Following the Ions through a Mass Spectrometer with Atmospheric

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Following the Ions Through a Mass Spectrometer with Atmospheric Pressure Interface – Simulation of Complete Ion Trajectories from Ion Source to Mass Analyzer Xiaoyu Zhou, and Zheng Ouyang Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b00461 • Publication Date (Web): 24 Jun 2016 Downloaded from http://pubs.acs.org on June 24, 2016

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Analytical Chemistry

Following the Ions Through a Mass Spectrometer with Atmospheric Pressure Interface – Simulation of Complete Ion Trajectories from Ion Source to Mass Analyzer Xiaoyu Zhou1,2 and Zheng Ouyang1,2,3,4* 1

State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments, Tsinghua University, Beijing 100084, China 2

Weldon School of Biomedical Engineering, 3Department of Electrical and Computer

Engineering, and 4Department of Chemistry, Purdue University, West Lafayette, IN 47907, USA Revised for Analytical Chemistry

*Corresponding Author: Prof. Zheng Ouyang Weldon School of Biomedical Engineering Purdue University 206 S. Martin Jischke Drive West Lafayette, IN 47907-2032 Phone: +1 765 494-2214 Fax: +1 765 496-1459 Email: [email protected]

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Abstract Ion trajectory simulation is an important and useful tool in instrumentation development for mass spectrometry. Accurate simulation of the ion motion through the mass spectrometer with atmospheric pressure ionization source has been extremely challenging, due to the complexity in gas hydrodynamic flow field across a wide pressure range as well as the computational burden. In this study, we developed a method of generating the gas flow field for an entire mass spectrometer with an atmospheric pressure interface. In combination with the electric force, for the first time simulation of ion trajectories from an atmospheric pressure ion source to a mass analyzer in vacuum has been enabled. A stage-by-stage ion repopulation method has also been implemented for the simulation, which helped to avoid intolerable computational burden for simulations at high pressure regions while allowing statistically meaningful results obtained for the mass analyzer.

It has been demonstrated to be suitable to identify a joint point for

combining the high and low pressure fields solved individually. Experimental characterization has also been done to validate the new method for simulation. Good agreement was obtained between simulated and experimental results for ion transfer though an atmospheric pressure interface with a curtain gas.


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Introduction Mass spectrometry (MS) plays an increasingly important role in chemical and biological analysis, due to its wide applicability as well as high sensitivity and specificity.

The

performance of a mass spectrometer largely relies on its capability for manipulating ions through the entire system. For a modern mass spectrometer with atmospheric pressure ionization (API) source, the ions are produced in an atmospheric environment, transferred through the atmospheric pressure interface and guided by the electric and gas hydrodynamic flow fields, processed by the mass analyzers, and eventually detected by the ion detector. While mass resolution and accuracy are determined by the quality of the mass analyzer, the sensitivity, however, is highly dependent on the ion transfer through the entire system, during which physical and chemical processes such as desolvation or reactions can occur. Design of such a complicated instrument is often facilitated by ion trajectory simulations.1,2 Simulation of the ion motions through a particular region or component, such as ion mobility drift tube,3 ion funnel,4 and ion trap,5 has been frequently done; however, it has been extremely challenging to perform a simulation of a complete journey of the ions through an entire mass spectrometer. This is especially difficult for mass spectrometers with atmospheric pressure interfaces, in which ions are generated in atmospheric environment and transferred to the mass analyzer at high vacuum. The ion motions are affected by the force due to the electromagnetic (E or B) field as well as the collisions with the background gas molecules.6-8 While the E or B field acts the same regardless of the pressure regions of the mass spectrometer, the gas hydrodynamic (H) flow field imposes significantly different effects, depending on the pressure of the region. In a mass spectrometer with API, the ions generated from sources, such as electrospray ionization (ESI)9 or atmospheric pressure chemical ionization (APCI),10 are transferred through a 3 ACS Paragon Plus Environment


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number of vacuum regions over a wide pressure range from 760 Torr to 1 mTorr or lower. At pressures lower than 1 mTorr, the collisions can be treated as rare events with a relatively long mean free path between collisions. The ion trajectory is typically treated with a free motion in electric field subsequently modified by stochastic Monte-Carlo collisions, typically used for static molecular flow model. This has been implemented in SIMION,11-13 ITSIM,13-16 ISIS,13,17 and some other home written simulation programs.18-21 Our recent study, however, has shown that the flowing motion of the gas molecules at pressures as low as 10-5 Torr could have a significant impact on the trapping of the ions.22 At pressures of 1 Torr and higher, collisions occur more frequently. In most of the cases, the ions exhibit a macro drift motion along a direction guided by the electric field, however, with a strong dispersion mode enforced by the frequent, random collisions.23-28 The collisions make the path of an ion much less definitive in comparison with those in high vacuum.

In the

transition pressure range between 1 Torr and 1 mTorr, the dynamics of the gas field becomes very complicated and it is very difficult to model the field analytically. This pressure range covers the typical differential pumping stages in a mass spectrometer, where a set of ion optical components are located and plays a critical role in the ion transfer, and ultimately the performance of the mass spectrometer.29,30

This is the case for many commercial mass

spectrometers, such as LTQ Velos,31 LTQ-Orbitrap (Thermo Scientific, San Jose, CA, USA),32,33 QTrap,34 and QStar (AB Sciex, Concord, Canada)35,36, which are representative systems with atmospheric pressure interfaces using heated capillaries or pinholes with curtain gas.

The

significant pressure drop from atmospheric pressure to several millitorrs creates a major hydrodynamic force pulling the ions into the mass spectrometer; a strong gas expansion also occurs in the region at about 1 Torr and can cause a considerable (ca. 95%) loss of ions.37,38 Ion


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optical components, e.g., skimmers, tube lenses and ion funnels, have been employed in the differential pumping regions to provide an efficient sampling of the ions while not admitting too many gas molecules into the downstream stages of the mass spectrometer.4 The complexity in the gas dynamic fields, not the electromagnetic fields, causes the difficulty in simulation of the ion trajectories through an entire mass spectrometer, which otherwise would be highly desirable for the MS instrumentation design. In this study, we explored a new method of simulating the ion motions through different regions of a mass spectrometer, from the ion source at 760 Torr to a mass analyzer at a pressure lower than 1 mTorr. The key to the solution for the challenge discussed above was the creation of a full H field with a good accuracy, which can then be used together with the E field for ion trajectory simulations. For simulation requiring a large number of ions surviving to the mass analyzer, a stage-by-stage ion repopulation strategy was also implemented to avoid the high computational burden for simulations at high pressure while providing statistically meaningful results for mass analyzers at low pressures.

Method There are effective tools for resolving the H field based on the instrument configuration, but the applicability is highly dependent on the pressure.

Computational fluid dynamics

(CFD)26-28 can be used to solve the continuum flow field between the ion source at 760 Torr and the first differential pumping stage at ca. 1 Torr (Figure 1); however, CFD cannot provide accurate results for non-continuum or molecular flow field at lower pressures. Recently, we have shown that direct simulation Monte Carlo (DSMC)29,30 method can be used to provide H field between 1 Torr and 1 mTorr or lower for simulations involving ion optics and mass



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analyzers. Theoretically, the DSMC method could be applied for generating H field at higher pressures as well; however, the computational burden becomes very significant and the accuracy of the field obtained using the currently available DSMC tools is questionable. We explored a method of producing an H field across the entire pressure range of a mass spectromter through the fusion of a continuum flow field solved by CFD and a non-continuum field solved by DSMC. The integrated H field could then be used for the electro-hydrodynamic simulation (EHS) of the ion trajectories22 from the ion source to the mass analyzer. In continuum flow region (>1 Torr), the properties of the gas flow, including density, pressure, temperature and velocity, are assumed to vary continuously from one point to another and can be averaged in the volume of each grid cell, based on which the CFD method is established.39 However, for transition and molecular flows at pressure lower than 1 Torr, the effects associated with discrete particles becomes significant and DSMC method has been shown to be effective field solving.40-43 DSMC simulates randomly selected individual gas molecules that represent a fixed large number of molecules in the real gas flow. Although this concept theoretically can be applied for solving H field at a pressure as high as 760 Torr, a large number of simulated molecules would be required, which could lead to an intolerable computational burden as pressure increases (Figure 1).


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Figure 1. Computational burden for CFD and DSMC methods and the concept of integrating fields individually solved by CFD and DSMC.

In order to take the advantages of both the CFD and DMSC methods to generate an H field with high accuracies at both high and low pressure regions of a mass spectrometer, we proposed to integrate two fields individually solved by CFD and DMSC with a fusion point selected at about 1 Torr, where both the CFD and DSMC methods can produce accurate results. In an MS system with atmospheric pressure interface (Figure 1), the vacuum manifold typically has a region at about 1 Torr. This is a transition pressure stage where typically a skimmer or ion funnel is installed for ion transfer. CFD can certainly solve the H field from 760 to 1 Torr, while DSMC can also provide an H field for regions at 1 Torr or lower, both with high accuracies but low computational burdens.

For practical implementation, a proper fusion point needs to be

carefully selected based on the instrument configuration. The field from the ion source to the region next to the fusion point was first solved using CFD. At the fusion point, the properties of 7 ACS Paragon Plus Environment


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the H field, including the flow velocity, pressure and temperature, were then directly used as the boundary condition (or input parameters) for solving the field from the fusion point to the mass analyzer using DSMC. Supersonic expansion at about 1 Torr could be simulated by both by CFD39 and DSMC.40 After multiple iterations, the difference between the H fields at the fusion point solved by both methods shall be within an acceptable range so the upstream and downstream fields can be combined at this point with a minimal mismatch. In our model system, rotational symmetry was considered in the H field simulations. Ansys Fluent (ver. 14.0, Cecil Township, PA) was used to perform CFD. DS2V,44 was used to perform the DSMC, which is a freely available software developed by Dr. G.A. Bird from the Department of Aerospace Engineering, University of Sydney, Australia. DS2V is only applicable for two-dimensional (2D) or rotationally symmetric gas flows. For mass spectrometer systems with lower symmetries, such as the “Z” configuration in Synapt (Waters, Milford, MA, USA),45 use of 3D CFD and DSMC would be necessary, although the method for extracting the full H field would remain the same. Independently, the 3D E field of the entire instrument was solved based on its configuration using COMSOL (ver. 4.3a, COMSOL AB, Stockholm, Sweden). A home-written electro-hydrodynamic simulation (EHS) program22 was used to perform the ion trajectory simulations. Briefly, for each step in the EHS simulation, the ion was first allowed to move along a collision-free path determined by the pure electric field and then collide with a gas molecule that modified its velocity. The length of each collision-free path and the property of the gas molecule were determined by the solved H field. With the full E and H fields in the EHS program, the tracking of ions in the entire mass spectrometer from ion source to mass analyzer was enabled. The complete ion trajectories could be obtained by a single simulation, without the


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need of performing multiple simulations and then concatenating the fragment trajectories together. This would facilitate a direct evaluation of the design of mass spectrometer as well as the study of the physical and chemical processes during the ion transfer. A significant ion loss is expected during the ion transfer through a mass spectrometer. In the case where a statistic characterization, such as using contour maps, is required, an initial large number of ions starting from the ion source would be required. To avoid the ultrahigh computational burden for simulations at high pressures, a stage-by-stage ion repopulation strategy could be used in the simulation. The detailed treatments will be further described below. Non-uniform triangular grids were used in the E field solving using COMSOL, whereas non-uniform tetragonal grids were employed in the H field solving using CFD or DSMC. For E field and CFD simulations, the grid sizes were first automatically selected by the software and subsequently manually specified for critical regions for refinement, for instance, the area between the orifice and skimmer where shock waves were expected. Using the orifice as an example, the maximum grid size used was smaller than 1/10 of the aperture radius. For CFD, boundary layer was used to improve the calculation accuracy. For DSMC, the grid sizes were all manually specified, in order to match the CFD field solved at the fusion point. The solved E and H fields were sampled with square grids in the EHS using an interpolation method.46

Results and Discussion Comparing atmospheric pressure interfaces using a heated capillary and a pinhole with curtain gas, the latter can produce a much more complicated gas hydrodynamic flow field, and thus was used in this study to demonstrate the simulation of complete ion trajectories through an entire mass spectrometer. The model system is shown in Figure 2a. This system has all the



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critical features of a QTrap mass spectrometer. It included a pinhole atmospheric pressure interface using curtain gas at an input flow rate of 2 L/min, which imposed a very complicated gas dynamic effect for the interface. A nanoESI tip was placed 8 mm away from the MS inlet and dry ions were assumed in the simulation. The ions passed through the first two orifices entering the vacuum stage I at 2 Torr, where a skimmer was placed to take the ions into the vacuum stage II at 5 mTorr with a quadrupole ion guide. A linear ion trap was installed in the vacuum stage III at 2×10-5 Torr. The inner diameters of the first two orifices, the holes on the skimmer and the inter-quadrupole lens are 1 mm, 0.4 mm, 0.6 mm and 6 mm, respectively. The quadrupole ion guide and linear ion trap (LIT) had the same radii r0 = 3 mm for the electric field and were driven by a 300V0-p radio-frequency (RF) voltage at a frequency of 1 MHz. The electric fields for direct-current (DC) and RF potentials were solved using COMSOL, as shown in Figure 3


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Figure 2. (a) Configuration of a model mass spectrometer with an atmospheric pressure interface using curtain gas. (b) H fields, 760 – 2 Torr solved by CFD and 2 – 10-5 Torr solved by DSMC. (c) Gas speeds along the z axis from point A to B, calculated based on H fields solved by CFD (black) and DSMC (red). (d) Combined H field. (e) Mean free path (red) and gas speed (blue) along the ion transfer axis of the mass spectrometer.



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Before creating the gas flow field, the instrument configuration was carefully studied for selecting the fusion point for the continuum and non-continuum flow fields. CFD can solve the field with good accuracy from the ion source at 760 Torr to the vacuum stage I at 2 Torr and the DSMC can solve the field from vacuum stage I to III without a significant computational burden. The region from the 2nd orifice to the skimmer orifice was proper for identifying a fusion point, since it was at a pressure range suitable for field solving by both CFD and DSMC. The orifices were identified as good candidates simply because smaller regions were to be of concern during the process of combining the upstream and downstream gas fields. Comparing 2nd orifice and the skimmer orifice, the 2nd orifice was determined to be a better choice. An important step in the process of combining the two fields was to reach a good match at this fusion point for fields solved individually by CFD and DSMC. High accuracy in field solving could be obtained at 2nd orifice by both CFD and DSMC; however, this was not the case for skimmer orifice when using CFD, since the exit side of skimmer was at a pressure of 5 mTorr, much lower than 1 Torr. To obtain the overall H field for the simulation, the upstream field from the ion source to vacuum stage II was first solved using CFD (Figure 2b). The pressure at the 2nd orifice was about 320 Torr, which confirmed it as an appropriate selection for the fusion point of the two fields.

The obtained flow properties at the 2nd orifice, including flow velocity, pressure and

temperature, were extracted from the solved field for use as the boundary conditions to solve the downstream field using DSMC. Note that the boundary conditions typically are modified during the process of field solving, which uses multiple iterations. The degree of changes in the flow properties at the 2nd orifice was checked after the downstream field was solved using DSMC. A good match was observed with the original conditions obtained from CFD, as shown in Figure 2c for the flow speed at point A as an example. As pressure decreased from point A to B, a


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discrepancy began to appear and was as large as 25% for the flow speed at the skimmer (point B in Figure 2c). The CFD is not suitable for solving the field at this pressure. The full gas dynamic field was produced by combining the upstream and downstream fields with the fusion point at the 2nd orifice (Figure 2d).

The flow properties and the collision conditions could then be

continuously extracted along the ion path from the ion source to the linear ion trap. The mean free path and the flow speed were extracted along the ion path as shown in Figure 2e.

Figure 3. Fields solved for (a) DC potentials (absolute value) and (b) RF potentials.

The full E fields (Figure 3) were then used with the integrated H field (Figure 2d) to perform ion trajectory simulation using the EHS program.22 For the simulations, the space of interest was divided using equally spaced, square grids. The properties of the E and H fields were sampled for each grid, including the local electric field strength, pressure, temperature, number density, velocity, and the mean free path. A grid size of 0.02 mm was used for



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calculating ion trajectories (Figure 4a-c). For deriving the contour maps of ion number density (Figure 4d-f), a larger grid size of 0.1 mm was used for sampling. Within the collision-free path, an ion was moving under the guidance of the electric field. At the end of each path an ion-neutral collision was simulated. The actual collision-free distance and the velocity of the neutral molecules were sampled from the local H field. The modified velocity vector of the ion after the collision was then used for simulation of the collision-free motion under a pure electric force in the next step. These steps were repeated to produce an ion trajectory within a specified time period. Ion trajectories were calculated using the Runge-Kutta (R-K) method,46-48 in which the time step was chosen as the smaller one between 1/20 of an RF cycle (5×10-8 s for 1 MHz) and the actual collision-free time. This means that the time step in simulation was pressure-dependent. For example, in the air at 760 Torr, the actual collision-free time, typically around 10-11 - 10-9 s, was used for each step; in vacuum stage II at 5 mTorr, however, 5×10-8 s was then used as the time step because the actual collision-free time periods were much longer (typically 10-5-10-6 s). In the simulations performed in this study, the complex physicochemical effects associated with electrospray ionization,38 such as droplet size reduction,49 macromolecular diffusion within the droplet,50 and droplet fissions for ion formation,51 were not considered. Dry ions of m/z 400 were placed at the tip of the ion source. The initial emitting speed of the ions was set as 20 m/s with a thermal Gaussian distribution, within an emitting angle range of 45 o (inset of Figure 4a).38,52 Three ion trajectories simulated for ions emitted at an angle of 10° were selected to show in Figure 4a. The gas flow had a significant impact on ion trajectories in the continuum flow (pressure > 1 Torr) (Figure 4b). Ions drifted in the electric field toward the MS inlet but with a significant dispersion due to the extensive ion-neutral collisions.53-55 At the same


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initial emitting angle of 10o, the actual individual motion for each of these three ions exhibited a large degree of randomness (Figure 4b). In the molecular flow regime ( 1 Torr), dispersion effect due to the gas hydrodynamic force was significant for all the four ion species, and a transfer efficiency of ca. 1% was observed at the skimmer (Figure 4g). Ions with larger collision cross sections (corresponding to higher m/z values here) would be subjected to more ion-neutral collisions, giving rise to a lower ion transfer efficiency at the skimmer inlet. In the quadrupole ion guide and LIT (< 1 mTorr), the electric focusing of the RF field became effective and a much higher transfer efficiency of ca. 60% was observed. In the LIT, the trapped ions were cooled down for 10 ms and then mass-analyzed by scanning RF with an axial resonant ejection using an alternating current (ac) voltage at 380 kHz. The RF was ramped from 300 to 900 V0-p with a scan rate of 1000 Th/s, and the ac was also ramped from 0.5 to 1 V0-p simultaneously. The simulated mass spectrum is shown in figure 4h.


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Figure 4. (a) Ion trajectories simulated for 3 ions of m/z 400, all at the same ejection angles of 10o. Zoom-in views of ion trajectories (b) in air and (c) in LIT of vacuum stage III, inset of (b) showing a zoom-in view of the ion trajectory. Contour maps of ion number density in the region of (d) ion source, (e) between the 1st and 2nd orifices, and (f) the vacuum stage I. (g) Surviving yield of three ion species, protonated cocaine (m/z 304), heroin (m/z 370), and imatinib (m/z 494), along the transfer axis of the mass spectrometer. (h) Simulated mass spectrum of these ions.



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Experimental characterization was also done to validate the strategy of generating the full gas hydrodynamic field for ion trajectory simulation. Figure 5a shows a schematic of the Qtrap 4000 system (AB Sciex, Concord, Canada) used for experimental testing, which has a similar setup as described in Figure 2a. In this instrument, there is a 1 mm distance between the curtain plate (1st orifice i.d. = 2.2 mm) and the 2nd orifice (i.d. = 0.32 mm) and 2 mm between the 2nd orifice and skimmer (i.d. = 2.6 mm). Similarly, the 2nd orifice was used as the fusion point for combining the gas fields solved using CFD (Fig. 5b) and DSMC (Fig. 5c). The flow property at the 2nd orifice in the upstream gas field solved by CFD (Figure 5b) was used as the boundary conditions for solving the downstream field using DSMC (Figure 5c). The supersonic expansion from 760 Torr to 2 Torr was disturbed by the skimmer between the vacuum stage I at 2 Torr and II at 5 mTorr.

The combined H field was used with the electric field for ion trajectory

simulations. In experimental testing, a methanol solution containing cocaine at 10 ppb was sprayed at 1500V using a borosilicate capillary (o.d. 1.5 mm, i.d. 0.8 mm) with a pulled tip. The intensity of protonated cocaine ions at m/z 304 was monitored while three experimental parameters were varied for the atmospheric pressure interface, including the sprayer-to-inlet distance d, the curtain gas flow rate Q, and the declustering potential (DP) applied on the 2nd orifice plate. The ion intensities as functions of these three parameters were simulated and experimentally measured, with the comparisons shown in Figure 5d-f.


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Figure 5. (a) Schematic of the atmospheric pressure interface of QTrap 4000 mass spectrometer. Contour maps of gas speed in the API derived from the gas field solved by (b) CFD and (c) DSMC. Relative ion intensity as a function of (d) the sprayer-to-inlet distance d, (e) the curtain gas flow rate Q, and (f) the voltage DP applied on 2nd orifice plate. The black and red curves represent the experimental and simulation results, respectively.

In the first experiment, the curtain gas was turned off and the DP voltage was set at 20 V. The sprayer-to-inlet distance d was increased while the ion intensity was monitored.

In

simulation, 104 ions were ejected from the sprayer and the absolute ion intensity was obtained by counting the ions reaching the end of the quadrupole ion guide. Note that the ion repopulation was not implemented for this study. The relative intensities were obtained by normalizing the absolute intensities with the intensity simulated or experimentally measured for d = 4 mm, respectively, which was the highest. An exponential decrease in ion intensity as the increase of d was observed, with a perfect match between the simulation and experimental results. The ions would experience more ion-neutral collisions at larger d, which would lead to a higher ion loss as 19 ACS Paragon Plus Environment


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the diffusion become greater. The electric field and sprayer-to-inlet distance were then kept constant, while the curtain gas flow rate Q was varied for investigation (Figure 5e). The simulated ion intensities were lower than the experimental results at higher flow rates (up to 2 L/min), which is probably because the improved desolvation at higher flow rates were not considered in the simulations. At higher flow rates, e.g. 3-5 L/min, a sudden drop in ion intensity was observed in both simulation and experiment. This was because the hydrodynamic force due to the counter flow became too strong for the steering by electric field.

Finally, the

gas flow rate and the sprayer-to-inlet distance were kept constant, while the electric voltage DP applied to orifice 2 was varied (Figure 5f). As the DP voltage increased, ion intensity decreased in both simulation and experiment. At high DP voltages, the ion intensity drop was more significant in the experiment. Presumably, the fragmentation of the ions would increase at higher DP voltages, which would cause the loss of the precursor ions, which was not considered in the simulation.

Conclusion In this study, for the first time we demonstrated an effective means of simulating the ion trajectories through an entire mass spectrometer with an atmospheric pressure ionization source. The complexity of the gas dynamic field was overcome by combining the upstream and downstream fields individually solved using methods suitable for continuum and molecular flows, respectively. The fusion of the gas fields provided the freedom of simulating complete ion trajectories or segments of the ion paths without worrying about the discontinuity in the gas field over a wide pressure range. The EHS method for simulation, in conjunction with the stageby-stage repopulation of the ions, has been shown to be practically useful for the simulations


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involving a wide pressure range. Please note that, unlike the selection of the fusion point, the selection of the times and locations of the repopulation is not restricted by the gas dynamic features. In the reported study, only dry ions were used in the simulation. However, with the full gas field generated at high accuracy, the velocity, temperature and density of the neutral molecules can be accurately extracted for studies involving physicochemical effects much more complicated, such as the desolvation of charged droplets as well as the heating or cooling of the ions along the transfer. Notes The authors declare no competing financial interest.

Acknowledgments The authors thank Dr. James Hager and Dr. Bruce Collings at AB Sciex for helpful discussions. The work was supported by National Science Foundation (Grant CHE 0847205) and the National Institutes of Health (Project 1R01GM106016).

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Following the Ions through a Mass Spectrometer with Atmospheric

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