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Atmospheric Pressure Ion Source Development: Experimental Validation of Simulated Ion Trajectories within Complex Flow and Electrical Fields

  • Walter WissdorfEmail author
  • Matthias Lorenz
  • Thorsten Pöhler
  • Herwart Hönen
  • Thorsten Benter
Research Article

Abstract

Three-dimensionally (3D) resolved ion trajectory calculations within the complex viscous flow field of an atmospheric pressure ion source are presented. The model calculations are validated with spatially resolved measurements of the relative sensitivity distribution within the source enclosure, referred to as the distribution of ion acceptance (DIA) of the mass analyzer. In previous work, we have shown that the DIA shapes as well as the maximum signal strengths strongly depend on ion source operational parameters such as gas flows and temperatures, as well as electrical field gradients established by various source electrode potentials (e.g., capillary inlet port potential and spray shield potential). In all cases studied, distinct, reproducible, and, to some extent, surprising DIA patterns were observed. We have thus attempted to model selected experimental operational source modes (called operational points) using a validated computational flow dynamics derived 3D-velocity field as an input parameter set for SIMION/SDS, along with a suite of custom software for data analysis and parameter set processing. Despite the complexity of the system, the modeling results reproduce the experimentally derived DIA unexpectedly well. It is concluded that SIMION/SDS in combination with accurate computational fluid dynamics (CFD) input data and adequate analysis software is capable of successfully modeling operational points of an atmospheric pressure ion (API) source. This approach should be very useful in the computer-aided design of future API sources.

Key words

CFD SIMION SDS DIA APLI 

1 Introduction

The introduction and rapid evolution of novel atmospheric pressure ionization methods [1, 2, 3] (e.g., the emerging methods based on electrospray ionization [ESI] [4, 5, 6], atmospheric pressure chemical ionization [APCI] [7, 8]) including the numerous discharge-based methods (e.g., low temperature plasma [LTP] [9] or flowing atmospheric pressure afterglow [FAPA] [10], atmospheric pressure photoionization [APPI] [11], and atmospheric pressure laser ionization [APLI] [12]), have led to a large number of ion source varieties and geometries. Generally, atmospheric pressure ion (API) sources are designed to accept the liquid effluent of a chromatography stage (e.g., HPLC) at flow rates up-to several mL/min. With the exception of ESI and all its derivatives, all API methods are directly operating on the vaporized analytes within the gas phase. Furthermore, mass selective analysis generally occurs in high vacuum environments; the introduction of liquids into the mass transfer/analyzing region is generally strongly avoided. Consequently, within all API sources, the liquids are vaporized either prior to ionization (APCI, APPI, and, to some extent, APLI) or after charge separation in the liquid phase via ion evaporation/Coulombic interaction (ESI).

In virtually all cases, the vaporization process of the liquid flow is pneumatically assisted (vaporizer or nebulizer stage). The first step of the vaporization process is commonly the mechanical generation of a “spray” within a heated gas flow. Most recent API source designs apply considerable amounts of thermal energy to the spray region to drive the vaporization process as close as possible to completion; this is particularly true for APCI and APPI [1]. At least one additional gas flow is generally supplied to the API source serving as “curtain” in front of the mass analyzer sampling orifice, preventing the entry of remaining droplets and/or neutral bulk source gases; in some source designs, this flow is directed to interact with the nebulizer gas stream. It is frequently concluded that such directed flows facilitate the further “desolvation” or “drying” of the primarily generated analyte cluster ions [1].

There are at least two gas sinks: the analyzer sampling orifice and the source vent. The former establishes a flow generated by the pumping system of the mass analyzer. The first pressure reduction stage is in many cases a critically operated inlet capillary (length about 10–20 cm and an inner diameter in the order of several hundred microns). Skimmers or flat orifices are less frequently used. The resulting sampling gas volume flow is on the order of L/min. The source vent is a far less well defined sink. Generally, the source vent is not operated in a controlled fashion; rather it is often hooked up to an in-house venting system. It is emphasized that this essentially uncontrolled flow may significantly affect the performance of an API source and needs careful attention. Whereas active control would be the optimum, a constant pumping speed at the venting port of the source appears to be highly desirable for stable source operation. Figure 1 shows a schematic of the gas sources and sinks in a typical API MS set-up.
Figure 1

Schematic of a generic atmospheric pressure ion source and location of the scanned area with respect to the MS inlet geometry. 1: Inlet capillary into MS; 2: capillary cap; 3: spray shield; 4: heated nebulizer; 5: drain flange; (a) gas flow into MS; (b) dry gas inflow into ion source; (c) nebulizer and analyte gas flow into ion source; (d) gas flow into drain

In all API source designs, ions are dragged through the provided gas flows by electrostatic forces generated by electrical field gradients. The gradients are established by application of voltages to metal surfaces/electrodes; the source enclosure is generally grounded. At atmospheric pressure, however, each ion experiences about 109 collisions per second with the neutral gas molecules [13] (i.e., there are extensive molecular interactions with respect to both elastic kinetic energy transfer resulting in directional momentum change as well as inelastic collisional activation, deactivation, and chemical transformation processes). Consequently, the dynamics of the neutral bulk gas (i.e., the fluid dynamics) as well as molecular ion diffusion have a significant impact on the ion trajectories. Furthermore, considerable ion transformation processes may occur depending on the presence of reactive neutral species, which may also be generated in situ. This is in sharp contrast to vacuum environments, where the mean free path of the ions is orders of magnitude larger than the spatial dimensions of the system. Here, the ion travel path is solely determined by electrical gradients, and the chemical fate of primarily generated ions depends only on the internal energy acquired during the ionization process.

In the last couple of years, we have been developing diagnostic tools for the experimental characterization of API sources. Most of these tools are based on APLI (i.e., resonantly enhanced two-photon ionization at 248 nm (KrF* exciplex emission) or 266 nm (quadrupled Nd:Yag emission) at atmospheric pressure. The most valuable advantages of APLI in the framework of the present paper are as follows: (1) Highly selective and sensitive ionization of aromatic compounds, such as polycyclic aromatic hydrocarbons (PAHs) [14, 15]. Generally bulk matrix compounds present in large excess (N2, O2, and LC solvents including acetonitrile, methanol, aliphatic hydrocarbons, chlorinated compounds, and water) are not ionized, nor are they electronically excited to any noticeable extent upon 248 or 266 nm laser light irradiation. This is in sharp contrast to APCI and APPI, where abundant neutral radical generation via VUV photolysis is inevitable [16]. (2) The spatial region of ionization is restricted to the laser light travel path, which is easily manipulated; thus a high degree of spatial resolution is established. (3) Ions are generated temporally well resolved within the laser pulse duration (1 to 10 ns). As a result, APLI generates temporally and spatially well-defined ion “packages.” Depending on the extent of downstream dispersion and chemical transformation processes, such a package may partially or entirely lose its integrity upon arriving in the collision-free analyzer ion acceleration stages.

In this paper, we are combining our previously reported research results (evaluation of particle tracing versus electrokinetic flow modeling approaches [17] and experimental validation of computational fluid dynamics (CFD) calculations of complex flow geometries [18] as well as the implementation of a numerical method for gas phase ion kinetics [19]) for application in API source design. In the present contribution, the quality of calculated ion trajectories is analyzed using spatially and mass resolved experimental data sets. The entire computational approach is described in some depth. A comprehensive ion acceptance distribution (DIA) data set is used for this analysis. As will be shown, the model data represent experimental observations at a surprisingly high level. It is concluded that ion trajectory simulations with high quality CFD data input are becoming a powerful tool in the computer-aided design of API sources, ion optical devices operating in collision controlled environments, and atmospheric pressure ion mobility spectrometers.

2 Methods

2.1 Experimental: DIA Measurement

The acquisition of the DIA was thoroughly introduced in preceding publications [20, 21, 22, 23]; therefore, we describe the experimental method only briefly. The DIA is the distribution of the ion signal intensity recorded by a mass spectrometric analyzer in dependence of the location of ionization. To acquire such a distribution, a confined and controlled zone of primary ionization is necessary. Such requirements are ideally fulfilled by laser-based photo ionization methods such as the recently introduced atmospheric pressure laser ionization (APLI) [12]. This method utilizes a two-step mechanism (1 + 1 resonance enhanced multiphoton ionization) to selectively ionize analytes with appropriate spectroscopic characteristics, which are (1) strong linear absorption coefficients in the near UV, (2) stable and long lived corresponding intermediate electronic states, and (3) stable and long lived radical cations. Many PAHs feature such characteristics and are thus ideally suited for APLI.

In the present work, DIA are recorded for a commercially available multipurpose ion source (MPIS; Bruker Daltonics, Bremen, Germany) attached to a commercial API-TOF instrument (micrOTOF, Bruker Daltonics) with a custom computer controlled two-dimensional (2D) translational stage holding a quartz lens with a focal length of 120 mm. This stage allowed shifting the laser beam focus in 2D by translation of the lens position perpendicular to the main axis of the MPIS, cf. Figure 1. With this setup, the area in front of the MS inlet was scanned and the resulting ion signal was recorded in dependence of the position of the beam travel path.

Due to the high linear absorption coefficient of the tracer used (see below), ions were generated along the entire beam path. The experimental data of the experiment thus represent the 2D projection of the 3D DIA on a plane perpendicular to the laser propagation direction. Unless otherwise noted, the term “DIA” refers herein to this 2D projection if not noted otherwise; see [21, 22, 23] for further details and discussion. The ion source and the gas flow within the source chamber are depicted schematically in Figure 1.

Pyrene (Merck KGaA, Darmstadt, Germany), dissolved in methanol (HPLC grade Fisher Scientific, Waltham, MA, USA) was used as a tracer. The tracer solution was introduced into the ion source by a LC Pump (Hitachi Ltd., Tokyo, Japan) through a heated conventional LC-MS nebulizer (Bruker Daltonics). The pyrene concentration was 1 μmol/L and the liquid inflow into the ion source was 100 μL/min. All DIAs shown result solely from the mass selected radical cation (M•+) signal of the tracer. The electrical potentials of the electrodes of the MS inlet geometry (i.e., “spray shield” and “capillary cap”) were always attractive for positive ions and, therefore, negative in the positive mode of the MS; the nebulizer and the entire ion source enclosure was grounded. In the remaining part of this paper, the minus sign is omitted for the voltages. All voltages are given relative to ground potential.

The laser light source was a KrF Excimer Laser (Atlex 300; ATL Lasertechnik GmbH, Wermelskirchen, Germany) operated with a pulse energy of about 3 mJ at a repetition rate of 100 Hz. The size of the scanned area was 13 × 18 mm with a spatial resolution of 0.5 mm and an integration time of about 3 seconds per spatial position. The origin of the coordinate system used for the visualization of the DIAs is the intersection of the main axis of the ion source with the front face of the spray shield, as depicted in Figure 1.

The DIA measurements were fully automated using custom driving electronics and software. At the final development stage, the experimental setup performed autonomous DIA measurements with a predefined set of ion source parameters (gas flows, gas temperatures, and electrical potentials) for several hours. For the analysis and visualization of the acquired DIA measurements, we used a custom set of software tools, developed in Matlab [24], Python [25], SciPy [26], and Java [27].

2.2 Numerical Methods

A numerical model for the calculation of ion trajectories at atmospheric pressure conditions requires information about the gas flow dynamics in the volume of interest attributable to the coupling of ion and bulk gas motion. More specifically, the field of bulk gas flow velocity vectors (“velocity field”) and the temperature and pressure distribution in the simulation domain are needed as input parameters for the ion migration model. This input data may be measured with appropriate methods (e.g., particle image velocimetry [PIV] [18, 28]), but in most cases it is more convenient to obtain the input from a computational model as well because spatially resolved accurate flow measurements represent a considerable challenge and experimental effort.

In general, the motion of the highly diluted analyte ions has no effect on the dynamics of the bulk gas flow, and it is possible to entirely decouple the computational fluid dynamics (CFD) from the ion migration model. Thus, both models can be solved independently; the results of the CFD calculations are used as input data for the ion migration model. Our general approach to numerically reproduce the spatially resolved ion signal measurements (DIA) is as follows:
  • Record experimental DIAs in dependence of various experimental parameters at fixed gas flows, which define a fluid dynamic “operation configuration” (cf. [18]) of the source.

  • Solve and experimentally validate a CFD model of the ion source domain to get detailed information about the bulk gas flow dynamics in the area of interest at the selected operation point.

  • Use the resulting data set from the CFD model as an input parameter for an ion transport simulation. In this transport model, the specific characteristics of the performed spatially resolved measurement are reproduced. This model also includes a chemical kinetics module, which takes into account possible ion transformation processes and adjusts relevant data such as ion mobility.

  • Finally, the resulting data from the ion transport model are analyzed to derive a numerical DIA.

Figure 2 shows an overview of the simulation process including the software packages used for the numerical simulation of DIA.
Figure 2

Tool-chain overview. Schematic overview of the simulation process, with utilized software packages and libraries. U = gas velocity vector field, T = gas temperature scalar field, p = gas pressure scalar field

2.2.1 Computational Fluid Dynamics and Validation

The gas flow in the entire ion source geometry was modeled with a commercial CFD solver (Ansys CFX ver.12.1 [29]). Details of the numerical fluid dynamic model, the spatial resolution of the numerical mesh, the boundary conditions, and a detailed analysis of the results can be found in previous work [18]. The CFD model was validated with experimental fluid dynamic measurements using particle image velocimetry [28, 30]. This technique uses the optical scattering signature of small particles (e.g., oil droplets), which follow the gas flow without disturbances from particle inertia. Details of the technique and the fluid flow measurement in the MPIS are also given in [18].

The CFD model was experimentally validated using an authentic MPIS and MS pressure reduction stage but without an attached mass analyzer. The ion source operation configuration at which the model verification was performed differed slightly from the ion source configuration used for routine analytical measurements, but the deviation was not as severe to render the model verification invalid. The validated CFD model was then utilized to determine the gas flow in the ion source at its actual analytical operation point, which was studied in the DIA measurements.

The relative distribution of a neutral analyte in the ion source was also calculated by the numerical solution of a convection/diffusion model, embedded within the CFD model. The convection/diffusion equation [31, 32] was solved with a diffusion coefficient of 7×10–6 m2/s for pyrene, an assumption of convective flow at the outlet ports of the ion source (drain port and MS inlet capillary), and a convective inflow of analyte at the nebulizer inlet port. The chamber walls were assumed to be inert.

2.2.2 Ion Migration Model

SIMION (ver. 8.0.4 [33]) along with the statistical diffusion simulation (SDS) algorithm was used to numerically describe the migration of ions in an electrical field and a bulk gas flow. SDS was introduced by Appelhans and Dahl in 2005 [34]. We used a modified version of the Lua implementation of SDS, shipped with the SIMION 8 package.

The SDS model implementation requires several input data sets. Each data set represents one parameter of the bulk gas flow (velocity in all three spatial dimensions, neutral analyte distribution, pressure, and temperature) at the spatial node positions of the rectangular calculation grid of SIMION. In general, the spatial discretization mesh of CFD simulation software is not rectangular, but rather irregular with several different mesh element types (e.g., tetrahedrons and/or prisms) and sizes. The results from CFD calculations thus have to be transformed to serve as accurate input data for ion migration calculations with SIMION/SDS. For this purpose, we have developed a custom program using Matlab [24], which generated the required SDS input files from data sets directly exported from CFX. This program reads the spatial positions of the CFD discretization mesh nodes along with corresponding values of the several parameters to perform a linear interpolation in 3D to calculate values at the corresponding SIMION simulation mesh node position.

Since the CFX export data are delivered in a binary format (binary EnSight case file format [35]), a preceding interface layer was used to generate ASCII files containing the node data described before. For this purpose and for visualization of the CFD results, the open source software Paraview (ver. 3.8.1; Kitware Inc., New York, NY, USA) was used, which is a frontend to the open source visualization toolkit (VTK) library [36].

2.2.3 DIA Simulation Process/Simulation Automation

For the numerical simulation of a DIA, we replicated the processes occurring in an actual DIA measurement. In the experiment, ions are generated in a zone sharply defined by the laser beam geometry. These ions migrate through the ion source, driven by viscous drag, the present electrical fields, and diffusion. The mass spectrometer samples only the fraction of ions transported into a small area in front of the inlet capillary where the viscous drag forces of the gas flow entering the capillary dominate. In addition, the ions potentially undergo chemical transformation processes while they are transported through the ion source.

Due to the high two-photon ionization cross section of the PAH used as a tracer, ions are formed along the entire laser beam path. Thus, the experimental setup determines a projection of the 3D DIA onto a 2D plane. In the numerical model, there is no such restriction; therefore, we calculated the fully resolved 3D ion acceptance distributions. The 2D projection onto a plane is readily calculated by summing the simulation result data in one spatial dimension. To calculate the 3D DIA, we defined a rectangular mesh with a minimum and maximum position and with a step width for every spatial dimension. For every node of this mesh, the following simulation loop was performed:
  • Define a start zone for the ion “package.” A typical starting condition was a space filled sphere with the position of the mesh node as center and a radius of 0.4 mm. The number of ions per package is scaled by the relative local neutral analyte concentration, which is determined from the interpolated CFD simulation result data passed to the ion trajectory simulation via the neutral analyte concentration distribution file.

  • Perform an ion migration simulation run with the defined ion package. The termination positions and the migration time from start to termination of the simulated ions are recorded into a result file.

  • Analyze the result file: Ions which terminate in a predefined “target zone” around the capillary inlet are considered as “successfully” sampled by the MS.

The numerical result of a DIA simulation is the number of “successfully” sampled ions in dependence on the starting position. It is possible to reinterpret the raw simulation data for any chosen target zone or to perform migration time analyses on the raw results without the need to rerun the simulation because the termination data for every simulated ion are retained. This is a significant advantage of the chosen simulation approach. As stated earlier, the used SDS implementation was modified: for automation purposes the simulated voltages on the spray shield and the capillary cap electrodes were changed to variables, which could be controlled by an external automation script.

First order ion depletion processes were modeled by integration of an ion destruction reaction with a fixed rate constant into the simulation. To model such a reaction in a Monte Carlo simulation fashion, a random value between 0 and 1 for every ion in every time step was generated. If this random value was smaller than a given normalized depletion probability (p), scaled with the length of the time step, the ion was terminated. We essentially used the same method to simulate reaction kinetics in combination with the migration of ions in an atmospheric pressure ion mobility spectrometer (IMS; for details see Ref. [19]).

The automation of the simulation process and the analysis software was developed in the Python [25] programming language environment. For data handling and visualization the NumPy [37], SciPy [26], and Matplotlib [38], open source Python libraries were used. All SIMION/SDS simulations were performed on a Dell Precision T7500 Workstation (Dell Inc., Round Rock, TX, USA).

3 Results

3.1 Experimental Results

The automation of the experimental procedure allowed the systematic collection of over 650 individual DIA, which results in a comprehensive overview of the dynamic behavior of the MPIS. A detailed analysis of the whole set of experimental results is beyond the scope of this work and will be shown in a subsequent paper, which is currently in preparation. A brief analysis of the interesting findings in the acquired data was already shown in [39]. In the present work, we focus the examination of the experimental results on aspects relevant to the validation of the developed numerical models.

The preliminary analysis of the experimental data set revealed some distinct characteristics of the experimentally found ion acceptance distributions, which needed to be at least qualitatively reproduced by the numerical ion trajectory models. All experimental ion acceptance distributions show two notable features: the distribution is generally asymmetric, with a global signal maximum significantly off from the center axis of the ion source where, instead, a local minimum is usually located (see Figure 3a, top, for example). A second initially surprising signal minimum is located in the close vicinity to the mass analyzer’s sampling orifice, which is observed throughout all shown experimental DIA. The variation of the ion source parameters reveals some interesting effects on the ion acceptance distribution: by increasing the inlet capillary cap voltage (capillary cap labeled “2” in Figure 1) the ion acceptance signal shifts away from the sampling orifice with a noticeable change of its general shape (compare the upper panels in Figure 3a and c or Figure 3b and d). The DIA is surprisingly insensitive to the capillary voltage; even a voltage of 2000 V shifts the signal maximum in the DIA only about 4 mm (upper left and upper center panels in Figure 3b and d).
Figure 3

Experimental and simulated DIA: (a) capillary voltage 1000 V; simulated dry gas flow 2.0 L/min; (b) capillary voltage 1000 V; simulated dry gas flow 3.8 L/min; (c) Capillary voltage 1000 V; simulated dry gas flow 2.0 L/min; The (d) capillary voltage 3000 V; simulated dry gas flow 3.8 L/min; ion depletion probability 10–5; the spray shield voltage is given in the insets. The maximum signal level (brightest contour) is given above each plot. The spatial axes are in mm

In contrast, the spray shield voltage has a pronounced effect on the spatially resolved ion signal distribution, as shown in Figure 3a–d. Even with a voltage as low as 50 V, the shape of the ion signal changes significantly compared with the 0 V signal. Generally, it becomes more confined on the vertical axis and stretched out horizontally with increasing electrical potential on the spray shield.

The systematic variation of the gas flows in the ion source revealed a clear effect of the flow conditions on the DIA: The sudden shift of the signal maximum from a zone below the center axis to a zone above the center axis of the ion source with increasing dry gas flow. As Figure S1 of the Supplemental Material shows exemplarily, at a typical operation point of the source (dry gas heater temperature 200 °C, nebulizer pressure 3.0 bar, nebulizer temperature 320 °C), the signal maximum suddenly shifts at a dry gas flow of approximately 3.0 L/min. The abruptness of the transition is underlined by the fact that it is completed within a dry gas flow variation of at most 0.2–0.3 L/min as shown in supplemental Figure S1.

These initial findings in the brief analysis of the DIA measurement results led to the choice of the input parameters for the fluid dynamic simulation. The described sudden shift of the signal maximum is especially well suited to be used as a benchmark in a numerical ion migration simulation because it is a distinct and easily identified feature, which most probably depends on a sudden change in the overall flow structure in the investigated zone. To ensure that the completed transition is replicated in the calculations, the simulations were done safely away from the actual experimental turning point with 2.0 and 3.8 L/min as the lower and upper dry gas flow boundary condition in the CFD model.

Figure 3a–d show the experimental reference data in comparison to the numerical results. In this figure the above-mentioned shift of the signal maximum towards the upper half of the scanned area with increasing dry gas flow is clearly discernible in the experimental results as well as in the simulation (cf. Figure 3a, b versus 3c, d).

3.2 Numerical Results and Comparison with Experimental Results

3.2.1 2D DIA/DIA Projections

Figure 3a–d depict the numerical results of the DIA simulations in direct comparison to the corresponding experimental results. Considering the high complexity of the DIA genesis by combining the neutral analyte distribution with electrical and fluid dynamical forces acting on the generated ions, the level of overall agreement between simulated and experimental DIA is notably. The rough general shape and some of the prominent features of the experimental DIA are at least qualitatively reproduced in the simulations:
  • The pronounced signal minimum in direct proximity to the spray shield (to the left margin of the simulation domain) is clearly reproduced. The spreading of this minimum with increasing capillary and spray shield voltages is also observed in the simulations.

  • The deviation of the global signal maximum from the center axis of the ion source (intersecting the origin on the vertical axis in the DIA plots) and the distinct signal minimum near this axis found in many experimental DIA is reproduced by the simulation.

  • The inclination angles of the frontal border of the zone with significant signal intensity in the simulations are comparable to the experimental data (most prominently in Figure 3a and c).

  • Finally, the shift of the signal maximum from the lower half of the scanned area (Figure 3a and c) to the upper half (Figure 3b and d) with increasing dry gas flow is observable in many of the numerical results.

A striking common finding is the signal minimum in direct proximity to the mass spectrometer inlet or the spray shield and on the central horizontal axis of the scanned area. The latter is most clearly observed in Figure 3a and c, whereas the former is discernible in the entire experimental dataset. At a first glance, both minima are somewhat surprising because there is no obvious reason why fewer ions reach the mass spectrometer inlet from areas in direct proximity or the center axis region than from the more remote off-axis regions. Selected ion trajectories, as depicted in Figure 4, show that both minima have similar but quite complex causes. In close proximity to the spray shield, only ions from a relatively small area around the center axis are transported into the capillary because the ions starting in greater distance from the center axis terminate on the spray shield, as clearly discernible in Figure 4a and b. However the neutral analyte concentration close to the central axis is very low because the neutral analyte is washed out by the clean dry gas flow. This is clearly visible in the neutral distribution data obtained from the CFD model also shown in Figure 4. As a result, essentially no ions reach the inlet capillary from the zone in close proximity to the spray shield. Either they terminate on the spray-shield or they are not generated at all because no neutral analyte was present.
Figure 4

Individual ion trajectories. Selected ion trajectories from SIMION/SDS and neutral analyte concentration distribution from the CFD model. The starting positions of the ions were uniformly distributed on a line, irrespective of the neutral analyte mixing ratio. Capillary voltage 1000 V; spray shield voltage 50 V; dry gas flow 3.8L/min. The parameter “D” represents the distance of the ion starting zone from the spray-shield: (a) D = 1 mm, (b) D = 3 mm, (c) D = 5 mm, (d) D = 14 mm

With increased distance to the MS inlet orifice, the situation changes significantly. As Figure 4c and d show, only ions from off-axis regions are transported to the capillary inlet. This is caused by the electrical field gradient, which quickly becomes rather shallow with increasing distance from the spray shield. Here, the fluid dynamic forces generated by the dry gas flow readily overcome the residual electrical attraction of the MS inlet. Therefore, beginning from a minimum distance, which is dependent on the voltage on the inlet capillary cap and the spray shield, ions close to the center ion source axis are transported away from the MS inlet. In addition, even if favorable ion trajectories exist, the mixing ratio of the neutral analyte in the zone around the center axis would still be significantly lowered due to the dry gas flow drag.

One of the most prominent features observed in the experimental data is the rapid shift of the signal maximum with increasing dry gas flow, as stated earlier. A direct comparison of the calculation results for 2.0 and 3.8 L/min dry gas flow shows that in many cases, such a signal shift is also qualitatively reproduced by the simulations. For example, the global signal maximum in the lower half of the simulated DIA for 2.0 L/min dry-gas flow, 1000 V capillary potential, and, respectively, 25 V or 50 V spray-shield potential (Figure 3a, 25 and 50 V), almost disappears in favor of a much more balanced situation at 3.8 L/min dry gas flow (Figure 3b 25 V and 50 V). It is apparent that the signal shift is much less pronounced in the numerical results. However, the general notion that the balance of the signal distribution shifts to the upper half of the simulation domain with increasing dry gas flow is clearly reproduced in a subset of the simulations. Despite this, there are also significant nonsystematic deviations between simulation and experiment observed in the data. A striking example is shown in Figure 3c and d. While in the experimental DIA the change of the dry gas flow leads to a shift of the bimodal distribution to a single maximum in the upper half of the scanned region, the numerical result remains bimodal.

Given the complexity of the entire MPIS system, the match between experiment and simulation is surprisingly good; however, there are also some systematic deviations. Most noticeable is the finding that all simulation results are shifted approximately 2 mm horizontally towards the MS inlet (cf. left plots in Figure 3) and that the simulated spatially resolved ion signal tends to extend more into the ion source volume than experimentally observed. A detailed analysis of individual ion trajectories (see for example Figure 4) reveals that ions from areas more distant to the spray shield are largely transported indirectly to the inlet capillary (cf. Figure 4d) (i.e., they dwell considerably longer in the source enclosure compared with a direct passage). Therefore, the probability of chemical transformation may become significant. Since the concentrations of all neutral species present in the source (i.e., N2, solvents, background oxygen, and background water) are in large excess over the laser-generated ion population, ion molecule reactions are always first order with respect to the ions. We have thus included first order ion decay kinetics in the trajectory model (for details see Experimental and Ref. [19]). As expected, the spread and the intensity of the simulated ion signal, as shown in Figure 5, is affected. With increasing ion reaction probability, the signal from more remote areas is suppressed and the simulated DIAs become narrower. The reaction probability is, therefore, an additional simulation parameter, which has to be estimated correctly for meaningful simulation results when working at elevated pressure.
Figure 5

Variation of ion depletion probability. DIA simulations with different ion depletion probabilities (p). Dry gas flow 2.0 L/min; capillary cap voltage 1000 V; spray shield voltage 25 V

The direct comparison of the simulations and the experimental data in Figure 3 in combination with the reaction probability variation in Figure 5 suggests that the reaction probability was slightly underestimated in the preceding DIA simulations. It should be noted that the actual value of the reaction probability (and, strictly speaking, the reactive behavior of the generated ions in general) is currently not known; without detailed knowledge of the individual reaction pathways in the ion source domain, the reaction probability thus represents a large uncertainty. This issue is subject to a major research effort in our group. Most importantly, the mixing ratios of the reactive background “residual” gases, such as H2O and O2, as well as the LC solvents, have to be known accurately.

Preliminary ion trajectory simulations demonstrated that the position of the capillary cap, which differed slightly in the CFD model and the SIMION model because of the much lower spatial resolution of the calculation mesh in the latter, has a strong effect on the calculated ion trajectories. Therefore, we generated two additional SIMION models with modified geometries in which the capillary was moved 1 mm in both directions on the horizontal (x) axis. Figure S2 in the Supplemental Material shows the results of a simulation subset in comparison to the original geometry (“0 mm” plots in Supplemental Figure S2, the entire simulation data set is also given in the Supplemental Material). The shift of the inlet capillary has indeed a significant effect on the simulated DIA, but not on the general shape of the spatially resolved signal. Instead, the signal distribution is simply shifted on the horizontal axis without severe changes in the signal intensity. The comprehensive set of performed simulations with all geometries, including additional ion trajectory plots, is given in the supplement material.

For the simulation set shown in Figure 3, this finding suggests that the horizontal shift of the simulation results with respect to the experimental DIA is most probably attributable to a slightly inaccurate SIMION geometry. This results partly from the fact that SIMION generally operates with a uniformly-spaced calculation mesh, whereas the resolution requirements differ in the simulation domain. Simply doubling of the spatial resolution would result in an 8-fold memory requirement of the potential arrays and increased simulation runtimes. Despite the higher numerical effort, subsequent simulations with higher spatial resolution, at least in the critical regions, are likely to be justified by the probably higher quality of the simulation results.

3.2.2 3D DIA

Figure 6 shows two examples of fully resolved 3D DIA simulation results. The analysis of the full result data set (cf. Supplemental Material) reveals that the zone where the dry gas flow significantly affects the ion distribution is nearly cylindrical. The rotation symmetry of the ion signal distribution is broken by the nebulizer gas flow, which is injected into the simulation domain in the vertical (y) direction. As a result, a quite complex shape of the 3D DIA is obtained, which is defined by the gas flow structure in the ion source. This is clearly discernible even in the reduced exemplary result set discussed here (cf. Figure 6). The cylindrical segments with low signal intensity in x and y directions are observable in the entire simulation result set (cf. supplemental material).
Figure 6

Examples of simulated 3D DIA. Two examples of 3D DIA simulation datasets. The origin of the coordinate system (0,0 in Figure 1) is marked by the tip of the black cone which corresponds to the orifice of the inlet capillary

With increasing voltages at the MS inlet orifice, the simulated distribution becomes conically shaped and extends further into the volume. The simulation suggests that the pinch visible on the vertical axis is also present in the laser propagation direction, which principally cannot be observed in the 2D DIA projections.

The fully spatially resolved DIA is a complex 3D object. To improve the understanding of the ion acceptance distribution in the spatial dimensions, we created a simple web browser-based viewer, the “DIA explorer”1. This tool allows browsing through the ion source parameter space and the inspection of the 3D DIA from different viewpoints. The full set of DIA simulations and the DIA projections of an experimental dataset are available at the given web address as well.

4 Conclusions

Considering the high complexity of the fluid and electrodynamic conditions present in the MPIS source enclosure, the experimental and numerical results are in very good overall agreement. It follows that the entire simulation process, including the underlying ion trajectory model (SIMION/SDS), the numerical description of the fluid dynamics, and the neutral analyte distribution, as well as the approach to model the DIA measurement process, reasonably describes the actual physical conditions in the ion source. This finding supports the notion that the effects of the investigated ion source parameter variations (i.e., voltages on the MS inlet orifice and dry gas flows) have similar effects on the simulated DIAs as observed experimentally. Based on the quite high complexity of the dynamics in the investigated ion source, we conclude that the chosen numerical approach is generally appropriate to model atmospheric pressure ion optical devices of comparable complexity with reasonable quality.

Given a highly convoluted and, thus, rather difficult to interpret experimental data set as the recorded ion acceptance distribution, the benefits of a comprehensive numerical model for such a system become obvious: generally it appears to be highly challenging—if possible at all—that deeper insights into the dynamics of an ion optical device operated at atmospheric pressure are gained by the examination of experimental results only. The lack of experimental methods that directly observe undisturbed ion trajectories thus can be substituted by a validated numerical model. This validated model allows performing further studies under experimentally inaccessible conditions. In the case of the investigated MPIS AP ion source, the full numerical model, including fluid dynamics, electro dynamics, as well as chemical kinetics, is required to understand the complex genesis of the spatial ion distribution. Despite the useful knowledge provided by the CFD simulation of the ion source, it is rather difficult to deduce the effects that lead to the actual shape of the DIA. In contrast, even the analysis of relatively few simulated ion trajectories gives a very good idea of the dynamics governing the motion of ions within the source. In addition to the general agreement of model and experiment, there are some notable differences. At the current state, the simulations generally tend to overestimate the size of the dynamic ion acceptance volume [20]. This could be readily refined by adjusting critical parameters such as the ion reaction probability but requires further experimental validation. It is noted, though, that in some rare cases this particular adjustment would not necessarily lead to a better agreement.

Considering the complexity of the conditions in the MPIS ion source, a perfect agreement between simulation and experiment is currently not feasible, mainly because at the present stage the numerical model ignores some critical dynamic forces acting on the analyte ions. Probably one of the most important influences is the additional turbulent diffusion, which could significantly increase the dispersion of the individual ion trajectories. It should be possible to estimate the level of additional turbulent diffusion from the local parameters of the turbulence model used the fluid dynamic simulation. Details will be worked out in the future. Other currently missing effects are time-dependent oscillations in the gas flow (for which experimental evidence exists for the present setup when operated at elevated gas flows), a detailed chemical ion–molecule reaction system for the ion source volume domain including wall reactions and space charge effects. Future experimental and theoretical work will focus on these critical aspects of the simulation process.

Despite the approximations used at the current development stage, the effort to generate such a model appears to be justified. Nevertheless, it has to be considered that the generation of a high quality numerical model needs high-level expertise from rather different and often not closely interacting professions, such as fluid dynamics, electro dynamics, gas phase chemistry, and software development.

Footnotes

  1. 1.

    Freely accessible at http://dia.ipams.uni-wuppertal.de

Notes

Acknowledgments

Financial support of the German Research Foundation (DFG project BE BE2124/6-1) is gratefully acknowledged. W.W. acknowledges support through a graduate student research stipend from the Institute of Pure and Applied Mass Spectrometry, University of Wuppertal, Germany.

Supplementary material

13361_2013_646_Fig7_ESM.jpg (160 kb)
Figure S1

Effects of dry-gas volume flow variation in experimental acquired DIA. Capillary voltage 500 V; spray shield voltage 50 V; the dry gas flow is given in the insets. The maximum signal level (brightest contour) is given above each plot. The spatial axes are in mm (JPEG 160 kb)

13361_2013_646_MOESM1_ESM.tif (313 kb)
High resolution image (TIFF 313 kb)
13361_2013_646_Fig8_ESM.jpg (270 kb)
Figure S2

Geometry variations. DIA simulations with different positions of the capillary cap (given in the inset in the plots) in the horizontal direction. The base position (0 mm) was used for the simulations shown in Figures 3 and 4. The dry gas flow (DG) is given on the left side. Capillary voltage 1000 V; spray shield voltage 50 V; ion depletion probability 10–5 (JPEG 269 kb)

13361_2013_646_MOESM2_ESM.tif (527 kb)
High resolution image (TIFF 527 kb)
13361_2013_646_MOESM3_ESM.png (1.4 mb)
Figure S3 Additional set of ion trajectory simulations. Additional set of ion trajectories resulting from SIMION/SDS and the relative neutral analyte concentration distribution from the CFD model for three different positions of the inlet capillary cap (“cap pos.”). The starting positions of the ions were uniformly distributed on a line, irrespective of the neutral analyte mixing ratio. The spray shield voltage was 50 V and the dry gas flow 3.8L/min. The parameter “D” represents the distance of the ion starting zone from the spray shield. The complex electrostatic and fluid dynamic forces acting on the ion motion are clearly observable. The experimental DIAs result from the convolution of the relative neutral concentration with the ion trajectories (PNG 1400 kb)
13361_2013_646_MOESM4_ESM.jpg (46.4 mb)
Low resolution image (JPEG 46 mb)
13361_2013_646_MOESM5_ESM.jpg (87.6 mb)
Low resolution image (JPEG 87 mb)
13361_2013_646_Fig9_ESM.jpg (1.8 mb)
Figure S4

Full set of performed DIA simulations (projections) for three different positions of the inlet capillary cap (“geometry”). The base position (geometry: 0 mm) was used for the simulations shown in Figures 3 and 4. “Sp.-Sh.” is the spray shield voltage, “cap” the inlet capillary voltage, and “dry gas” the dry gas volume flow. The ion depletion reaction probability was set to 10–5 (JPEG 1884 kb)

13361_2013_646_Fig10_ESM.jpg (1.7 mb)
Figure S5

Full set of performed DIA simulations (3D volume renderings) for three different positions of the inlet capillary cap (“geometry”). The simulation raw result data set was the same as in S2. DIA simulations with different positions of the capillary cap (given in the inset in the plots) in the horizontal direction. The base position (geometry: 0 mm) was used for the simulations shown in Figures 3 and 4. “Sp.-Sh.” is the spray shield voltage, “cap” the inlet capillary voltage, and “dry gas” the dry gas volume flow. The ion depletion reaction probability was set to 10–5. The origin of the coordinate system is marked by the tip of the black cone on the left side of the simulation domain (JPEG 1761 kb)

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Copyright information

© American Society for Mass Spectrometry 2013

Authors and Affiliations

  • Walter Wissdorf
    • 1
    Email author
  • Matthias Lorenz
    • 2
  • Thorsten Pöhler
    • 3
  • Herwart Hönen
    • 3
  • Thorsten Benter
    • 1
  1. 1.Institute for Pure an Applied Mass Spectrometry, Physical and Theoretical ChemistryUniversity of WuppertalWuppertalGermany
  2. 2.Chemical Sciences DivisionOak Ridge National LaboratoryOak RidgeUSA
  3. 3.Institute of Jet Propulsion and TurbomachineryRWTH Aachen UniversityAachenGermany

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