Numerical Simulation of Reacting Flows of Ions at
Atmospheric Pressure - the Reactant Ion Peak in IMS
1 Physical & Theore>cal Chemistry University of Wuppertal, Germany
Ins>tute for pure and applied mass spectrometry
Walter Wissdorf ; Valerie Derpmann ; Sonja Klee ;
1
1
2
Hendrik Kersten ; Thorsten Benter ; Wolfgang Vautz
1
In common atmospheric pressure ion sources, the total transforma>on of any set of reac>ve ions is almost inevitable due to the long residence Smes of ions in the ion source and the high concentraSons of possible reacSon partners.
Therefore, a comprehensive model of the dynamics of ions at AP condiSons has to include a chemical reacSon model in addiSon to a numerical descripSon of the pure ion transport effects. In efforts to achieve a step towards such a complete descripSon of the dynamics at AP, we have developed a reac>on simula>on (RS) extension for a previously exisSng ion transport model (SIMION / SDS). To validate and test this new model we performed simulaSons of the reactant ion peak (RIP), which is a common observaSon in Ion Mobility Spectrometry (IMS) and served as a demanding benchmark problem for the reacSon simulaSon. In this contribuSon we present a detailed discussion of the developed numerical model, the simulaSon results and a comparison of the numerical results with another chemical kineScs model and experimental data.
The ReacSon SimulaSon (RS) Module uses a Monte Carlo approach to simulate chemical reacSons. Instead of calculaSng an exact result with a determinisSc algorithm, Monte Carlo methods use random sampling to describe a system staSsScally. They o_en allow the numerical simulaSon of complex systems, which would be difficult with other methods.
Current Implementation
The actual implementaSon of RS is capable of simulaSng reacSons of ions with neutral reac=on partners (no ion-­‐ion reacSons at present)
i
Generate a uniform distributed random value r
If p < r the reacSon event is considered “successful”: • remove educts from simulaSon • add products to simulaSon
• move on to next reacSon
•
Custom developed chemical reacSon simulaSon (RS) extension for SIMION / SDS
Chemked reacSon kineScs solver (Version 3.3)
Experimental Methods
•
•
(3)
(4) (1)
(6) (3)
(4)
(5)
Ring Electrodes (connected via resistors)
Electrical g
gradient: 317 V/cm
•
RIP dri_ Sme is directly dependent on the water mixing raSo due to the mean cluster size which is water dependent (see Fig. 2) • If the ion mobility (K0) of the individual cluster species is esSmated from their mass [1], (ignoring ion geometry) the simulaSon diverges from the experimental data (“uncorr.” in Figure 5).
• A slight correcSon of the es>mated ion mobiliSes of disSnct cluster species gives a very good agreement between simulaSon and experiment (“corr.” in Figure 5)
Ion Mobilities:
12.1 cm dri_ distance, 317 V/m linear electrical gradient
Faraday Plate detector
Entrance shu[er grid: Bradbury Nielsen grid, opened for 300 µs every 100 ms
Atmospheric Pressure Chemical IonizaSon (APCI), primary electrons are generated by a TriSum β radiaSon source (500 MBq)
Nitrogen with 2000 ppmV water was provided by a calibraSon gas generator (HovaCAL 3834-­‐VOC, IAS, Frankfurt, Germany)
Lower water mixing raSos were generated from this gas by exponenSal diluSon in a flushed glass bo[le
Figure 5) Dependence of experimentally recorded
ion current on the deflection voltage
Cluster Size
K0 (uncorrected) K0 (corrected)
n=1
3.57
3.57
n=2
2.76
2.76
n=3
2.35
2.35
n=4
2.09
1.97 (-­‐5.5%)
n=5
1.90
1.88 (-­‐1.0%)
n=6
1.77
1.77
reduced ion mobilites (K0) are given in 10-­‐4 m2 V-­‐1 s-­‐1
•
The results from RS are in very good agreement to the results from a mathemaScally different numerical model (Chemked)
•
The simulated peak shape of the reactant ion peak (RIP) is in good agreement with actual experimental data
•
Considering the given uncertainSes in the simulaSon input parameters (ion mobiliSes, reacSon rates) the simulated RIP dri_ Smes are in very good agreement with the experimental results
•
The RIP simulaSon is numerically very demanding (fast reacSons, high water concentraSons). Therefore the RS extension appears to be suitable for modeling of most reacSon systems in terms of numerical costs •
If the thermochemical data are available, most of the usually encountered reac=on systems in API can be modeled with RS, for example: Figure(6)
1) Schematic of the simulated IMS geometry
RIP Peak
• Good agreement between Figure 4) Simulated and measured RIP of
the proton bound water clusters [H(H2O)n]+
experiment and simulaSon in terms of basic peak shape • The axial diffusion of ions, which leads to peak broadening, is underesSmated by the simulaSon with SIMION / SDS / RS. • Space charge effects, which were not considered in the calculaSon could lead to an increased axial diffusion Numerical Quality
Simulation Particle Number
•
100 Ions
•
Cluster
1000 Ions
•
The level of numerical noise decreases with increasing number of simulated par*cles
Even with only 100 simulated ions, the rough temporal concentra*on development is observable
1000 simulated par*cles allow to model the RIP driC *mes with sufficient accuracy: The numerical noise is well below the uncertain*es of the simula*on input parameters
Figure 6) Effects of simulation
particles number on RS simulations
Simulation Time Step Length
a) dt = 0.025 µs
•
•
•
b) dt = 0.003 µs
•
If the *me step becomes too long, the local reac*on probability p can become > 1
If the number of such “invalid” reac*on events gains significance, the simula*on result becomes invalid
A typical effect of this is the occurrence of severe oscilla*ons (see a) aCer 3µs)
Inappropriate *me step lengths lead also to wrong final concentra*on distribu*ons (note the difference in a) and b) in the stable region)
Figure 7) Effects of simulation time
step length (dt) on RS simulations
(600 ppmV water mixing ratio)
A new extension to SIMION / SDS for the simulaSon of chemical reacSons (RS) of ions at atmospheric pressure was developed and validated
The system of proton bound water clusters [H(H2O)n]+ at “moist” atmospheric pressure condiSons was successfully modeled with the RS extension (5) (2)
Chemked and SIMION / RS
• Very fast relaxa>on of the proton bound water cluster system: The equilibrium is reached a_er at last 3 µs.
• Short relaxaSon Smes correspond to very high reacSon rates
• Individual clusters undergo dissociaSon and associaSon reacSons with high frequencies
• The whole cluster system is detected as only one ion mobility signal in IMS (see Fig. 4 on the right)
RIP Drift Time vs. Water Concentration
Custom made IMS (ISAS, Dortmund, Germany)
The water mixing raSos were checked with a moisture monitor (Panametrics, Series 35, Hoheim a.T., Germany)
(2)
Conclusions
•
(1)
• Very good agreement between Figure 3) Simulated evolution of the water
cluster distribution (water mixing ratio 50 ppmV)
(CK = Chemked; RS = Reaction Simulation ext.)
Figure 2) Simulated equilibrated distribution of
proton bound water clusters [H(H2O)n]+
DriO Gas Dilu>on: •
+
·
+
+
·
charge to the analytes by chemical reac*ons. H2 O+ + H2 OThe → rHelaxa*on Hf 2tO
H2 O →
(4)His 3m
Ouch +fOH
3 O + OH
*me o
his e+quilibrium aster + +
+
+ water the me in N+
IMS [O
3], +therefore in (H
the whole One important RIP results from proton bHound H2 O + N2than → [H
(Hd3riC O)*
H
]
O
+
H
N
→
(5)
[H
O)
]
+ N2
3O +
3
2
2
2
3
2
2
cluster occurs as one dis=nct signal -­‐ t+he �
�+
� distribu*on clusters. + �+
H (H3 O)n−1 + H2 O + N2Reactant � [H
H (HIon ] +
N
+2 H2 O + N2 �
(6)[H (H3 O)n ] + N2
3 O)Pn
n−1
eak (RIP)
depends on the water mixing raSo in the background gas:
• Primary cluster at 10 ppmV water is n=4
• At 1000 ppmV the primary clusters are n=5 and 6
• The water dependent mean cluster size results in a water dependent mean ion mobility
• Virtually no small clusters (n= 1,2,3) even at very low water mixing raSos
Ion Source: •
Ion Mobility Spectrometry (IMS) separates ions by [H(H2O)n]+ from Chemical Ionization
their electrical mobility at elevated gas pressure:
Chemical ioniza*on ini*ally forms H3O+: −
−
−
• Ions are gated into an driC tube with an linear N2 + e− →NN2+
+
2e
(1)
+
e
→
N+
+
2e
(1)
2
2
electrical gradient
++ e− →
−
− N+
+
+ + 2e−
N
(1)
N
+
e
→
N
+
2e
(1)
2
N+
+
2N
N
(2)
(2)
2 N2 +
2
2 2
4 2N2 2→ N2
4 + N2
• Ions with low mobility have lower driC veloci*es +
+ 2N
+ → N+ +
++N
+ N2
N
+
(2)
N+
+
2N
→
+
N
(2)
2
N
+
H
O
H
O
+
2N
(3)
2 N42 +
2→
H
O
H
O
+
2N
(3)
4
2
2
2
2
4
2
2
2
4
and therefore longer driC *mes
+
++
+
− H· O+
−
+O →
+H
·
N
+
H
+
2N
(3)
N
+
e
→
N
+
2e
(1)
N
+
H
O
→
2N
(3)
2
2
2
H
O
O
+
OH
(4)
2
2
2
+
H
O
+
H
O
→
H
O
+
OH
4
−
−
2
3
+
2
4
−
−
2
2
3
• DriC *me directly corresponds to the ion mobility N2 + e →NN22++e2e→ N2 + 2e
(1) (4)
+
+++
· O+++ OH
+
+H O+ + H+H
+·
O
+
H
O
→
H
(4)
N
+
2N
→
N
+
N
O
→
H
O
+
OH
2
2
3
the O)
c
lusters w
ith w
ater: H3 O +2 H
Or3esul*ng + 2N
[H
(H
O)
N
(5)
2 + N2 (4)
+ H(2H
+]2 [H+
33
O
+
O
+
N
→
(H
O)
]
(5) (2)
+
+
2
4
2H
2
3
2
2
3
2
2
N2 + 2N2 →
N
+
N
(2)
N
+
2N
→
N
+
N
2
2 4 + 22
4+
RIP: Signal of Primary Ions
�
�+
+
+
+
�
�
+
+
+ 2N
+
H2[H
O
N
→
[H
(H
O)2 ]+
N
(5) (3)
N4+
+
H�
→
H
H3 H
O (H+
+3 O)
H22H
O
+
N
→
[H
(H
O)
]
N
(5)
3O
2
322O
22O
2
2 2 (6)
+
++
2 �
3
+
++
H
(H
O)
H
O
+
N
(H
O)
]
+
N
+
H
O
+
N
[H
(H
O)
]
+
N
(6)
3
2
3
2
2
3
2
N
+
H
O
→
H
O
+
2N
(3)
n−1
n
N
+
H
O
→
H
O
+
2N
n−1
n
In IMS with chemical ioniza*on (APCI) d�is*nct ion � �
2
22
2
4 2 2
�+ 4
+
+ +
·
+
+
H22Cluster
O+
H�
O] [H
→
H
O
+
H
O
N
(H
O)·n+
] +OH
+ N2 (6)
(6) (4)
2Equilibrium
3
++
Fast
Water
Ha(H
+3−O)
H2n−1
OH+
N+
[H
(H+
O)
N
·
2
32−
signals occur, which do not correspond to nalytes. 3 O)n−1H (H
2 �
3+
+
+
−
−
n
O
+
H
O
→
H
O
+
OH
(4)
H
O
+
H
O
→
H
O
+
OH
2 2
3 N2
2+e →
3 N + 2e
N2 + e → N22 + 2e
(1)
+ 2+
+
A d+
istribu=on o
f p
roton b
ound w
ater c
lusters [
H(H
O)
]
3
n
They are called Reactant Ion Peaks (RIP).
H
O
+
H
O
+
N
→
[H
(H
O)
]
+
N
(5)
+
3
2
2+
3
+ 2
+
2+
+
+
H
O
+
H
O
+
N
→
[H
(H
O)
]
+
N
(5)
+
N
→
(H
] 2 + N2
3→
2 H2 O
3 issocia*on 22N
N2 + �2N2is N+
N4 +2�bH
N
→
(2)
N432eO)
+2N
2 2 [H
formed y 32aOn forma*on d
quilibrium: 2 / +
+
+
Those signals result from primary ions, generated � i+n � 3�O)
+ n−1+ +�+
H (H
H2 O + N+2 � [H (H
N2
(6)
+ 3 O)n ] ++ +
H
(H
O)
+
H
O
+
N
�
[H
(H
O)
]
+
N
(6)
H
(H
O)
+
H
O
+
N
�
[H
(H
O)
]
+
N
N
N
+
H
O
→
H
O
+
2N
+
H
O
→
(3)
H
O
+
2N
3 2n−1
2 4 3 2 2n
32 n
2
22
2
2 2
the chemical ioniza*on process which transfer the 4 3 2n−1
• The water cluster distribuSon Ion Mobility Spectrometer:
•
•
•
•
•
Proton Bound Water Clusters
4,5
Cluster Concentration Time Series
Cluster Species Distribution
Ion Trajectory Simula>on: •
Model Geometry
Results
Numerical Methods
Reac>on Simula>on:
(ci ) · k · dt
k = reac*on rate constant, ci = concentra*on of i-­‐th reac*on partner
dt= *me step length
•
•
Methods
SIMION charged parScle simulator (v8.01) with StaSsScal Diffusion SimulaSon (SDS) Extension
Ion Mobility Spectrometry (IMS)
The reacSon simulaSon module performs the following operaSons in every Sme step of the trajectory calculaSon of SIMION / SDS: • For every ion, calculate the local reacSon probability p: p=
WissenschaOen -­‐ ISAS -­‐ e.V.
Reactant Ion Peak (RIP)
Basic Simulation Loop
�
2 Leibniz-­‐Ins>tut für Analy>sche 0V
At atmospheric pressure (AP), ions experience a very high collision rate with bulk gas parScles. In addiSon to the electrical force, the moSon of ions under AP condiSons is governed by viscous drag / viscous transport and molecular diffusion. In the past years, the successful simulaSon of ion transport phenomena at AP condiSons became possible through the development of powerful numerical models like the sta>s>cal diffusion simula>on (SDS) extension for the commercial ion opScs simulaSon so_ware package SIMION [1][2].
In addiSon to pure transport, reacSve ions can undergo complex chemical transforma>ons at AP due to the high collision rate. Due to the resulSng high number of possible reacSve collisions, even reacSons with relaSvely small rate constants may proceed efficiently.
Monte Carlo Reaction Simulation (RS)
1
3830 V
Introduction
1
‣
Clustering of analyte ions in Ion Mobility Analyzers
‣
Cluster Systems relevant in Atmospheric Pressure IonizaSon (See also Session MP29, Poster 672 and our Talk in Session MOG)
‣
Declustering processes in ion funnels and similar ion opScal devices
Literature
1) Appelhans, A D.; Dahl, D A. SIMION ion op+cs simula+ons at atmospheric pressure. 2)
3)
4)
5)
Int. J. Mass Spectrom. 2005, 244, 1-­‐14. Wissdorf, W.; Pohler, L.; Klee, S.; Müller, D.; Benter, T. Simula+on of Ion Mo+on at Atmospheric Pressure: Par+cle Tracing Versus Electrokine+c Flow. J. Am. Soc. Mass Spectrom. 2012, 23(2), 397-­‐406.
Lau, Y. K.; Ikuta, S.; Kebarle, P. Thermodynamics and kine+cs of the gas-­‐phase reac+ons H3O+(H2O)n-­‐1 + water = H3O+(H2O)n. Journal of the American Chemical Society, 1982, 104(6), 1462-­‐1469
Carroll, D. I.; Dzidic, I.; SSllwell, R. N.; Horning, E. C. Iden+fica+on of posi+ve reactant ions observed for nitrogen carrier gas in plasma chromatograph mobility studies. AnalyScal Chemistry, 1975, 47(12), 1956-­‐1959
Kim, S. H.; Be[y, K. R.; Karasek, F. W Mobility behavior and composi+on of hydrated posi+ve reactant ions in plasma chromatography with nitrogen carrier gas. AnalyScal Chemistry, 1978, 50(14), 2006-­‐2012.
Acknowledgement
Financial support is gratefully acknowledged:
•DFG (BE2124/6-1)
•Bundesministerium für Bildung und Forschung
•Ministerium für Innovation, Wissenschaft und Forschung des
Landes Nordrhein-Westfalen