^  626  Mass (m/z) Figure 5.5 Peak shapes and resolution with axial ejection of trapped ions, and dipole excitation between the larger (y) rods. a) reverse scan, ejection at q = 0.80 , 1570 Th/s b) reverse scan, ejection at q = 0.80 , 5000 Th/s.  90  (a)  Resolution = 1580  (b)  Resolution = 1600  1.0  E"' 0  a) as 0.5  0.0  1.0  0.5  0.0 608  ^  610  ^  612  ^  614  Mass (m/z) Figure 5.6 Peak shapes and resolution with axial ejection and dipole excitation between the smaller (x) rods. a) forward scan, ejection at q = 0.80 , 1500 Th/s b) forward scan, ejection at q = 0.80 , 5000 Th/s.  91  5.3.2 Quadrupole Excitation with a Quadrupole with a 2.0% Added Octopole Field  Auxiliary quadrupole excitation was applied to the quadrupole rods with a 2.0% added octopole field to give parametric excitation at twice the fundamental frequency of ion oscillation. As with a conventional rod set (section 4.3.2) ions were trapped at  q = 0.7002 (excitation frequency 676.00 kHz). The optimal excitation amplitude for low scan speeds (10-15 Th/s) was 1.14 Vp-p and the highest possible excitation amplitude for higher scan speeds (3000-5000 Th/s) was 3.64 Vp-p. With forward scans at 15 Th/s, a resolution of about 1800 was obtained. With reverse scans at 15 Th/s a resolution of about 3100 was possible (Figure 5.7). In both cases no resolving dc was added to the rods. These resolutions are similar to those obtained with dipole excitation between the larger rods. Quadrupole excitation excites ion motion between both the smaller and larger rods. It appears as if the motion between the larger rods dominates the ejection process. Most experiments with quadrupole excitation investigated reverse scanning because this yields higher resolution. With reverse scans at 1200 Th/s and 7.0 V dc between the rods, a resolution of 2300 was obtained, and at 4200 Th/s, a resolution of 1200 was achieved (Figure 5.8). Overall, no advantage to using quadrupole excitation was found.  92  Resolution = 1800 1.0 -  0.0 Resolution = 3100  1.0 -  0.5 -  0.0  ,..",...,  608  ^  610  ^  612^614  Mass (m/z)  Figure 5.7 Peak shapes and resolution with axial ejection of trapped ions, and quadrupole excitation between the rods. a) forward scan, ejection at q = 0.7002 , 15 Th/s b) reverse scan, ejection at q = 0.7002 , 15 Th/s.  93  Resolution = 1200 1.0 -  0.5 -  0.0 620  622  624  626  Mass (m/z)  Figure 5.8 Peak shapes and resolution with axial ejection of trapped ions, and quadrupole excitation between the rods. a) reverse scan, ejection at q = 0.7002 , 1800 Tla/s b) reverse scan, ejection at q = 0.7002 , 4200 Th/s.  94  5.3.3 Dipole - Dipole Excitation with a Quadrupole with a 2.0% Added Octopole Field Experiments were tried with dipole excitation applied simultaneously between the smaller and larger rods with no resolving dc added to the rods, and with scan speeds of 10 Th/s. When the same excitation frequency and amplitude (413.14 kHz and 0.2 Vp-p) were applied to both rod pairs, with forward and reverse scanning the ions were ejected mainly at the apparent masses of tn/z= 686.15 and m/z=689.32 respectively. These are the apparent masses at which ions are ejected with excitation between the larger rods alone. Approximately 10% of the ejected ions appeared at the apparent masses corresponding to excitation between the smaller rods, m/z=685.56 and m/z=688.53 for forward and reverse scans respectively. The excitation frequency applied to the smaller rods was then increased to 413.9 kHz, so that ions were ejected at the apparent masses corresponding to excitation between the larger rods. With reverse scanning and a scan speed of 10 This, a resolution of 2000 was possible. This gave resolution lower than that with dipole excitation between the larger rods alone. With forward scanning the resolution decreased to 1200. Thus no improvements were obtained by applying dipole excitation simultaneously between both rod pairs and no additional experiments with faster scans were done. Figure 5.9 shows a comparison of scan speeds and resolutions achieved with each mode of excitation for a conventional quadrupole and a quadrupole with a 2.0% added octopole field. In general, increasing scan speed decreases resolution. The quadrupole with a 2.0% added octopole field shows somewhat lower resolution than a conventional  95  rod set at a given scan speed. In all cases resolutions of 1000 or more can be obtained a scan speeds up to 5000 This.  6000 Dipole Excitation Larger Rods Dipole Excitation Smaller Rods Quadrupole Excitation Smaller & Larger Rods Dipole Excitation Conventional Rods Quadrupole Excitation Conventional Rods  5000  4000 0  Z u) 3000  a) 2000  1000  0 0  ^  1000^2000^3000^4000  ^  5000  ^  6000  Scan speed (Th/s)  Figure 5.9 Resolution vs. scan speed with different excitation modes, with a conventional quadrupole and a quadrupole with a 2.0% added octopole field.  5.3.4 Optimum Operating Mode with a Quadrupole with a 2.0% Added Octopole field Mass selective axial ejection of trapped ions that have a broad range of mass to charge ratios requires ejection at a high q value with forward scans. In this case, dipole excitation between the smaller rods gives the highest resolution and is the preferred mode  96  of operation. Conversely, with reverse scans, a broad range of mass to charge ratios can be mass analyzed with ejection at low q . For reverse scans, excitation between the larger rods gives higher resolution and is preferred. However any gain in resolution from exciting between the larger rods is offset by ejecting at lower q . Forward scans with ejection at q = 0.80 were compared to reverse scans with ejection at q = 0.20 , with the +3 ions of renin substrate tetradecapeptide with a conventional quadrupole rod set and a rod set with a 2.0% added octopole field. In all cases 10 V dc was added between the rods. Figure 5.10a shows the resolution achieved with a conventional rod set with forward scanning and ejection at q = 0.80 , at 3000 This scan speed and a step size of 0.08 mass units. The resolution is just sufficient to separate the isotopic peaks. Figure 5.10b shows the peak shape and resolution with the quadrupole with a 2.0% added octopole field, dipole excitation between the smaller rods, ejection at q = 0.80 , a forward scan at 3000 Th/s, and step size of 0.08 mass units. Although the resolution is slightly lower than with a conventional rod set, the isotopic peaks are (just) resolved. With dipole excitation between the larger rods, reverse scanning and ejection at q = 0.20 at 3000 Th/s and a step size of 0.08 mass units, it was not possible to resolve the isotopic peaks, Figure 5.10c. Thus, of all the operating modes investigated here, dipole excitation between the smaller rods with ejection at high q is preferred when ions of a broad range of m/z are to be mass analyzed.  97  1.0-  0.0  1.0 -  b  0 a) co 0.5  a)  0.0  1.0 -  C  0.0 584  592  Figure 5.10 Axial ejection of +3 ions of renin substrate tetradecapeptide with dipole excitation applied to a) conventional rods with a forward scan and ejection at q = 0.80 , b) the smaller rods of a quadrupole with a 2.0% octopole field with a forward scan and ejection at q = 0.80 and c) the larger rods of a quadrupole with a 2.0% octopole field with a reverse scan and ejection at q = 0.20. The scan speed in all cases is 3000 Th/s.  98  5.3.5 Ejection Efficiencies  With trapped ions, the operating conditions can be chosen to give the highest resolution or to give the highest sensitivity at each scan speed. Lowering the exit barrier increases sensitivity but decreases resolution. The ejection efficiencies of the conventional rod set and the rod set with a 2.0% added octopole field were measured with the results shown in Table 5.2. Here the system was optimized for the highest resolution with dipole excitation to eject ions at q = 0.80 with forward scans. The ejection efficiency decreases as the scan speed increases. The two rod sets show similar efficiencies. The system was then optimized for the highest ejection efficiency while keeping R 112 •■••' 1000 at each scan speed, and the ejection efficiencies with the quadrupole with a 2.0% added octopole field were re-measured, with the results shown in Table 5.3. The ejection efficiencies here are higher, with the greatest increases at the higher scan speeds. Hager found efficiencies of 2-18% with ejection of ions from q2 of a triple quadrupole system with operating pressures of ca. 1x10 Torr to 2x10 -3 Torr. [72]. Higher pressures gave higher efficiencies. Because of the much higher operating pressures in those experiments, the results cannot be compared directly to the experiments here.  99  Table 5.3 Ejection efficiencies (%) with the system optimized for the highest resolution.  Scan speed This  Conventional quadrupole  Quadrupole with a 2.0% added octopole field  15  30  60  600  2.3  2.0  1500  2.0  1.8  3000  1.3  1.0  5000  0.5  0.4  Table 5.4 Ejection efficiencies with a quadrupole with a 2.0% added octopole field and the system optimized for the highest sensitivity at R 112 "-.,' 1000 .  Scan speed (This)  Ejection efficiency (%)  15  67  267  38  671  5.6  1706  3.7  2542  2.5  3917  2.4  100  5.4 Summary Mass selective axial ejection of ions with a quadrupole with a 2.0% added octopole field is possible. With low scan speeds of 10-15 Th/s, resolution of several thousand was achieved. At higher scan speeds, up to 5000 Th/s, at least unit resolution is possible. Comparison of different excitation modes shows that the optimum operating mode of MSAE with this quadrupole is forward scanning and ejection at q = 0.80 with dipole excitation applied to the smaller rods. Nevertheless for some applications where a large mass range need not be scanned, reverse scanning with dipole excitation applied to the larger rods and ejection at q = 0.80 can also be used to give high resolution.  101  Chapter 6 Mass Analysis Using an Island of Stability with a Quadrupole with a 2.0% Added Octopole Field 6.1 Introduction This chapter describes experimental investigations of mass analysis using an "island of stability" with a linear quadrupole with 2.0% added octopole field. The theory behind this method of mass analysis will be explained briefly. Experimental settings and methods specific to these experiments will be discussed. Results from these experiments are compared to previous simulation studies.  6.1.1 Theory and Background  Mass analysis with linear quadrupoles is also possible using islands of stability [76, 87]. These islands are formed by parametric excitation of ions, either with an auxiliary quadrupole rf field [76] or by amplitude modulation of the rf voltage [87]. In a pure quadrupole field the potential is described by equations (1.1) and (1.2). With quadrupole excitation, the time dependent potential applied to the electrodes, co(t), is given by (9(0 = U — V cos(Qt — 7) — V' cos(cot — y')^(6.1)  102  where V' is the amplitude of the quadrupole excitation voltage with angular frequency . With the initial phase angles y and 7' set to zero for simplicity, motion of an ion in  the potential of equations (1.1) and (6.1) is determined by d x  d  2  d2 y  d  2  + [a – 2q cos(2 – 2q' cos(2/4)].x = 0^(6.2)  [a – 2q cos(2) – 2q' cos(2c4)]y = 0  (6.3)  where the dimensionless parameters are defined as: 8zeU^4zeV q=^ a= ^ m r-% 2_2 " ro^" ro  (6.4) , 4zeV'^V ' v= -61^ q =^ mo2r02 =  C2  where v is the ratio of excitation angular frequency to drive if angular frequency and q' is the ratio of excitation voltage to rf voltage of the specific m / z multiplied by its q -  value. The angular frequencies of ion motion, ou , (with u =x or y) are given by equation (1.11). The excitation frequencies of ions with quadrupole excitation are described in 0^  section 1.3.3 through equation (1.14) ( we, = 1 + fu1—where K =1,2,3... an and K  1= 0,±,1 2,...). If v = — where Q and P are integers, ions are excited when their /3  values satisfy Q^+ flul P K  (6.5)  103  The stability diagram splits into islands, with multiple operating tips available for mass analysis [76, 87]. Figure 6.1 and Figure 6.2 (adapted from reference 77) show the stability boundaries and islands of stability calculated for a quadrupole with a 2.0% added octopole field when a>0 and a<0 respectively. Ions can be mass analyzed by adjusting the applied rf and dc voltages to place the ions at the tip of an island. A mass scan is performed by changing the rf and dc voltages with fixed ratio U / V to bring ions of different m / z to the tip of the stability island. At the same time, the excitation amplitude, V' , can be scanned to keep q' constant [76, 77, 87]. The excitation parameters v and q' are adjusted to give islands spaced such that a scan line passes through the tip of an island without intersecting other islands.  104  0.245  0.240 -  0.235 -  0.230  •  •V■ •  Boundary without excitation Island A Island B Island C Island D Boundary of an ideal quad  -  co ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■  0.225 -  0.220 -  0.215 -  0.210 ^ 0.64  ■ 0.66  ^  0.68  ^  0.70  0.76  q  Figure 6.1 Stability boundaries and islands of stability ( q' = 0.02 , v = 9 /10 ) for a quadrupole with 2.0% added octopole field with a > 0 .  105  • 0.25 -  •  •  0.24 -  •  Boundary for an ideal quad Boundary without excitation Island A Island B Island C Island D  cy 0.23 -  V  Or  ♦ ••  • 4  0.22 it  0.21 ^ 0.64  • • 0.66  •^ ^t • ^•^•  •^• •  ■ ■  v,11  •^• •  "  •  •  •• • •  0.68^0.70^0.72^0.74^0.76  q Figure 6.2 Stability boundaries and islands of stability ( q' = 0.02 , v = 9/10 ) for a quadrupole with 2.0% added octopole field with a < 0 .  Recently, extensive computer simulations of mass analysis using islands of stability have been described for linear quadrupoles with added octopole fields [77]. Stability boundaries, island positions, peak shapes and ion transmission for linear quadrupoles with octopole fields of up to 4% were calculated. With an added octopole field, conventional mass analysis is possible with the dc voltage applied to the rods so that the Mathieu parameter a > 0 ; with the dc polarity reversed so that a < 0 , conventional operation results in very low resolution [56]. However the computer simulations [77] suggest that when a < 0 , mass analysis comparable to that with a > 0 should be possible, provided an island of stability is used with operation at the correct tip. In this case there is 106  little practical analytical advantage in running with a < 0, because adequate performance can be obtained with a > 0 and without use of an island. However the observation that use of an island allows mass analysis when a<0 demonstrates that islands might generally be useful to overcome at least some field imperfections in quadrupole mass filters.  6.2 Experimental Experiments were performed using the single quadrupole instrument and the quadrupole rod set with 2.0% added octopole field described in section 2.1. Voltages applied to the various elements are shown in Table 6.1. With the positive de applied to the smaller (x) rods, a > 0 ; with the positive dc applied to the larger ( y ) rods, a < 0 .With this rod set, there is a dc axis potential A o U in addition to the rod offset [56], where Ao = —0.020 and U = ±149 V for a > 0 and a < 0 respectively. Thus the axis potential when a > 0 was +1.0 V and when a < 0, +4.0 V.  107  Table 6.1 Operating Voltages.  sprayer  +3700  curtain plate  +500  orifice  +50  QO rod offset  +2  interquad lens  -20  Q1 rod offset  +1, a <0; +4 a >0  .Exit lens 1  -100  Exit lens 2  -300  The quadrupole excitation circuit, Figure 6.3, was assembled in house and is similar to that of Collings and Douglas [75]. The major difference is that capacitors that block the dc of the quadrupole power supply from reaching Q1 were removed. For these experiments the resolving dc of the quadrupole supply must be applied to the rods. Removing the blocking capacitors increased the capacitive load on the quadrupole power supply. To tune and balance the quadrupole power supply, the operating frequency was lowered from 1.2 to 1.0 MHz and a 12.5 pF capacitor was added across the supply output. Variable capacitors  CI and C2 ( 10-100  pF) were used to minimize the feedback from the  main rf into the auxiliary excitation electronics. The auxiliary rf was produced by the SRS waveform generator described in section 2.1 and amplified by an rf power amplifier (model 240L, ENI, Rochester, New York).  108  Auxiliary rf  I QO Rod Offset  Figure 6.3 Quadrupole excitation circuit.  109  For these experiments, values of q' = 0.020 ( V' = 25 Vo_p pole to ground) and v = 9/10 were chosen because simulations show these values produce an island with a scan line that does not intersect other islands. Because only a very limited mass range was scanned in these experiments, V' was not scanned with mass. The island with the greatest value of lal (termed "island A") was used. Mass analysis at the two tips of this island with the greater and lesser values of la was investigated. Scans over extended mass ranges with different rf/dc ratios confirmed that scan lines through these tips do not intersect other islands. The ratio of rf/dc voltages applied to the rods was set through computer control by a software parameter RE1 with values between 1 and 255. The numerical value of RE1 has no direct relation to mass resolution. For a given rf voltage, the dc voltage, U , increases linearly with RE1. At m / z 609.28 and with the quadrupole used here, the dc voltage pole to ground increased from 148.8 V at RE1=170 (a = 0.2358) to 154.6 V at RE1=220 (a = 0.2450) to give ratios U/ V from about  0.1694 to 0.1760. The system was mass calibrated with a > 0 and without excitation so that the monoisotopic peak of protonated reserpine (exact mass 609.28) appeared at m / z 609.00. Spectra were then recorded with operation in the island with the dc applied to give a > 0 , and with and without the island and a < 0 . The apparent m / z of the monoisotopic peak shifts because the operating tips have q values that differ from the tip without excitation and a > 0 . Values of mass resolution are reported as resolution at half height (R1 , 2 = m/Amv2 ).  110  6.3 Results and Discussion  6.3.1 Positive a Figure 6.4 shows spectra of reserpine ions recorded with a > 0 with and without excitation. With no excitation, (conventional mass analysis, Figure 6.4a) the resolution is about R 112 = 1500. The resolution setting was RE1 = 170. With the excitation applied, a scan at the upper tip (greater al) of the stability island produces a similar spectrum (Figure 6.4b) with R112 Z. 1100. Here RE1 = 187, giving a greater slope to the scan line, demonstrating that the upper tip of this stability island is located above the tip of the stability diagram, as shown in simulations [77] and Figure 6.1. With this setting of RE1, and a conventional scan, no ions are detected because the scan line is outside the stability region. A scan at the lower tip of the stability island (lesser l al) can be produced by reducing RE1 to 163. In this case a broad peak is produced, Figure 6.4c, and the isotopic peaks are not resolved. Lowering the resolution setting causes signal losses but does not improve the resolution. Thus the tip with the greater lal is necessary for mass analysis, as seen in the computer simulations [77]. The transmission and resolution in Figure 6.4a and 6.4b are comparable. With a > 0 , there is little advantage in using the island of stability for mass analysis.  111  5.0e+5  (a) 4.0e+5 a) • 3.0e+5 -  > 2.0e+5  -  1.0e+5 -  0.0 2.5e+5  606  608  610  612  614  (b) 2.0e+5 11) 1.5e+5 0 • > 1 • Oe+5 co  co  5.0e+4  _J  0.0 606  608  610  3.0e+6  614  612  (c)  2.5e+6 ,Z) 2.0e+6  1.5e+6 c.) a) 1.0e+6 ). 5.0e+5 0.0 606^608^610^612^614 111/Z  Figure 6.4 Mass analysis with a > 0 and (a) with no excitation (b) with the stability island at the tip with the greater I al and (c) with the stability island at the tip with the lesser la .  112  Figures 6.5a to 6.5h show mass analysis of reserpine ions in different stability islands with a> 0 . The resolution setting was changed so the scan line crossed different islands. This experiment confirms the positions of the islands predicted by the simulations [77]. In Figure 6.5a the reserpine peak is at the lower tip of the stability island A since RE1=165 and as was shown in Figure 6.4c the lower tip (lesser lal ) of the stability island A is at RE1=163. In Figure 6.5b where RE1 is decreased to 150, the slope of the scan line is decreased, and a scan crosses island B. The peak around m z =595 starts to appear. Figure 6.5c with RE1=145, shows this more clearly. By lowering RE1 further to 115, Figure 6.5d, the scan line crosses islands B and C but not island A, producing the peaks in/ z =587 and 616. Figure 6.5e, with RE1=105, shows that with a further decrease of RE1, the scan line still crosses islands B and C. When RE1 is reduced to 90, Figure 6.5f, the scan line begins to cross island D, and a low intensity peak appears at m / z =601. Figures 6.5g and 6.5h with lower RE1 values show that with additional decreases of the slope of the scan line, the scan line passes through three stability islands, B,C and D with the peak of the stability island C giving the most intense peak which is saturating the detector.  113  1.5e+^  2.5e+  C  (e)  (a)  1  2.0e+5  1.0e+  B  RE1 = 105  RE1 = 165 1.5e+5  1.0e+5 5.0e+  5.0e+4  0.13e+5  0.08+5  A  (b)  C ti  (f)  2.0e+5 3.0e+5  RE1 = 150  RE1 = 90  1.5e+5 2.0e+5 1.08+5  UT  1.0e+5  0.5.0.04  B N  0.8e+5  C  L__7\___  11.0e+5  C  (g)  A  (c)  a)  1  3.0e+5  RE1 = 145 1.00+5  B  RE1 = 85  B 2.0e+5  5.0e+4 1.0e+5  10e+5  0.6e+5  (d) 1.5e+5  (h)  3.0e+5  RE1 = 115  RE1 = 75  2.5e+5  2.0e+5 1.0e+5  B  C 1.50+5  1.0e+5  5.0e+4  5.0e+4  0.0  \..7--/  0.0  500 520 540 560 580 600 620 640  Mass (m/z)  500  ^  520  ^  540^560^580^600^620^640  Mass (m/z)  Figure 6.5 Mass analysis of reserpine ion in different stability islands with a > 0 . Peaks are labeled with the name of the corresponding island used for mass analysis.  114  6.3.2 Negative a  Figure 6.6 shows spectra of reserpine ions with a < 0 recorded with and without excitation. With no excitation, Figure 6.6a, a broad peak (nominal R112 = 125) is produced and the isotopic peaks are not resolved. This is as expected and has been described previously [56]. For this scan RE1 = 220. An rf/dc ratio higher than that used for a > 0 is required because the stability boundaries shift out when a < 0 [56, 77]. With excitation, a scan at the tip with the greater la' results in a broad peak (nominal R 112 = 280) (Figure 6.6b). Here RE1 = 194 which shows that the tip with greater la is located under the tip of the stability diagram without excitation. With the excitation applied, and with scanning at the tip with the lesser' al , the resolution is dramatically improved to R 112 = 1170 (Figure 6.6c). The resolution in Figure 6.4c is comparable to that with  conventional mass analysis with a > 0 and no excitation applied; the transmission is about six times less. This lower transmission was not seen in the simulations. At this tip, RE1 = 169, indicating the required rf/dc ratio is less than with no excitation and a < 0 and that the island tip is under the tip for operation without excitation. Therefore as predicted by the simulations, and as shown in Figure 6.2, with a < 0 , the stability island is completely located under the tip of the stability diagram for a quadrupole with a 2.0% octopole field.  115  3.5e+5 ^ 3.0e+5 2 2.5e+5 ea L. .... 2.0e+5 0  g  c.) a)  > 1.5e+5 as L a- 1.0e+5 -  5.0e+4 0.0 7.0e+4  606  608  610  612  614  606  608  610  612  614  6.0e+4 4)  r at L  5.0e+4 -  t 4.0e+4 -  =  0 o a) 3.0e+4 '  > el  -  2.0e+4 1.0e+4 0.0 8.0e+4  (c) 6.0e+4  sc .._C 3 4.0e+4 0  a)  >  to  cc  E  2.0e+4 -  0.0 606^608^610^612^614 rrI/Z  Figure 6.6 Mass analysis with a < 0 (a) with no excitation (b) with the stability island at the tip with the greater a! and (c) with the stability island at the tip with the lesser la! .  116  6.3.3 Apparent Mass and Island Positions  The apparent m / z values of the peaks give approximately the q values of the operating tips. With a > 0 and without excitation, the stability diagram for a quadrupole with 2.0% added octopole field is very similar to that of a pure quadrupole field, and so the operating tip is at q = 0.7060 and a = 0.237 [7]. With other modes of operation, the q value of the operating tip can be calculated from q = [(apparent m / z )/609.0]0.7060^ (6.6) and corresponding a values can be calculated using the instrumental parameters and measured dc voltages (U) during experiments as following a=  8x1.602 x10 -19 xU ^(6.7) (609.28/ 6.023 x10 26 )x (2 x n x1.2 x10 6 ) 2 x (4.5 x10 -3 ) -  These experimentally determined a and q values are shown in Table 6.2 and compared to the operating a and q values calculated in the simulations in ref 11. In some cases a range of q values is reported for the simulations because a rounded or poorly defined tip is formed. It is seen that the observed a and q values agree well with the a and q values of the simulations. Thus these experiments confirm the simulations, and show that the best resolution and peak shape are obtained with operation at the tip of the stability island with the greater la with a > 0 and the tip with the lesser la with a < 0 .  117  cl  ,-, •o -1E1  E  • en  E c•  E  " C.)  -5 ,-,  s:1 )< a)  cn 0  0 •-• 'al  E  •cn  oE  c.  1-1 Ckl 1-'. , i-4 cP•-■ 0  s=1 a)  71-  ,:.,.)  00 en en N  .1-  •tt.  0 0 tr) N g g  6  0  N co  o  00 en en N  6 6  ,--1 0 tr) ■—• ":1- 71-  o 6  clN  6. co 8 0 r.... 6 N c;  "1" ,...., —  0  o  cc) tn en N  g d CI 6 ,--i qR 71N ■C  6  N CA en N  o vo  6  o 716 . o 8 N 6  N 00 --1 0 N N  6, o c8 1.-6  6 6  0 N  ,_, N — N 6  6  N  6  t:) Ch  0 VD  c,1 I) e6  oo  V")  CD ,--, VD VD  a.)  (1.) 4c1  oc; 6 CD VD  CI ;_,  r--:  Li') N ,--1 N cc) ■40 7itr) 00 tr) 00000 N N N N N  0  6  a cu^v) V:) til^`43 cs;  1-,  Z 1..,  153 4,.) 14  1.0 • 1.  r.  &) 2 a) .•,-Ci 14  ,■1 14  V ezt  co  *1  to  -1-  a)c4  cl)  $••i  Z  f:,, = 0 VD CI  a) "cl o  E  bA CI;  0 ••••I  sa. o  VV cd 03  *R 0 " *I -• c) o o A czt  I -• co  118  6.4 Summary With a quadrupole with a 2.0% added octopole field, and with the dc applied to the rods so that the Mathieu parameter a > 0 , mass analysis does not benefit greatly from the use of an island. However when a < 0 , the added octopole severely limits the resolution with conventional mass analysis. By using the stability island when a < 0 , the performance is greatly improved. In this case use of an island overcomes the deleterious effects of the added multipole field. With mass analysis, the transmission of this rod set is very low (ca. 10 -3 ) compared to a conventional rod set. The reason is uncertain. Similar rod sets have shown transmission comparable to conventional rod sets up to R 112 =2000 [56]. Unfortunately, rod sets with added octopoles with this higher performance are no longer available here. Nevertheless, the results here qualitatively confirm the predictions of computer simulations of the position of stability boundaries without excitation, and island tip positions. Most importantly these experiments show that use of an island of stability may allow improved resolution or peak shape under conditions where an added multipole field, in this case an octopole field, otherwise degrades performance.  119  Chapter 7 Summary and Future Work The increasing role of linear quadrupole ion traps and their advantages were discussed in chapter one of this thesis. Linear ion trap mass spectrometers were described in section 1.5. These instruments provide high resolution and scan speeds and have already been incorporated in several commercial instruments. It is well established that 3D traps benefit from stretched or other geometries that introduce field distortions, described by the addition of higher order multipoles to the potential [40]. Douglas and co-workers [53, 55] were first to explore the addition of 2-12% higher order multipole fields to linear quadrupole ion traps. They reported higher MS/MS efficiencies and new methods of mass analysis with linear quadrupole ion traps with added multipole fields [56, 57, 77, 78]. These rod sets have the potential to become improved ion traps. Nevertheless, much work remains to investigate the effects of these multipoles on the performance of linear quadrupole rod sets operated as traps and mass filters. The work presented in this thesis was part of this investigation. In this thesis different mass analysis methods for a quadrupole with a 2.0% added octopole field were described and experimental results were presented. Experiments using islands of stability confirm the results of previous computer simulations and demonstrate the possibility of mass analysis under conditions where the octopole term in the potential severely degrades conventional mass analysis. Comparison of MSAE with a conventional quadrupole rod set and a quadrupole with a 2.0% added octopole field with different modes of excitation shows similar resolutions and ejection efficiencies, with somewhat higher resolution obtained with a conventional quadrupole rod set. Mass selective axial ejection with quadrupoles with added octopole 120  fields is possible with a resolution of several thousand and scan speeds of at least 2000 Th/s. Thus quadrupoles with added octopole fields can be used as rf/dc mass filters, demonstrate higher efficiency in MS/MS experiments, and can eject ions axially in a mass selective manner with high resolution and scan speed. 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