3D SIMULATION OF QUADRUPOLE MASS FILTER …...both peaks exhibiting the small shoulder on the high...
Transcript of 3D SIMULATION OF QUADRUPOLE MASS FILTER …...both peaks exhibiting the small shoulder on the high...
TO DOWNLOAD A COPY OF THIS POSTER, VISIT WWW.WATERS.COM/POSTERS ©2013 Waters Corporation
OVERVIEW
We present numerical simulation of ions from a gas cell through an exit aperture and into a quadrupole mass filter
The method includes simulation of gas flow through the exit aperture and modelling of the quadrupole entrance fringe fields in 3D
We find generally good agreement between the simulated results and experimental data from a tandem quadrupole instrument
INTRODUCTION
The quadrupole mass filter (QMF) is widely used as a mass
analyser. Numerical simulation of quadrupole mass filter performance is demanding owing to a number of factors:
Highly accurate fields are required to correctly determine
stable ion trajectories through the filter.
Ion motion is strongly affected by the entrance fringe fields,
hence the fields must be solved in 3D.
Ion motion is strongly dependent on the initial conditions of
the ions on entry to the quadrupole.
Due to these difficulties prior quadrupole simulations were
often restricted to 2D fields, with approximations used for the 3D fringe fields and for the initial ion distributions. While such
2D calculations often show good general agreement with experimental results they are rarely quantitatively accurate.
Owing to recent advances in computing power and numerical
methods it is now feasible to fully simulate QMFs in 3D on typical desktop computers. In this poster we present the
simulation of ions from a stacked ring ion guide (SRIG)
through an aperture plate into a quadrupole mass filter. Figure 1 shows a schematic of the geometry used for the
simulation, corresponding to the collision cell and second analyser in a tandem quadrupole mass spectrometer.
3D SIMULATION OF QUADRUPOLE MASS FILTER PERFORMANCE WITH REALISTIC ION INPUT CONDITIONS
David Langridge
Waters Corporation, Manchester, UK
METHODS
Simulation
Ions are created in the SRIG gas cell and are driven towards the exit aperture by a low amplitude T-Wave. To speed up
repeated calculations the ions are recorded at a plane near the exit end of the SRIG gas cell, these ion initial conditions can
then be re-used for further calculations where we have the same ion mass/charge and SRIG gas cell settings. The SRIG
gas cell is typically at 2.6e-3 torr while the quadrupole analyser is at 1.9e-5 torr. Gas flow through the exit aperture
was modeled using the Direct Simulation Monte-Carlo (DSMC) method [1], hence in the region of the exit aperture we have
variation in the pressure, temperature and velocity of the
background gas. Figure 2 shows an example of the calculated pressure and axial gas velocity distributions. A hard sphere
collision model was used for the interaction of the ions with the background gas.
References
1. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, Oxford, 1994).
2. SIMION 3D v8.1, Scientific Instrument Services Ltd.
3. Gibson, J.R., Evans, K.G., Sarfaraz U.S., Maher S., Taylor, S.: A Method of Computing Accurate 3D Fields of a Quadrupole Mass Filter and Their Use for Prediction of Filter Behavior. J. Am. Soc. Mass. Spectrom. 23, 1593–1601 (2012)
RESULTS
Figure 4 plots the experimental and simulated resolution vs
transmission curves for singly charged ions of m/z 175, 556
and 732, with the ion energy set at 10eV (i.e. a 10V DC drop from the SRIG to the quadrupole). Transmission is given as a
percentage of the peak height vs the unresolved peak height, resolution is calculated as m/ m where m is the FWHM of
the peak.
The results are in relatively good agreement. For the m/z 175 ion the simulated results give 10-15% higher transmission at a
given resolution, while m/z 556 and 732 are in very good agreement except at the higher resolution settings where the
experimental results tend to drop in transmission. This is not unexpected as any mechanical or electrical imperfections in
the quadrupole field will limit the physical system as we narrow the transmission window at the apex of the stability
diagram. There is considerable scatter in the experimental
results since we cannot acquire resolved and unresolved data simultaneously, we have to compare consecutive acquisitions
leading to possible errors if the signal intensity varies.
Figure 5 plots the experimental and simulated peaks for the 10eV m/z 556 ion at two resolution settings (about 650 and
1400 m/ m). The peak height and resolution are consistent as
shown in the previous plot, however we can also see that the
peak shape is almost identical between the experimental data and the simulation. Given that there are no empirical
corrections applied to the simulated data (beyond correction for the mass position on the mass scale) this level of
agreement is very encouraging.
10eV is significantly higher than the usual operating ion energy of a tandem quadrupole, hence the resolution is quite poor and
the peak shapes have large tails. At 10eV we might expect
small variations in the actual experimental ion energy and any on-axis RF effects to be minimised relative to the high ion
energy, thus there is likely to be better agreement between experiment and simulation.
CONCLUSION
We demonstrate simulation of ion motion from a gas
cell into a quadrupole mass filter
Generally good agreement between experiment and
simulation, although further work is required to determine the source of discrepancies
Allows rapid prototyping of new analyser designs
Figure 3. Plot of the A6 and A10 multipole field components
for a hyperbolic quadrupole system at differing grid scaling, with and without surface enhancement.
Figure 1. Diagram showing the partitioning of the simulation regions. At a sufficient distance from the ends the SRIG gas cell and
the quadrupole rods can be treated in 2D, hence we only need 3D solutions for the transition regions into and out of the SRIG/quadrupole.
Figure 2. Heat map plots of Ln pressure (top) and axial gas
velocity (bottom). The 1mm radius exit plate orifice is located at 0mm axial distance. The region of the simulation with vary-
ing gas parameters is from –10mm (inside the SRIG) up to 20mm (the start of the main quadrupole rods).
SIMION 8.1 [2] with surface enhancement was used to solve
the Laplace equation to determine the fields throughout the system. Surface enhancement corrects for the errors
introduced by representing curved electrode surfaces with a rectilinear grid. Figure 3 plots the natural log of the A6 and
A10 multipole components for a 2D hyperbolic quadrupole geometry solved for differing grid scales with and without
surface enhancement. For a perfect quadratic field we expect these components to be zero. With surface enhancement at a
grid scale of 40 gu/r0 (i.e. the radius of the inscribed circle is 40 SIMION grid units) we see smaller components than the
scale 2560 gu/r0 system without surface enhancement. The memory requirements for a 3D system at such a fine grid scale
are prohibitive, hence surface enhancement is critical to obtain accurate quadrupole fields for 3D systems. Surface
enhancement and a scale of 40 gu/r0 was used for the results
in this poster, calculations at 80 gu/r0 show no significant change suggesting that 40 gu/r0 is a sufficiently fine scale.
Figure 1 shows a diagram of the geometry simulated, to
reduce memory usage we model the main body of the SRIG and quadrupole rods in 2D. Results from calculations that
include the 3D region comprising the end of the quadrupole, the post-filter and the detector show no significant deviation
from calculations that assume all ions reaching the end of the main quadrupole rods are detected. This is consistent with
results in the literature [3], therefore for the calculations presented in this poster we omitted the end region.
Experiment
The simulated geometry was chosen to match a Waters Xevo TQ tandem quadrupole instrument on which experimental
results were obtained for comparison. A standard set-up solution containing a range of masses was infused and single
isotopes were isolated with the first quadrupole. In order to compare the experimental and simulated results we compare
the transmission for an ion at a given resolution against the unresolved transmission of the same ion. The experimental
parameters were set to typical values for this instrument, and the same values were used for the simulations where present.
Figure 4. Transmission vs resolution at 10eV ion energy for
experimental and simulated peaks.
Figure 6. Transmission vs resolution at 0.5eV ion energy for
experimental and simulated peaks.
Figure 6 plots the experimental and simulated resolution vs
transmission curves with the ion energy set to 0.5eV, a typical experimental setting. In general the agreement is somewhat
worse than we see at 10eV. For all three ions we now see the experimental data showing higher transmission at a given
resolution, except at high resolution values where, as at 10eV, the experimental transmission drops rapidly.
Figure 7 shows the experimental and simulated peaks for the
0.5eV m/z 556 ion at two resolution settings (about 650 and 2100 m/ m). The lower resolution peak is from the part of the
curve where the simulated transmission is about 10% down on the experimental transmission. Apart from the reduced
transmission the peak shape looks in good agreement, with both peaks exhibiting the small shoulder on the high mass side
of the peak.
Figure 5. Peak plots for 10eV m/z 556 ions, comparing experi-
mental and simulated ions at two resolution settings.
Figure 7. Peak plots for 0.5eV m/z 556 ions, comparing ex-
perimental and simulated ions at two resolution settings.
The higher resolution peak is close to the point where the two
curves cross over, in this example the transmission is almost identical while the resolution of the simulated peak is slightly
lower (2100 vs 2200). In this case the peak shape agreement is slightly less good, although again the small high mass
shoulder is present. If the resolution of the experimental system is being constrained by imperfections in the quadrupole
field then we might expect that the peak shapes would show some differences.
The general agreement between simulated and experimental
data is encouraging, however the agreement is far from perfect. Further work is required to determine the source of
the discrepancies. Considerable variation is observed between differing experimental quadrupole instruments, hence
repeating the experimental work on other instruments would
give an estimate of the experimental variability. Comparison of differing instrument settings (e.g. pressure, RF frequency) or
instrument geometries would also be of great benefit.