c

1
Dipolar Resonant Excitation Resolution
Enhancement for Linear Quadrupole Simulations
213
Sheldon M. Williams1 K.W. Michael Siu1 Frank A.
Londry2 Vladimir I. Baranov2
1Dept. Of Chemistry and Centre for Research in
Mass Spectrometry, York University, 4700 Keele
Street, Toronto, Canada, M3J1P3
2MDS Sciex, 71 Four Valley Drive, Concord,
Canada, L4K4V8
Methods of Increasing Resolution of Resonant
Ejection
Introduction
Effects of Prime Periodic Functions for Prime ?
Values on Resolution of Resonant Ejection
Phase Lock Angle and Resolution
Methods

• 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 N2
• Auxiliary dipole AC resonant excitation
  originating from round rods

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. 12.0 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

• 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

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.
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 180o lt ? lt 225o, than if random
phase or an arbitrary phase-lock of ? 0 (for
example) is used.

• A new approach to improve the resolution of an
  ions 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
  ? 0.292566, 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).

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.
b
a
a
b
Mechanics of Ions in Quadrupole Electric Fields
Effects of Collision Gas and Non-hyperbolic Rods
on Ion Trajectories
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.
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).
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.
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.
d
c
Results and Discussion
Experimental Results in Support of Simulations
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.
Ion of 609 Th ? 1/3
Ion of 609 Th ? 0.292566
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.
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
a
b
At ? 1/3 ? (23)/ (816,000 kHz) 7.35 ?s

• Figure 4. Frequency bandwidth versus ?x for
  quadrupole cell with round rods at zero pressure
  at
• ?x 0.250 ? 0.010 and Vac 0.09 volts,
• b) ?x 0.500 ? 0.013 and Vac 0.13 volts, and
• c) ?x 0.666 ? 0.022 and Vac 0.13 volts.

a
b
c
???(max) 16.0
???(max) 19.1
???(max) 14.3
a
b
Figure 1. Ion trajectories for prime and
ordinary ? values a) ? 1/3 and b) ? 0.29256.

• 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 ionsbut 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

Figure 2. Effect of Gas Pressure on Resolution
and Efficiency of Resonant Ejection. Frequency
response profiles for ? 0.5027, 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.
References
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 lt ? lt 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 ions trajectory will increase
until the ion strikes a rod. A non-zero pressure
and field imperfections can oppose the ions
increasing amplitude.
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, 1130-1147. 3.
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,
622-634. 4. Stott, W.R. Collings, B. Londry,
F. Hager, J. Axial Ejection Resolution in
Multipole Mass Spectrometers, US20030222210A1,
2003. 5. 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, 87-103.
? 2?o / ?
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.
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.
Adding Collision Gas to the Simulation
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.
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.
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.
Table 2. Reductions in bandwidth (Hz) for prime
vs. ordinary ? values with varying pressure of
nitrogen gas for linear quadrupole cell with
round rods.
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.
Acknowledgements
We thank the Natural Sciences and Engineering
Research Council (NSERC) of Canada, MDS SCIEX and
York University for financial support.