simulation of ion motion in a travelling wave …...investigate ion motion in a travelling wave...
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OVERVIEW
PURPOSE
Investigate ion motion in a travelling wave mobility separator.
METHODS
SIMION 8 with a hard-sphere collision model, and Waters
Synapt HDMS.
RESULTS
Simulated drift times in agreement with experimental data.
Relationship between drift time and mobility is consistent for a
given travelling wave pulse voltage.
INTRODUCTION
The theory of ion mobility separation in conventional DC drift
tubes is well understood; under low electric field conditions
drift time is linearly related to the mobility of an ion facilitating
direct measurement of mobility values which relate to the size/
shape of the ion through the collision cross-section. A recent
design of mobility separator uses an RF ion guide with a
travelling wave field to propel ions through the drift gas, in this
case the macroscopic linear relation between drift time and ion
mobility no longer holds. To gain more insight into the
separation process and the effect of operational parameters on
performance, computer simulations of ion motion in the
travelling wave device have been undertaken and compared
with experiment.
METHODS
Experimental data was acquired on a Waters Synapt HDMS
system (shown in figure 1), incorporating a travelling wave ion
mobility separator. This separator comprises a gas-filled
stacked ring ion guide (SRIG), with alternating phases of RF
applied to the rings to give radial confinement of ions. Ions
are propelled through the device by repeating patterns of DC
voltages (waves) applied to the ring electrodes. The yeast
enolase digest used in these experiments was continually
infused into an electrospray ionisation source at 5 µ l/min.
Simulations were performed using SIMION 8 and a hard-
sphere (HS) collision model developed in-house. The collision
model has been rigorously tested and reproduces the expected
results from mobility theory, e.g. thermalisation temperature,
diffusion rates, linear field drift times, etc.
Ensembles of ions are flown to generate sufficient ion statistics
to assemble a drift time peak. Cross-section values used for
the ions in the simulation were taken from the literature [1].
Simulation of Ion Motion in a Travelling Wave Mobility Separator using a Hard-Sphere Collision Model
David Langridge, Kevin Giles, John B Hoyes Waters Corporation, Manchester, United Kingdom
The mobility is related to the cross-section via:
where q is the ion charge, µ the reduced mass, N the gas
number density and Ω the collision cross-section of the ion.
The drift times here are plotted vs reduced mobility, related to
the mobility by:
HS ensemble calculations require a considerable amount of
computer time, especially at high pressure due to the large
number of collisions that occur. While some statistical
variation will inevitably be present in the calculated results
presented here, the trends observed over ranges of ions and
pulse voltages are quite clear.
RESULTS
Unless otherwise noted these results were obtained with 2.5
mbar He in the IMS cell, and a 300 m/s travelling wave.
Figure 2(a) shows the drift times predicted from mobility
theory, and the HS calculated drift times ,for a range of ions in
a 500 V/m linear field over 183mm. The drift times are
inversely proportional to the mobility and the agreement
between the theory and the HS simulation is excellent.
Figure 2(b) compares experimental and HS simulated mean
peak drift times in 2.5 mbar He at several travelling wave
pulse voltages. No correction was applied to the simulated
results beyond adding 0.45ms to account for the transit of ions
through the transfer region after the IMS cell. References
[1] S. J. Valentine, A. E. Counterman and D. E. Clemmer, J Am Soc Mass Spectrom. 10, 1188 (1999).
The agreement between the experimental and simulated drift
times is excellent, better than 5% across the range of ion
mobilities and pulse voltages. As noted, the form of the drift-
time vs mobility curve for the travelling wave case is not
simply proportional to 1/K, as it is for a linear field.
Figure 3 compares experimental and simulated drift times for
doubly charged ions, again the agreement is generally very
good. For a given mobility, compared to the singly charged
ions, the doubly charged ions have roughly twice the cross-
section and are significantly higher in mass.
The 2nd trace uses an analytic approximation for the effective
potential confinement from the RF. The 3rd trace is an
analytic effective potential again, but with the axial field
component set to zero (removing the axial corrugations). The
4th trace has normal RF but uses an analytic model for the
travelling wave pulse, with the pulse value held constant with
respect to radial position (instead of increasing with radial
position as in the physical device). In this case the pulse is
equivalent to an 8.25V pulse seen on the optic axis.
As is clear from the graph, there is no significant difference in
the behaviour of the drift times between these different
systems. The two analytic RF cases exhibit lower drift times,
but the form of the curve is not changed. The radially
constant pulse case is very close to the normal 8V system.
These results suggest that there is no significant distortion to
the drift time—mobility curve from the effects of the SRIG RF
confinement, or from the radially dependent nature of the
travelling wave pulse.
CONCLUSION
• Have demonstrated the validity of the HS method for
calculating drift times in a travelling wave separator.
• Peak widths are consistently underestimated by the
HS simulations, suggesting an ideal case of the
physical system.
• Results indicate that while not linearly related drift
time is a unique function of the mobility, and thus
with appropriate calibration cross-sections can be
obtained. For more details see poster WPB043.
Figure 4 overlays singly and doubly charged ion drift times,
focusing on the region in which the mobilities overlap. For a
given pulse voltage the two charge states are located on the
same mobility vs drift time curve (as would be the case in a
linear field drift tube) despite the significant difference in mass
and cross-section between ions with differing charge states but
comparable mobility.
Peak Widths
Figure 5 shows the standard deviation of Gaussian fits to the
experimental and HS drift time peaks for a range of ions. The
simulated peaks are consistently narrower than the
experimental peaks, by a factor of about 1.3. This is
consistent with the HS calculated system being an ideal case of
the physical device. There are several possible sources of the
difference in peak widths, including variation in the travelling
wave pulse, space charge effects, physical imperfections in the
device and gas flow or localised pressure differences.
Field conditions tests
Confinement of ions in the SRIG RF field and the radially
dependent nature of the travelling wave pulse represent
significant departures from conventional DC IMS systems.
Figure 6 plots the RF effective potential seen by an ion of m/z
100 for the SRIG geometry and typical voltages used in the
IMS cell. The axial corrugations in the effective potential
increase in magnitude with radial position, while the effective
potential itself scales with the inverse of m/z. Figure 7 shows
the DC potential from applying 10V to a single pair of the SRIG
electrodes, thus representing a typical travelling wave pulse.
Clearly this potential is at a minimum on the optic axis and
increases with radial position.
The fields experienced by ions are thus quite different from the
ideal linear field drift tube case, with axial corrugations and
fields dependent on m/z and radial position. HS simulations
allow the significance of these effects to be evaluated by
methods that are impossible with a physical system.
Figure 8 shows simulated drift times for singly charged ions
with differing RF and pulse voltage models, in 0.53 mbar N2.
The 1st trace is a normal 8V travelling wave pulse calculation.
K0 =P
760
273.15
TK
K =
√18π
16
qõkT
1
NΩ
1.5 mm
2.5 mm
10 V
Field2.2 V/mm (Max)
Axial Potential6.4 V (Max)
1.5 mm
2.5 mm
10 V
Field2.2 V/mm (Max)
Axial Potential6.4 V (Max)
Figure 7. DC potential in a SRIG system with 10V applied to a single pair of electrodes.
0 1 2 3 4 5 6 0
0.5
1
1.5
0
0.5
1
1.5
2
Effe
ctiv
e po
tent
ial (
V)
Axial position (mm)
Radial position (mm)
Figure 6. Effective potential due to the RF in a typical SRIG system for an ion of m/z 100.
Figure 2. (a) Mobility theory and HS calculated drift times over 183mm for a 500 V/m DC field. (b) Experimental and HS calculated drift times vs reduced mo-bilities for singly charged ions at several different travelling wave pulse voltage values.
0
5
10
15
1.5 2 2.5 3 3.5
Drif
t tim
e (m
s)
K0 (cm2/ Vs)
(b)EXP 9V
EXP 10VEXP 11VEXP 12V
HS 9VHS 10VHS 11VHS 12V
3
4
5(a) 500 V/m theory
500 V/m HS calc
Figure 1. Waters Synapt HDMS instrument geometry.
Figure 3. Experimental and HS calculated drift times vs reduced mobilities for doubly charged ions at several different travelling wave pulse voltage values.
2
4
6
8
10
2.75 3 3.25 3.5 3.75 4
Drif
t tim
e (m
s)
K0 (cm2/ Vs)
EXP 7VEXP 8VEXP 9V
EXP 10VHS 7VHS 8VHS 9V
HS 10V
2
4
6
8
2.5 2.75 3 3.25 3.5 3.75 4
Drif
t tim
e (m
s)
K0 (cm2/ Vs)
8V
9V
10V
EXP z=1EXP z=2
HS z=1HS z=2
Figure 4. HS calculated drift times vs reduced mobilities for sin-gly and doubly charged ions at several different travelling wave pulse voltage values.
Figure 5. Standard deviation (ms) vs reduced mobility for the Gaussian peak fits to experimental and simulated data. The in-set panel shows the Gaussian drift time peaks for the ion with K0 = 2.67, as indicated by the arrow.
0.1
0.2
0.3
0.4
0.5
2 2.5 3 3.5
Std
Dev
(m
s)
K0 (cm2/Vs)
EXP
0.1
0.2
0.3
0.4
0.5
2 2.5 3 3.5
Std
Dev
(m
s)
K0 (cm2/Vs)
EXPHS
4 4.5 5
Drift time (ms)
4 4.5 5
Drift time (ms)
Figure 8. HS calculated drift times vs reduced mobilities for sin-gly charged ions for differing field parameters.
2
3
4
5
0.7 0.8 0.9 1
Drif
t tim
e (m
s)
K0 (cm2/ Vs)
8V pulseAnalytic RFNo Axial RF
Constant Pulse