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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