Theoretical Mobility Analysis of Ion Mobility
Spectrometry
Alyssa R. Landin, William F. Siems, Herbert H. Hill, and Larry A. Viehland.
Washington State University, Department of Chemistry, Pullman, WA 99164
landal01@luther.edu
Overview
Objective
Methods
Results
The purpose of this research was to refine mobility theories in IMS
through computer simulated experiments. These programs generated
mobility results over a much greater range of parameters than can be
achieved in a lab setting, allowing theories to be tested and confirmed
in a much simpler way.
IMS simulation programs were run and reduced mobility constants of
ions were found in the noble gases at a constant temperature with
varying electric field intensities and at negligible electric field at
varying temperatures. The masses of both the ion and drift gas were
then manipulated to explore the relationship between mass and
mobility.
Trends in mobility were found based on the identity of the ion and
drift gas and their respective masses. This project will be continued to
explore new theories of mobility and lead toward a clearer theory and
understanding of mobility in IMS.
Results
Mass Manipulations of 133Cs+ 40Ar
Mass Ratio Manipulations of 133Cs+ 40Ar
Reduced Mobility (cm2V-1cm-1)
Reduced Mobility (cm2V-1cm-1)
3.5
3
2.5
1/2 Mass
2
1x Mass
2x Mass
1.5
3x Mass
4x Mass
1
0.5
0.01
0.1
1
10
100
1000
10000
3.2
3
2.8
2.6
2.4
100:1 Cs+ Ar
2.2
10:1 Cs+ Ar
2
1:1 Cs+ Ar
1.8
1:10 Cs+ Ar
1.6
1:100 Cs+ Ar
1.4
1.2
0.01
0.1
1
10
10000
Figure 3. Reduced mobility vs. E/N was calculated at 300K for artificially assigned
ion/neutral mass ratios of 133Cs+ 40Ar with the same reduced mass. The same trend was
found for all ion/neutral combinations.
Figure 2. Reduced mobility vs. E/N was calculated at 300K for different combined ion
and neutral masses. The ratio between the ion mass and neutral was held constant and
all the curves coincide if multiplied by the square root of their changed mass factor. This
pattern was seen for all ion/neutral combinations.
Mobility vs. E/N at Various Temperatures
Alkali Metal Ions with 40Ar
35
7
6
7Li+
5
23Na+
39K+
4
85Rb+
133Cs+
3
223Fr+
2
1
Reduced Mobility (cm2V-1cm-1)
8
Reduced Mobility (cm2V-1cm-1)
1000
E/N (Towsends)
E/N (Towsends)
Figure 1. IMS Model
100
30
25
200K
300K
400K
20
500K
600K
15
10
1
10
100
1000
10000
0.01
0.1
1
10
100
E/N (Towsends)
Temperature (K)
Figure 4. Reduced mobility vs. temperature at a negligible electric field was calculated
for the alkali metals ions with each noble gas. A similar trend was exhibited in each gas.
Figure 5. Reduced mobility vs. E/N was calculated for 7Li+ 4He at various temperatures.
All other ion-neutral combinations calculated exhibited a similar trend
Theoretical Methods
All programs were run through the Silverfrost FTN95 compiler using various ions
and drift gases. Only single atom molecules were studied due to the complexity
of molecular collisions. The programs accurately approximated mobility values
based on calculated averages of ion-neutral interactions and energy exchange
during collisions, simulating a true IMS experiment. These programs were used
in the mobility calculations:
• Ccgen.exe- generates a list of points and weights for the Clenshaw-Curtis
quadratures of various orders that is used in calculating cross sections in
PC.exe.
• PC.exe- generates sets of transport cross sections at different energies from a
set of potential energy surfaces of the ion and neutral molecule.
• Vary.exe- generates reduced mobility, Ko, at a wide range of temperatures
and negligible electric field from the output given in PC.
• GC.exe- generates reduced mobility, Ko, at a wide range of E/N and a set
temperature from the output given in PC.
1000
Acknowledgements
Thanks to the Hill lab and Dr. William Siems for his support and guidance, and to Larry Viehland, who wrote the
programs and made available the potential energy surface lists being used in this project. This work was supported
by the National Science Foundation’s REU program under grant number NSF #0851502.