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Differential Mobility Spectrometry-Mass Spectrometry for Atomic Analysis Francy L. Sinatra, Tianpeng Wu, Spiros Z. Manolakos, Jing Wang, and Theresa Evans-Nguyen Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/ac503466s • Publication Date (Web): 18 Dec 2014 Downloaded from http://pubs.acs.org on December 23, 2014
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Differential Mobility Spectrometry – Mass Spectrometry for Atomic Analysis Francy L. Sinatra†, Tianpeng Wu‡, Spiros Manolakos†, Jing Wang‡, and Theresa G. Evans-Nguyen†* †
Draper Laboratory, 3802 Spectrum Blvd. Ste 201, Tampa, FL 33612 Department of Electrical Engineering, 4202 E. Fowler Ave., ENB 118, The University of South Florida, Tampa, FL 33620 ABSTRACT: Analysis and separation of atomic ions within a portable setting is studied in forensic applications of radiological debris analysis. Ion mobility spectrometry (IMS) may be used to show separation of atomic ions, while the related method of differential mobility spectrometry (DMS) has focused on fractionation of primarily molecular components. We set-out to investigate DMS as a means for separating atomic ions. We initially derived the differential ion mobility parameter, alpha, from classic empirical IMS data of atomic ions, cesium and potassium, each showing its own distinct form of alpha. These alpha functions were applied to DMS simulations and supported by analytical treatment that suggested a means for a rapid disambiguation of atomic ions using DMS. We validated this hypothesis through the prototype cesium-potassium system investigated experimentally by DMS coupled to mass spectrometry (MS). Such a feature would be advantageous in a field portable instrument for rapid atomic analyses especially in the case of isobaric ions that cannot be distinguished by MS. Herein, we first report this novel method for the derivation of alpha from existing field dependent drift tube ion mobility data. Further, we translate experimental DMS data into alpha parameters by expanding upon existing methods. Refining the alpha parameter in this manner helps convey the interpretation of the alpha parameter particularly for those new to the DMS field. ‡
INTRODUCTION Atomic analysis can be performed by various laboratory scale spectrometric methods with ICP-MS being the most universal and sensitive, according to a recent report by Hart et al.1 It was noted in the report, that for the small niche application market including nuclear forensic screening, portable elemental/isotopic MS instruments have yet to be realized. Portable MS analyses for public spaces (subway systems, administrative buildings and airports) would ideally leverage atmospheric pressure ionization (API) with minimal sample preparation. API is potentially problematic due to complex gas phase processes, which lead to the formation of a vast number of ionic molecular species. Such interferences in field conditions increase false alarm rates to unacceptably high levels. To mitigate this challenge, MS may be combined with other fast separation methods. This approach enhances the detection accuracy of the system as a result of: (a) selection of targeted species before introduction in the MS analyzer and (b) providing additional orthogonal chemical information for targeted species in a portable format. In elemental analysis using gold standard laboratory ICP-MS, small polyatomic interferences are reduced by collision/reaction cells.2 However, isobars of other elements (e.g., Nickel-59 and Cobalt-59) can interfere in the accurate and quantitative analysis of atomic species. Ion mobility spectrometry3 (IMS) separates ions along a static electric field parallel to a gas flow. Based on their individual low field mobilities, ions achieve different terminal velocities to yield different times of flight to the detector. On the other hand, the derivative technology differential mobility spectrometry (DMS),4 selectively passes targeted ions by employing a dynamic electric field perpendicular to the flight path. Based on individual alpha parameters that characterize differential ion mobilities between high and low electric fields, only certain ions reach the detector. In operation, DMS is comparable to the quadrupole mass filter in that RF and DC
voltages are set to allow only a narrow range of ions to pass. In DMS, sample ions are transported by a flow of clean carrier gas (e.g. air or nitrogen) between two parallel plate electrodes. Transverse to the flow, the electrodes impart an asymmetric RF electric field whose amplitude in one polarity is defined by the high field dispersion voltage (Vrf). The RF electric field causes the ions to move with a ―zigzag‖ up/down motion as they move towards the channel’s exit.5 When Vrf is large enough (E > 1000 V/cm), the resulting trajectories of the different ion species produce a net displacement along the axis of the electric field. Ions which accumulate a net zero displacement pass through the analytical gap to be detected; otherwise, ions are neutralized on the electrodes. To ―tune‖ the DMS sensor to pass a desired targeted ion species, a variable DC potential, known as the compensation voltage (Vc), is additionally applied across the two analytical electrodes. Vc serves to finely adjust the ratio of the high and low field asymmetry. The characteristic Vrf x Vc dispersion plots in DMS, represent ion stability conditions that uniquely constitute a fingerprint identification of the ion species. Conditions under which the ions reach the exit subtly reveal the individual effective alpha parameters, αi(E/N) which can be considered analogous to the a, q terms of the Mathieu stability parameters defined for quadrupole devices. When certain Vrf x Vc combinations are applied, only ions with specific alpha parameters survive transport through the DMS. The tunable specificity that DMS imparts has been successfully implemented in defense,6 proteomics,7 and pharmaceutical8 applications, even unraveling structural isomers. 9 Nonetheless, these examples demonstrate primarily molecular ion separations while literature on atomic ion analysis by DMS is sparse.10–12 Furthermore, while DMS has become more widely practiced, the understanding of the alpha parameter remains superficial. In this work, we study the potential use of DMS for elemental/atomic analysis applications by first extrapolating elemental/atomic IMS data in terms of the DMS alpha
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Analytical Chemistry parameter. Furthermore, we apply SIMION simulations, analytical calculations, and DMS-MS experiments to a prototypical cesium and potassium system to explore DMS’ separation capability for these two atomic species. To characterize our investigation, a clear discussion and definition of the uniquely identifying ion signature, the effective alpha parameter, is required.
Ion Mobility, Field Dependence, and Alpha The relation between ion drift velocity and the electric field is related by the ion mobility coefficient under specific temperature and electric field conditions: vd K * E
(1)
where vd is the ion drift velocity, E is the applied electric field, and K is the ion mobility coefficient. According to Mason and McDaniel,13 the coefficient of mobility depends non-linearly on the strength of the electric field and the number gas density. Additionally, the mobility coefficient must be independent of the electric field polarity.14 Thus, the mobility coefficient can be presented by an n term even power polynomial series:
K ( E / N ) K (0)[1 2 * ( E / N ) 2 ... 2n * ( E / N ) 2n ] (2) where K(0) is the coefficient mobility of ions at low (E=0) electric field conditions, and the alpha coefficients: 2, 4, 6, …, 2n are dependent on the ratio of E (electric field) to N (gas density) usually represented by the Townsend unit (1Td = 10-17 V-cm-2). The mobility function then implicitly depends on pressure, recalling that P ~ 1/N. The combination of all alpha parameters can characterize the behavior of changing K under the effect of any electric field assuming constant pressure. Theoretically, the number of terms n in Equation 2 is unlimited but we studied 3 - 6 terms to sufficiently span the range of E/N used in our experiments. In 1993,15 the effective alpha parameter function, eff(E/N), was introduced as a ―fingerprint‖ for individual ion species:
(3) eff ( E / N ) 2 * ( E / N ) 2 4 * ( E / N ) 4 ... 2n * ( E / N ) 2n In this case, the coefficient of mobility can be presented by substituting Equation 3 into Equation 2: K ( E / N ) K (0)[1 eff ( E / N )]
(4)
By transformation of Equation 4, the effective alpha parameter can be defined from experimental measurements of K(E/N)16:
eff ( E / N )
K ( E / N ) K (0) K ( E / N ) K (0) K (0)
(5)
According to Equation 5, the alpha term is a unit-less parameter represented as the ratio of the differential mobility ΔK(E/N) = K(E/N) − K(0) to the value of low field ion mobility K(0). In this interpretation, the alpha parameter characterizes the level and direction of the changing coefficient of mobility under the influence of an electric field. Thus, if the ion’s coefficient of mobility increases with increasing electric field, then the alpha parameter is positive; and if the coefficient of mobility decreases with increasing electric field, then the alpha parameter is negative. This concept is the principle for chemical separation at ambient pressure conditions in the DMS method. Variations in the alpha parameter are based on the nonlinear dependence of the ion’s velocity on the electric field, causing changes in the effective cross-section and the mean free path.13,15–17 These changes are encompassed by five main physical-chemical mechanisms, which stem from ion molecule interactions18. 1) elastic scattering caused by polarization of gas molecules due to nearby slow moving ions; 2) resonant charge transfer be-
tween similar structure neutral molecules and ions; 3) scattering due to ―direct‖ contact (ion-neutral rigid sphere interactions); 4) clustering and de-clustering of ions imposed by the asymmetric RF waveform; and 5) changes in molecular conformation (dipole alignment) due to effective temperature (ion internal energy) and strong RF electric field. These individual mechanisms are described in detail by Mason and McDaniel13 and together contribute to the overall ion behavior observed in experimental DMS dispersion plots.
Transformation of atomic ion experiments from IMS to DMS Effective alpha parameters were obtained for DMS from existing experimental measurements of coefficients of mobility in IMS by means of Equation 5. Cesium19 and potassium20 ion mobility coefficients in nitrogen gas were taken from atomic tables collected by Ellis and McDaniel across a range of E/N (in which N was constant) and transformed into alpha effective as shown in Figure 1. For example for cesium, at an E/N of 120Td, K = 2.47; and, at an E/N of 7Td, we take K(0) = 2.21, so that eff calculates as 0.118 by Equation 5. In this manner, other similar atomic data for different ion-neutral systems19–21 could be transformed for estimations of alpha effective. The alpha effectives of both cesium and potassium were fitted to Equation 3 for the range of electric fields from 0 to 200Td used in practice. Expansion of alpha into a polynomial of five even order terms were shown to optimally characterize this range of E/N. The fitted alpha parameters are tabulated in Table 1, achieving a fit of 0.997 adjusted R-square for cesium and 0.99924 for potassium. The comparison of alpha effective particularly between 150 and 200Td suggests that DMS could easily differentiate the pair. Ion trajectory simulations were thus used to predict DMS separation in nitrogen for the prototypical cesium, potassium pair. 0.25 Cs Alpha Effective Cs Fitted Alpha
0.2
K Alpha Effective
Alpha Effective
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0.15
K Fitted Alpha
0.1 0.05 0 0
50
100
150
200
E/N (Td) Figure 1: A plot of fitted alpha effective for classical potassium and cesium in nitrogen gas drift tube IMS experiments from references 19 and 20.
Simulation and the alpha effective function input Modeling ion transport in the DMS sensor has been performed by a small number of groups to facilitate instrument design and development. The first reported method was the MicroDMx software developed in-house by Sionex which commercialized the DMS technology.22 Using SIMION’s Statistical Diffusion Simulation, or ―SDS‖ module,23 Prasad and co-workers developed the DMS model currently distributed with SIMION.24 The model directly incorporates empirical alpha effective parameters to two terms, and, more recently, flow profiles calculated from COMSOL Multiphys-
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ics.2524,26,27 DMS modeling using solely finite element analysis methods such as COMSOL has also been performed.28,29 Table 1: Fitted alpha effective parameters derived from Ellis and McDaniel data19,20 Parameter
Cesium
Potassium
-2
3.88E-6
1.02E-5
-4
9.14E-10
-8.89E-11
-6
α6 [Td ]
-6.11E-14
-3.11E-15
α8 [Td-8]
1.44E-18
6.61E-20
-10
-1.19E-23
-3.53E-25
α2 [Td ] α4 [Td ]
α10 [Td ]
In the interest of time, we adapted the default SIMION DMS model to include our derived alpha parameters. This practical model allowed us to relate the more widely available IMS data to the DMS platform and test our hypothesis regarding atomic ion separation. In this process, we translated derivations of ostensibly different alpha mobility parameters for cesium and potassium, and input them into the simulation methods to realize a theoretical DMS separation. We were then able to compare these simulations to experimental results on a custom-built DMS system integrated to a commercial mass spectrometer. Finally, we also investigated a numerical method translating experimental DMS ―spectra‖ comprised of Vrf x Vc dispersion plot data to the effective alpha parameter to seek agreement with the simulation methods.
METHODS Simulation methods Ion trajectory simulations were modeled primarily using SIMION 8.1 (Scientific Instrument Services, Ringoes, NJ) which was supplemented by COMSOL Multiphysics 4.3a (COMSOL Inc., Burlington, MA). They were performed to simulate the transport of ions within the prototype DMS sensor geometry, with effective electrode dimensions of 15mm x 5mm separated by a gap of 0.5mm. The SIMION model employed a three-dimensional geometric array, while also incorporating a three-dimensional carrier gas flow profile array from COMSOL. The primary geometry to simulate was the analytical gap between the DMS sensor electrodes, where the ions travel by flow of the neutral gas and experience oscillations due to forces applied by the RF asymmetric high electric field. The carrier gas profile in the SIMION field asymmetric waveform ion mobility spectrometry (FAIMS) model is set to uniform flow by default. However, a customized non uniform gas flow profile was implemented to the SIMION model, by importing the velocity data in the x, y, and z direction from a three-dimensional COMSOL Multiphysics model (Figure 2). With COMSOL, the laminar flow module was solved for steady state conditions of the Navier-Stokes equations detailed in Table S-1 of the Supplemental Information. The density and viscosity values were defined for a nitrogen carrier gas at a temperature of 200 °C and pressure of 1atm. A uniform normal velocity of 10 m/s was specified at the inlet, with a zero-pressure outlet and no-slip fluid—wall interface boundary conditions. The carrier gas flow profile followed a parabolic distribution, with a maximum x-direction velocity close to 14 m/s.
Figure 2: A 3D carrier gas flow profile is incorporated into the DMS model in SIMION, the x-y plane cross-sectional view shows that the carrier gas has a parabolic flow profile.
The dispersion voltage (Vrf) and compensation voltage (Vc) are applied together on the top DMS electrode, while the bottom electrode is grounded. For a specific Vrf, SIMION scans the Vc voltage over a designated range to calculate ion trajectories in each Vrf x Vc combination. The SIMION time step resolution is set at a constant 50 ns, during which the electric fields are calculated throughout the DMS potential array coupled with the gas flow profile as a composite of input forces to determine ion motion. The DMS model solves for ion speed and mean free path based on variables of mobility, alpha, ion mass, and hard sphere diameter. In our simulations, the default two alpha term model was augmented to five alpha terms to accommodate the fits of the cesium and potassium alpha effective. Additionally, at each time step, the SDS model incorporates the time-dependent electric field conditions determined by the applied waveform. In order to reduce the computational resources needed for the SIMION simulation, diffusion and space charge effect functions were disabled. 1
Normalized RF Amplitude
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0.8 0.6 0.4 0.2 0 -0.2
0
0.2
0.4
0.6
0.8
1
-0.4 -0.6
Normalized Time Period
Figure 3: The experimental Vrf waveform measured was condensed to 86 points and utilized in the SIMION simulation.
Simulations can easily incorporate idealized Vrf waveforms of a two harmonic generator using a bisinusoidal function. However, the true applied waveform shape is critical to the dynamics of ion motion.14 Therefore, we measured the experimental waveform from the Sionex flyback generator described by Krylov et al.30 The normalized waveform is shown in Figure 3 and was re-scaled to Vrf in SIMION to accurately depict the applied dynamic fields experienced by the ions. The duty cycle corresponds to 33% positive amplitude and 67% negative amplitude. To achieve a net ion displacement of nearly zero, the summation of the area under the curve of the combined positive and negative portions of the RF waveform must
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equal to zero. In SIMION, the Vrf is applied with maximum amplitudes ranging from 500V (64.5 Td) to 1500V (194 Td) with increments of 100V. Except where noted, the number of points used to characterize the waveform was limited to 86. Each Vc run is initialized with the set-up of ion source conditions. Ion introduction occurred from the front of the DMS sensor electrodes, with 10 ions released in a Gaussian distribution with a full width half maximum of 0.15mm centered across the y-axis. The ion initial velocity direction and magnitude were defined by the imported carrier gas profile. The input alpha terms allow for the DMS sensor to selectively transmit ions when sweeping the Vc for a specific Vrf. Under these conditions, the Vc compensates for the effect of the asymmetric waveform Vrf pulses on the effective trajectories of selected ion species along the axis of the analytical gap. In Figure 4a, a simulation of ion trajectories is simulated when a Vrf x Vc of 1000V x -13.5V is applied. SIMION predicts that for a potassium-cesium mixture, potassium ions (green), will exit the DMS sensor, while cesium ions (blue) will collide with the electrode walls before reaching the end of the analytical gap. Alternatively, in Figure 4b, the opposite case occurs at a Vrf x Vc of 1000V x -14.5V in which the cesium passes but the potassium ions collide with the electrodes. For each Vc run, SIMION reports the number of ions passing through the exit of the DMS sensor. Notably, simulations including the experimental interface between the DMS and MS inlet yielded no observable ion losses between the DMS exit and the MS inlet. The MS inlet was thus removed from all subsequent simulations for the sake of simplicity.
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pillary. The Sionex electronics were floated to accommodate the high voltage of the Agilent capillary inlet which typically employed from -1700V to -2000V nanospray voltage. The manual nanospray interface was used to introduce a flow of the salt solution in a 75/25 acetonitrile/water mixture. The cesium chloride was introduced with a concentration of ~10M. The cesium chloride/potassium chloride mixture also employed a concentration of ~10M of each salt. The 200˚ C drying gas (nitrogen) flow was operated at ~4L/min and used to heat the DMS chips via channels through the polyimide adapter. Notably, no accommodations are currently afforded in our experimental set-up to maintain constant ion source sampling conditions for system pressure and solvent exclusion from carrier gas composition. Synchronization was performed manually between the Sionex Expert control software and the Agilent MassHunter data acquisition software. Dispersion plot data was derived from extracted ion chronograms using Labview 2013 and visualized using OriginPro 9.0 (OriginLab Corp., Northampton, MA) software.
RESULTS & DISCUSSION Prior DMS literature has described the ion oscillation behavior over the residence time in alternating electric fields, as well as the role of diffusion and space charge effect on ion transmission efficiency and spectrum peak width. 24 In this work, the Vc scanning spectrum was studied to explore the ion behavior over a range of electric field strengths. We incorporated the experimentally derived RF waveform into SIMION simulations and analytical methods. Alpha parameters for potassium and cesium ions were derived from Table 1. Diffusion was not included within the simulations given that diffusive effects are insignificant during the short residence time (1-2milliseconds) ions spend in the DMS analytical gap.
DMS separation through simulation and experiment Simulation results of a Vc scan are shown for each incremental Vrf for the hypothetical mixture of potassium and cesium ions in Figure 5. A general trend exhibiting lower peak Vc at increasing Vrf are shown in the simulation series for both ions. Slight (~1V) separation between cesium and potassium across the explored range of Vrf is observed but appear inseparable at 900V at which point, the peaks switch their relative position. Both potassium and cesium are small ions with electron configurations of noble gases that belong to the alkali group in the periodic table. The relative effect of the heavier cesium ion with its more expansive valence shell configuration, versus the potassium electron configuration, is clearly influenced by different dominating phenomena at the lower and higher fields, indicated by the transition at 900V rf. The trend may be attributed to, among other phenomena, greater clustering and effective cross section of the cesium ion. Simulation results are displayed alongside experimental reFigure 4: The SIMION ion trajectories for cesium (Cs, blue) and potassium (K, green) at an RF dispersion voltage of 1000V. a) A sults for a cesium and potassium mixture in Figure 6a. Decompensation voltage of ~-13.5Vc is shown to pass K while noted by open circles, the simulation results, are achieved neutralizing Cs in the DMS channel. b) At ~ -14.5Vc, Cs survives using greater time-point sampling (up to 829 points for the the DMS filtration while K is terminated. input RF electronic waveform) than the simulations presented in Figure 5. The experimental DMS-MS data was derived Experimental DMS methods from extracted ion currents of m/z 38.9 and 132.9, An experimental design for the DMS was incorporated on representing the bare ions of potassium and cesium, respecan Agilent 6230 TOF-MS (Agilent Technologies, Santa Clara, tively. The experimental peak current results, indicated by the CA) and has been described previously.31 Briefly, planar cesolid circle markers, show considerable overlap between the ramic DMS chips featuring thin film metal deposition electwo species up until a Vrf of 1100V is reached. At 1300V, trodes from the commercial Sionex instruments were adapted ~2.5V separates cesium and potassium, which indicates pracin Vespel polyimide to the inlet of the TOF-MS, drawing tical filtration parameters between the two ions. The overall ~1.2L/min through a 0.6mm inner diameter glass transfer catrend of decreasing Vc with increasing Vrf is recapitulated exACS Paragon Plus Environment
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perimentally which lends confidence to our derivation methods and simulation model. Upon closer inspection, we note that the relative experimental position of the cesium and potassium are the reverse of the simulation at the higher observed electric fields.
a) Compensation Voltage - Vc (V)
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700
900
1100
1300
0 -5 -10 -15 -20
Cs, Simulation K, Simulation
-25
Cs, Experiment K, Experiment
-30
Dispersion Voltage - Vrf (V)
b) Cs+
[Cs+H2O] +
[Cs+CH3CN]+
K+
[K+H2O]+
Figure 6: a) SIMION and DMS-MS experimentally collected dispersion plot for a cesium and potassium mixture. b) The mass spectra collected at Vrf of 1400V: top at ~-22Vc, bottom at ~24Vc.
Figure 5: Vc scan spectra of successive Vrf simulations in SIMION illustrate separation between cesium and potassium ions across the compensation voltage at various Vrf.
We attribute the reversal between simulated and experimental data shown in Figure 6a to the different ion source conditions of the simulation (based on the IMS alpha derivation) and our DMS instrument. First, the simulation data was based on IMS data calculated from primarily neat analytes while the DMS practically used a mixture of the two analytes. Therefore, interactions between the primary cesium and potassium components are inherently excluded in the simulated separation. Second, the ions are introduced from a thermal ionization source in the IMS experiments but from a nanoelectrospray source in the DMS experiments. The presence of residual solvent vapor(s) in the DMS experiments introduces another chemical component to the ion-neutral system that is not matched in the simulations. Indeed, in the mass spectra of the mixture run at the Vrf of 1400V, shown in Figure 6b, the [M+H2O]+ water adducts are observed for both the cesium peak, at -22Vc, and the potassium peak, at -24V. Additionally, the acetonitrile adduct for cesium, [Cs+CH3CN]+ is seen at m/z 173. Overall, we observe a general agreement between the simulation and experimental Vrf x Vc pairs as we demonstrate proof-of-concept DMS separation for these closely related atomic species. Further comparison was made between the SIMION simulation results and experimental DMS-MS data gathered for cesium alone. As shown in Figure 7, trends are still similar for both the simulation and the experimental data, where the curves at the low RF voltages =
𝑇 𝑛 𝑓 0
𝑡 𝑑𝑡
(7)
where f(t) represents the function of the normalized RF waveform and T the waveform period. Errors are notably introduced during calculation of the form-factor dependent on the size of the time-step used. Using the coefficients of the fitted odd-polynomial and the calculated form-factors as inputs, the initial alpha coefficients are then calculated according to Krylov,14 by solving Equation 9 for alpha: 𝑐2𝑛+1 = 𝛼2𝑛 < 𝑓 2𝑛 +1 > − 1 𝛼2(𝑛−𝑘)
𝑛−1 𝑘=1 𝑐2𝑘+1
2 𝑛−𝑘 +
(8)
where 𝑐2𝑛 +1 is the corresponding coefficient for the experimentally fitted data, 𝛼2𝑛 yields the 𝛼2 term for n=1 and < 𝑓 2𝑛 +1 > is the form factor which equals to < 𝑓 3 > for n=1. In our final alpha calculation, we use five terms. So to calculate five terms of the initial alpha parameter (α2, α4, α6, α8, α10), it is necessary to start with fitting a five term polynomial to the experimental data (c3, c5, c7, c9, c11) and calculate six form-factors (< 𝑓 2 >, < 𝑓 3 >, < 𝑓 5 >, < 𝑓 7 >, < 𝑓 9 >, < 𝑓 11 >). In this manner, initial alpha parameters were calculated for two, three, four, five, and six alpha terms.
SIMION Simulation (Ellis & McDaniel Effective Alpha)
-55
Dispersion Voltage - Vrf (V)
Figure 7: Dispersion plots for cesium ions from SIMION simulation and experimentally DMS-MS collected data.
Alpha Effective Derivation from DMS Experimental Data To explore the variations in alpha effective between Ellis’ experimental IMS data and our experimental DMS data, we employed an analytical solver to calculate from alpha to V rf x Vc. This analytical method was found to be consistent with our simulations and is described in greater detail in the Supplemental Information. Conversely, we also leveraged a method to calculate, from experimental Vrf x Vc to alpha. The calculation of an initial set of alpha values from experimental Figure 8: Comparison of calculated and experimental peak posiVrf x Vc was developed following the methodology of Krylov tions for cesium by a retrofit of derivative initial alpha parameter 14 et al and subsequently adjusted in an iterative manner to from experimental DMS-MS data. The black trace corresponds to reach agreement with the experimentally collected DMS-MS experimentally measured DMS-MS data for cesium. The comdata. In other words, the conversion of a fit to the experimenpensation voltage and RF dispersion voltage pairs were rebuilt for tal Vrf x Vc data for effE/N) was validated by the forward effective alphas using two, three, four, five and six terms. conversion of effE/N) to Vrf x Vc through the analytical meThe fit of the calculated alpha parameters to the experimenthod. Ultimately, the final effE/N) values were used as input tal data was subsequently checked by calculating the respecinto SIMION to corroborate the evaluation. tive Vrf x Vc voltage pairs needed for ion detection as deA thorough derivation of the initial alpha parameters from scribed in the Supplemental Information. It was found that the corresponding DMS data can be found elsewhere.14 Briefly, dispersion plots for these initial alpha calculations yielded odd polynomials using two, three, four, five and six terms ACS Paragon Plus Environment
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poor agreement to the experimental data as shown by comparison of the black circles and the other traces in Figure 8, where the trends for the low Vrf voltages (0V – 800V) were similar, but significantly deviated for the high Vrf voltages (1000V – 1500V). Several errors were introduced during the initial alpha calculation; specifically, during the fitting of the polynomial to the experimentally gathered data and during the calculation of the form-factors. These errors are logically increased for higher calculated alpha terms (α8, α10) involving higher powers. This explains the relatively good match between the calculated alpha parameters for low electric fields, but the greater deviation seen for the higher electric fields. Subsequently, to achieve alpha values that more closely matched the DMS-MS experimentally gathered dispersion plot; a manual iterative process was followed to further refine alpha and achieve a final alpha effective for neat cesium data. This novel approach for calculation of a final alpha effective utilizes the initial alpha calculation mentioned above, which is described in detail by Krylov.14 The calculated five alpha term equation was used as the initial parameter, and through fine iterative tuning, final alpha values were achieved by reducing the variance between the Vrf x Vc dispersion curve from the calculated alpha and the DMS-MS experimentally gathered results. The initial and final alpha coefficients are listed in Table 2. Figure 9 shows the fitted dispersion curve for the final analytically calculated alpha effective from the experimental data, the raw experimental data points, and the SIMION simulation results. Agreement is seen between the experimental data and the SIMION simulation for low electric fields (500V – 1000V), where the slopes of both curves are almost identical (indicating a good effective alpha match) despite the ~2V difference between them. Slightly greater deviations are seen for the higher electric fields (>1000V), where the slope of the two curves start to slowly diverge from one another as the Vrf is increased. The Vc voltage difference between the experiment and the simulation can be due to numerical errors introduced during the effective alpha fitting, which are amplified as the electric field increases. Table 2: Comparison of initial and final calculated alpha parameters from DMS experimental data. Parameter
Initialized alpha
Refined alpha
α2 [Td-2]
-1.17E-05
-1.80E-05
α4 [Td ]
2.56E-10
6.40E-10
α6 [Td-6]
2.85E-14
2.81E-14
-8
α8 [Td ]
-2.46E-18
-2.44E-18
-10
5.68E-23
4.10E-23
-4
α10 [Td ]
The effective alpha parameter is unique to each ion species and theoretically independent of experimental physical conditions of pressure, temperature, flow, and the specific DMS sensor utilized. Thus, determination of alpha parameters from experimentally gathered data allow for ion identification, instrument comparison and a unification of data gathered across DMS sensors.
500
Compensation Voltage - Vc (V)
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Dispersion Voltage - Vrf (V) Figure 9: Comparison of experimental data and analytical calculation using alpha parameters fitted to experimental data for cesium.
CONCLUSION As part of a study for the analysis of inorganic species relevant to radionuclear forensics applications, we have described a modeling approach that informs the development of DMS for elemental/atomic ion separation directly in ambient pressure conditions. Furthermore, we have successfully performed experiments with an integrated DMS-MS instrument to corroborate the separation capability of the prototypical atomic ion pair, cesium and potassium. Finally, an analytical model from prior literature was implemented with further refinements, which yielded an alpha effective that closely matched the DMS-MS experimentally collected data and was subsequently compared to simulations. Initial inspection of drift tube IMS data for the alkali metal ions of cesium and potassium suggested a feasible, though small, DMS separation of the two alkali species at various E/N conditions. Though neither the simulations nor the analytical model incorporated diffusion phenomena or wide starting ion source conditions (to simply focus on average trajectory), the separation could have been negligible with respect to the effective peak-widths of the true ion swarm. The corresponding experimental DMS-MS separation of the two ions implied the same general trend but demonstrated a practical separation between cesium and potassium. The difference between the dispersion plots derived from IMS experimental data to the actual experimental separation, points to the different experimental conditions under which the mobilities were measured. From experience, the incomplete control of trace impurities in the carrier gas and water vapor content speaks to a chemical sensitivity with variable error from this dopant effect. Notably, the ion source conditions in the IMS used thermal ionization while those in the DMS were nano-sprayed from salt solutions. The neutral carrier gas thus potentially comprised volatile solvents from the solution in addition to the pure nitrogen carrier gas. By extension, an implicit limitation of the theoretical atomic ion separation is the assumption that negligible interaction exists between analyte species because, from the ion source, they may realistically exist in both the ion and neutral state and thus contribute to clustering interactions. In other words, a neat cesium ion sample in nitrogen gas will not necessarily exhibit the same alpha behavior as cesium in the presence of potassium because of an unaccounted for interaction potential. Under nominally concentrated ion source conditions, the separation of atomic ions may depend considerably on the ion sampling and transfer methods into the DMS.
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To aid in further definition of the alpha term for our atomic ion comparisons, a derivative process to translate DMS dispersion behavior into the effective alpha was leveraged from the literature. The comparative process of the clearly different experimental systems provides a means of standardizing the alpha parameter across instrumental differences. For our immediate purposes, this serves to guide our development of DMS for atomic ion separation but also may serve as a template for others seeking a unified interpretation of the alpha effective parameter. Future work will apply these methods to characterize specific isobaric systems comprising a homologous series such as cobalt, nickel, and copper.
ASSOCIATED CONTENT Supporting Information Supporting material include a list of the relevant equations used to derive the COMSOL flow model used in SIMION. Further details regarding the equations and the analytical solution to derive Vrf xVc pairs are provided in this supplement as well. This material is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION Corresponding Author
*To
whom correspondence should be addressed. E-mail:
[email protected], Phone: 813-465-5464
ACKNOWLEDGMENT This work was supported by grant number HDTRA-11-01-0012 from the Defense Threat Reduction Agency Basic Research Program in Nuclear Forensics. We recognize Mr. Adrian Avila at the University of South Florida for early COMSOL particle trajectory simulation studies. We express deep gratitude to Dr. Erkinjon Nazarov at Draper Laboratory for insightful discussion and abundant guidance. Additionally, at Draper Laboratory we thank: for assistance in the implementation of the DMS electronics, Mr. James Alberti; for the mechanical interface design: Mr. Kevin Hufford; and for technical assistance, Mr. Mark Sweeney. Finally, we thank Mr. David Manura at Scientific Instrument Services for aid in the modification of the SIMION user programs for our specific simulations.
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