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c d a b =1/ Normalized Radial Position t/mt/m b The RF drive voltage induces an ion to move in a cyclic trajectory in the x-y plane around the z-axis (Figure 1). The entire pattern traced by the ion in the x-y plane is highly dependent on the properties of the ion and the electric field produced by the quadrupole, and may be fairly simple or complex, requiring only one revolution around the z-axis to complete the period of its trajectory (Figure 1a) or requiring many revolutions (Figure 1b). Dipolar Resonant Excitation Resolution Enhancement for Linear Quadrupole Simulations A common-place obstacle in using tandem MS to identify an analyte is that the analyte ion may be in low abundance relative to another ion present at much larger quantities and with a similar m/z value. Masking of doping in athletic events Biomarker and tryptic digest peptide identification Goals Select or eject ions with greater m/z resolution Methods for selecting or ejecting ions with greater m/z resolution are needed so that an analyte can be identified more confidently in the presence of isobaric and/or greatly excessive components of a sample Simulations show the usefulness of a novel application of quadrupole field theory [1] with Resonance at values expressed as n/m, where n and m are small integers (‘prime’ values) Linear quadrupoles with round rods Pressures below 1 mTorr of N 2 Auxiliary dipole AC resonant excitation originating from round rods Introduction Mechanics of Ions in Quadrupole Electric Fields Reduce AC voltage Eventually increases ejection time Large increase in value (or RF drive frequency) = 1/4 2/3 produces 50% reduction in bandwidth Limits mass range and ion stability Stott, Collings, Londry, and Hager: Vary DC potentials on rods and exit lens with m/z in LIT [4] Effects of Prime Periodic Functions for Prime Values on Resolution of Resonant Ejection Methods Adding Collision Gas to the Simulation Pressure N 2 V ac (V) = vs = vs mtorr mtorr mtorr mtorr Table 2. Reductions in bandwidth (Hz) for prime vs. ordinary values with varying pressure of nitrogen gas for linear quadrupole cell with round rods. Figure 5. Changes in FRP resolution with varying phase angles in degrees: 0 (black square), 45 (white circle), 90 (red up-triangle), 135 (blue down-triangle), 180 (scarlet diamond), 225 (tan square), 270 (navy circle), and 315 (green up- triangle) a) at zero pressure with initial AC phase, , independent of RF drive phase and b) at zero pressure and initial AC phase, *, locked relative to RF drive phase, or c) the same as A, but at 0.8 mTorr nitrogen gas and d) the same as B, but at 0.8 mTorr nitrogen gas. A new approach to improve the resolution of an ion’s frequency response profile For values that can be expressed as two integers n over m, the ions trajectory is exactly periodic, with a period equal to = 4 m/ where is the RF drive frequency. The smaller the integers, the shorter the period for completing a trajectory. The graphs in Figure 1 compare ion trajectories with small n and m versus ones with large n and m. For = 1/3, the ion trajectory is completed in 7.35 s, while for = , the period of the ion trajectory is 1.23 s with = 816 kHz. Rational values where n and m are integers from 1 to 7 will be referred to as ‘prime values’. Other values are referred to as ‘ordinary values’. Ions with rational values have exact period trajectories, which means that the RF drive frequency of the quadrupole is an exact integer multiple of the fundamental secular frequency of the ion: = m o (m = 1, 2, 3…). An improvement in resolution occurs when the ion can complete more exact trajectories in a shorter time while in resonance with the AC voltage frequency, and therefore have improved relative magnitude and resolution compared to the frequency background. A theoretical calculation of the FRPs show in Figure 3a (normalized axes) that it will take several periods of the exact trajectory, N, to achieve a sharp resonance and, therefore, a shorter exact trajectory period should allow faster ion ejection. Figure 3b describes the results of related calculations for the increasing radial amplitude of an ion with time when experiencing resonant excitation at the prime value of 1/3 and two similar ordinary values. = 2 AC / N =1 N =3 N =2 Normalized Radial Velocity a Figure 3. a) Normalized intensity for radial velocity of ion versus the frequency interval = 0 to 1. Plot describes the frequency response profile for resonant excitation at = 0.5 for number of exact ion trajectories completed, N; b) Ion radial position intensity versus t / m. Table 2 shows the reductions in bandwidth of FRPs for prime prime values at various pressures. Significant improvements in resolution can be obtained at pressures less than 0.1 mTorr, at which point collisions occur on about the same time scale as the prime trajectory period. Further studies in correlation between phase-locking, rod shape, and rod position with the position and magnitude of stability holes and peaks in the bandwidth versus relationship may produce insights which will allow for the theory presented here to be extended to the higher pressures used in Paul traps and non-trapping linear quadrupole collision cells. The phase-locking of primary interest involves setting a fixed initial phase difference between the AC and drive RF. The initial AC phase shift ( *) is defined relative to a zero phase for RF. Sx32 v simulation package [2], being developed at MDS Sciex, allows for Linear quadrupole with collision gas of any mass and polarizability Ion-ion interactions to incorporate space charge Incorporation of drive RF, auxiliary quadrupolar or dipolar RF, and higher order fields Segmenting of space or time regions for lifetime of ion Fringing fields, exterior lenses, segmented quadrupole Identify physical properties of ions at several time or space intervals Ion molecule reaction kinetics Different geometries: round or hyperbolic rods, finite or infinite rod length Very extensive output of ion trajectory properties which can be further processed easily with Excel based graphical user interface Quadrupole Model for Simulation: Model for simulation is a quadrupole with circular rods of infinite length, to allow us to ignore the effects of fringing fields. The RF drive voltages are applied between opposing rods. An auxiliary RF voltage is applied across one pair of rods to produce dipolar resonant excitation and ejection of ions. Results and Discussion Figure 1. Ion trajectories for prime and ordinary values: a) = 1/3 and b) = At = 1/3: =(2*3)/ (816,000 kHz) = 7.35 s Ion of 609 Th = 1/3 Ion of 609 Th = a b Sheldon M. Williams 1 ; K.W. Michael Siu 1 ; Frank A. Londry 2 ; Vladimir I. Baranov 2 1 Dept. Of Chemistry and Centre for Research in Mass Spectrometry, York University, 4700 Keele Street, Toronto, Canada, M3J1P3 2 MDS Sciex, 71 Four Valley Drive, Concord, Canada, L4K4V8 213 Figures 5 and 6 demonstrates the increasing influence of phase-locking on FRP resolution and peak shape with increasing pressure for = 1/2. As shown in Figures 5a, 5b, and 6c, phase-locking has little effect on either resolution or shape of the FRP at zero pressure. However, for the FRP at higher pressures, such as the case for 0.8 mTorr of nitrogen gas in the quadrupole cell presented in Figures 5c, 5d, and 6b, the phase-locking between AC and RF significantly effects both the profile resolution and shape. Ultimately, one is able to achieve a much greater resolution via the correct phase-locking angle, in this case 180 o < * < 225 o, than if random phase or an arbitrary phase-lock of * = 0 (for example) is used. Phase Lock Angle and Resolution Methods of Increasing Resolution of Resonant Ejection We determined the half-depth bandwidth of the frequency response profiles for an ion of m/z = 609 Th in zero pressure at surrounding several prime values: 1/4, 1/2, and 2/3 (Figure 4a-c). In each case we see a significant decrease in bandwidth centered at or very close to the prime value (known as “stability holes”) showing an improvement in resonant frequency resolution of about 14 to 20% compared to the baseline. In some cases, the presence of the higher order fields due to the round rods creates stability peaks that significantly decrease the resolution. These significant increases and reductions in bandwidth provide valuable knowledge for optimizing resonance resolution. These simulations were carried out at AC voltages around 0.1 V. (max) = 16.0% a (max) = 19.1% b (max) = 14.3% c Figure 4. Frequency bandwidth versus x for quadrupole cell with round rods at zero pressure at a) x = and V ac = 0.09 volts, b) x = and V ac =0.13 volts, and c) x = and V ac =0.13 volts. We also conducted simulations of a more limited extent at higher AC voltages. In Table 1, we can see that significant reductions in bandwidth occur at higher AC voltages as well. The percentages in bandwidth reduction are smaller than at lower AC voltages, though. V AC values = vs = vs = vs V -16 Hz -25 Hz-24 Hz 0.4V -13 Hz -11 Hz-44 Hz 0.3V -6.3 Hz -11 Hz-36 Hz Table 1. Reductions in bandwidth (Hz) for prime vs. ordinary values with varying AC voltage, measured at half depth of frequency response profile minimum for linear quadrupole cell with round rods and zero pressure. Experimental results by Londry et al. [5] with ions in 3D quadrupole trap show that adjusting the phase lock of the drive RF with respect to the secular frequency of an ion could improve the frequency resolution of that ion when z was a prime value versus an ordinary z value. Improvement in resolution (decrease in signal width) was up to 20% Experimental Results in Support of Simulations b Figure 6. Variation in frequency response bandwidth at = ½ for variation in phase angle independent (square) and phase-locked (circle) relative to drive RF voltage phase at A) zero pressure and B) 0.8 mTorr nitrogen gas in quadrupole cell. DRF = drive RF voltage. a Conclusions Lower resonant excitation AC voltages can significantly improve resonant ejection resolution without significant loss of ejection efficiency Excessive gas pressure and round rods reduce average radial energy of resonant ions resulting in reduced ejection efficiency or radial energy insufficient for ejection May require higher AC voltage which can still benefit from prime values Prime values of provide at least 15% to 20% improvement in frequency resolution of resonant excitation ejection of ions…but excitation voltages must be carefully tuned and collision gas pressures must be less than 0.1 mTorr Frequency interference can occur during resonant excitation possibly due to the presence of higher order fields (hexapole, decapole, etc.); carefully choosing values for resonance can minimize loss of resolution due to interference frequencies Phase-locking both AC and Drive RF voltages relative to each other can significantly affect frequency band resolution at elevated pressures Optimum phase-lock changes 135 between 0.0 and 0.8 mTorr Acknowledgements References 1. Williams, S.M.; Siu, K.W.M.; Londry, F.A.; Baranov, V.I. “Dipolar Resonant Excitation Enhancement Characteristics for Quadrupole Collision Cell Simulation,” in preparation. 2. Londry, F.A.; Hager, J.W. “Mass Selective Axial Ejection from a Linear Quadrupole Ion Trap.” J. Am. Soc. Mass Spectrom., 2003, 14, Collings, B.A.; Stott, W.R.; Londry, F.A. “Resonant Excitation in a Low- Pressure Linear Ion Trap,” J. Am. Soc. Mass Spectrom., 2003, 14, Stott, W.R.; Collings, B.; Londry, F.; Hager, J. “Axial Ejection Resolution in Multipole Mass Spectrometers,” US A1, Londry, F.A.; March, R.E. “Systematic Factors Affecting High Mass-Resolution and Accurate Mass Assignment in a Quadrupole Ion Trap,” Intl. J. Mass Spectrom. Ion Process., 1995, 144, We thank the Natural Sciences and Engineering Research Council (NSERC) of Canada, MDS SCIEX and York University for financial support. The parameter for an ion in an ideal linear quadrupole field is defined by the following equation: Where o is the fundamental secular frequency of the ion (the rate at which the ion completes revolutions around the z-axis) and is the main drive RF frequency of the quadrupole. For 0 < < 1, the ion will have a stable trajectory until an AC voltage is applied that is resonant with the fundamental secular frequency of the ion ( 0 = AC ). Ideally, the radial amplitude of the ion’s trajectory will increase until the ion strikes a rod. A non-zero pressure and field imperfections can oppose the ion’s increasing amplitude. The graphs in Figure 2 show what are known as a ‘frequency response profiles’ (FRPs) which show how the ejection time for an ion varies with the AC frequency as it passes in and out of resonance with 0. Since 0 is related to the mass-to-charge ratio of an ion (m/z), decreasing the bandwidth is synonymous with increasing the resolution. In general, the ejection time increases and the bandwidth of the profile decreases as the AC voltage is decreased. However, at some point the ejection time becomes too great to be practical for use in a quadrupole. Also, when imperfections in the quadrupolar field and collisions with neutral gas in the quadrupole cell become significant, bandwidth and ejection time both increase significantly as well. = 2 o / Figure 2. Effect of Gas Pressure on Resolution and Efficiency of Resonant Ejection. Frequency response profiles for = , linear quadrupole with round rods, and AC voltages of 0.8 (square), 0.7 (circle), 0.6 (up-triangle), 0.5 (down-triangle), 0.4 (diamond), and 0.3 (plus sign) volts. a) 0.2 mTorr nitrogen; b) 0.8 mTorr nitrogen. a b Effects of Collision Gas and Non-hyperbolic Rods on Ion Trajectories The collision rate of ions with gas molecules present [3] The majority of collisions of an ion with a neutral gas cause ions to lose energy and radial amplitude. Frequency response profiles obtained with Sx32 at 0.2 and 0.8 mTorr (Figure 2) show that the increased pressure greatly increases the ejection time for the 609 Th ion at AC voltages of 0.3, 0.4, and 0.5 V, and the AC voltage must be increased up to 0.8 V to re-attain ejection times less than 1 ms. Fields due to deviation from ideal hyperobolic rods [3] In an infinitely long quadrupole cell with perfectly positioned, perfectly hyperbolic shape, extending infinitely in all directions, a perfect quadrupolar field will exist within the rods. Imperfections in rod shape and extent will result in higher order electric fields within the rods, such as hexapolar, octopolar and higher-order fields. The strength of these fields increase with distance from the z-axis of the quadrupole cell and the odd order fields (such as hexapolar, decapolar, etc.) apply a force on the ion to move back to the z-axis center. In order to counter these effects, the AC amplitude must be increased to improve the rate of radial amplitude increase of the ion, resulting in poorer resolution and/or an ion must be able to complete several prime trajectory periods between collisions, which can accelerate the rate of radial amplitude increase of the ion without loss of resolution. To study these effects we have performed simulations of ions in a quadrupole collision cell with round rods and collision gas using the Sx32 simulation package being developed at MDS Sciex.

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