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Ejection of Coulomb Crystals from a Linear Paul Ion Trap for Ion− Molecule Reaction Studies K. A. E. Meyer,†,‡ L. L. Pollum,† L. S. Petralia,† A. Tauschinsky,† C. J. Rennick,† T. P. Softley,† and B. R. Heazlewood*,† †

Department of Chemistry, University of Oxford, Chemistry Research Laboratory, 12 Mansfield Road, Oxford, OX1 3TA, United Kingdom ‡ Institut für Physikalische Chemie, Georg-August-Universität Göttingen, Tammannstraße 6, D-37077 Göttingen, Germany S Supporting Information *

ABSTRACT: Coulomb crystals are being increasingly employed as a highly localized source of cold ions for the study of ion−molecule chemical reactions. To extend the scope of reactions that can be studied in Coulomb crystals from simple reactions involving laser-cooled atomic ions, to more complex systems where molecular reactants give rise to multiple product channelssensitive product detection methodologies are required. The use of a digital ion trap (DIT) and a new damped cosine trap (DCT) are described, which facilitate the ejection of Coulomb-crystallized ions onto an external detector for the recording of time-of-flight (TOF) mass spectra. This enables the examination of reaction dynamics and kinetics between Coulomb-crystallized ions and neutral molecules: ionic products are typically cotrapped, thus ejecting the crystal onto an external detector reveals the masses, identities, and quantities of all ionic species at a selected point in the reaction. Two reaction systems are examined: the reaction of Ca+ with deuterated isotopologues of water, and the charge exchange between cotrapped Xe+ with deuterated isotopologues of ammonia. These reactions are examples of two distinct types of experiment, the first involving direct reaction of the laser-cooled ions, and the second involving reaction of sympathetically-cooled heavy ions to form a mixture of light product ions. Extensive simulations are conducted to interpret experimental results and calculate optimal operating parameters, facilitating a comparison between the DIT and DCT approaches. The simulations also demonstrate a correlation between crystal shape and image shape on the detector, suggesting a possible means for determining crystal geometry for nonfluorescing ions.

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adapted by fields ranging from fundamental research to the applied sciences. In the field of “cold chemistry”, the kinetics and dynamics of ion−molecule reactions are being increasingly studied using Coulomb crystals.2−6 Coulomb crystals are highly ordered and localized structures, formed when atomic ions held within an ion trap are laser cooled. The ability to “sympathetically cool” a diverse range of cotrapped (nonlaser-cooled) ionic species− both atomic and molecular−into a Coulomb crystal makes examining ion−neutral reactions in such an environment very attractive: one can exert significant control over the properties of reactant ions, and can also typically trap and cool product ions into the crystal, because of the depth of the traps employed. The exquisite control that can be exerted over

INTRODUCTION

Time-of-flight mass spectrometry (TOF-MS) has become an almost ubiquitous tool in chemical analysis, and is widely used throughout the scientific community to determine the masses of species in a given sample. In most applications, a mixture of ions with low initial kinetic energy and a narrow spatial distribution are accelerated through electrostatic potentials to near-identical kinetic energies. Species of a given mass are thus imparted with near-identical velocities. When the mixture passes into a region of free flight and onto a detector, species of the same mass exhibit near-identical arrival times. In 1955, Wiley and McLaren proposed a variation of TOF-MS with favorable mass resolution properties.1 The two-stage acceleration design of Wiley−McLaren TOF-MS serves to compensate for the initial spatial distribution of ion positions. Ions are formed between two electrodes, termed the repeller and extractor, which are charged such that they direct the ions toward a third (grounded) electrode and into a region of free flight. In the 60 years since the principle was first introduced, Wiley−McLaren TOF-MS has been widely adopted and © 2015 American Chemical Society

Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics Received: August 14, 2015 Revised: September 24, 2015 Published: September 25, 2015 12449

DOI: 10.1021/acs.jpca.5b07919 J. Phys. Chem. A 2015, 119, 12449−12456

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The Journal of Physical Chemistry A Coulomb crystals also makes these highly localized systems ideal for high-resolution spectroscopic measurements in molecular ions,7−9 with potential applications to frequency metrology, the refinement of fundamental constants and quantum logic.10−12 To probe the kinetics and dynamics of cold ion−molecule reactions, one must have the ability to quantitatively detect all product ions as a function of time. For simple reactions involving few ions, in situ radiofrequency (RF) mass spectrometry (MS) can be used, which takes advantage of the distinct motional frequencies of small crystals with particular mass combinations present.13−18 However, the technique has insufficient resolving power for larger crystals composed of several different species.3 Multispecies crystals are the likely outcome for reactions of molecular species with any degree of complexity. Mass identification for such crystals has recently been achieved using Wiley−McLaren TOF-MS, whereby the cylindrical ion trap electrodes adopt the role of repeller and extractor plates. The RF trapping voltages are switched off and static repeller and extractor voltages are applied to the ion trap electrodes, ejecting the ions toward a grounded mesh and into a time-of-flight (TOF) tube. A number of such TOF-MS approacheswith ions ejected from a linear Paul traphave been detailed.19−22 Of particular relevance is our previous work, with digital trapping fields, and the work of Hudson and coworkers.19,20 In this work, we introduce an alternative to the digital ion trap (DIT),19 a damped cosine trap (DCT), and present a detailed analysis of both traps through extensive simulations. The reaction of Ca+ with deuterated isotopologues of water, H2O and D2O, initially presented in ref 19, is scrutinized in further detail. The charge exchange reaction between Xe+ and deuterated isotopologues of ammonia is subsequently examined, illustrating the relevance of TOF-MS for studying complex reaction processes in Coulomb crystals. The dependence of arrival time, and thus mass resolution, on the initial ion position within a Coulomb crystal is discussed, along with suggestions for improving mass resolution for a given species. Simulations enable one to identify optimal experimental operating conditions, in addition to exploring potential improvements to the experimental design. Finally, the potential for spatial mapping of Coulomb crystals onto a positionsensitive detector is considered. The prospect of mass- and position-sensitive detection represents an interesting extension to existing TOF-MS methodologies for Coulomb-crystallized ensembles of ions.

ϕrf (x , y , t ) = ⎧1 ⎪ ⎪0 ⎪ Pτ(t ) = ⎨−1 ⎪ ⎪0 ⎪ ⎩1

Vrf ⎛ x 2 − y 2 ⎞ ⎟Pτ(t ) ⎜ 2 ⎝ r0 2 ⎠

(1)

if |t | ≤ τT /2 if τT /2 < |t | ≤ (1 − τ )T /2 if (1 − τ )T /2 < |t | ≤ (1 + τ )T /2 if (1 + τ )T /2 < |t | ≤ (2 − τ )T /2 if (2 − τ )T /2 < |t | ≤ T

Pτ(t + T ) = Pτ(t )

(2) (3)

The application of static voltages, Udc, to the end pieces of the trap electrodes achieves confinement in the axial plane. To ascertain the masses and relative numbers of each ionic species within a Coulomb crystal, ions are extracted from the trap and a TOF spectrum is recorded. Coulomb crystals are ejected from the DIT when the trapping voltages are switched off and dipolar repeller and extractor voltages of +220 V and +97 V (respectively) are applied. For the DCT, conventional cosine RF voltages of the form 1 ± 2 Vrf cos(Ω rf t ) are applied to the trap electrodes, where Vrf again represents the peak-to-peak voltage amplitude and Ωrf is the RF drive frequency (ωrf) multiplied by 2π, achieving a timedependent trapping potential in the radial plane. As with the DIT, axial confinement is achieved through the application of static voltages to the end pieces of each ion trap electrode. Under trapping conditions, the DCT system is operated at resonance; the trap electrodes form part of a resonant inductor−capacitor circuit. For ion ejection, the cosine RF trapping fields are switched off and quenching waveforms are applied to the toroid (synchronized with the RF waveforms) to dampen the ringing on the electrodes. After a delay of 1.26 μs, during which time the damped ringing decays, static dipolar repeller and extractor pulses of +305 V and +176 V (respectively) are applied, as depicted in Figure 1. In both the DCT and the DIT, the extraction voltages accelerate ions toward a grounded mesh, where they pass into a region of free flight and ultimately onto a microchannel plate (MCP) at the end of the flight tube for mass-sensitive detection. Schematic representations of the two TOF-MS

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EXPERIMENTAL SECTION Two linear Paul ion traps, with the same dimensions, are employed for the DIT and DCT experiments. Cylindrical trap electrodes, radius 4 mm, are held in a quadrupole arrangement with a diagonal electrode−surface separation of 2r0 = 7.0 mm. Each trap electrode is divided into three segments, with an endcap separation of 2z0 = 5.5 mm. The operation and characterization of the DIT has been described previously.19 Briefly, a combination of RF and static voltages are applied to the trap electrodes, with Vrf the peak-to-peak RF voltage amplitude. In place of the conventional cosine trapping wave function, a rectangular waveform of period T and fractional pulse width τ is employed, yielding a time-dependent trapping potential in the z = 0 plane of the form

Figure 1. Experimental waveforms applied to the four ion trap electrodes in the DCT, depicting the trapping (up to 0 μs), damping (0−1.26 μs), and ejection phases (1.26−3.56 μs). 12450

DOI: 10.1021/acs.jpca.5b07919 J. Phys. Chem. A 2015, 119, 12449−12456

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The Journal of Physical Chemistry A apparatus are provided in Figure 2. While the dimensions of the ion traps are identical in the two set-ups, there are differences in

Figure 3. Charge exchange reaction between Xe+ and ammonia, observed through changes to the fluorescing Ca+ Coulomb crystal framework. Panel A shows a Ca+-only Coulomb crystal. In panel B, Xe+ ions have been sympathetically cooled into the crystal, representing the t = 0 reaction conditions. Within 1 s of the introduction of ammonia, the beginnings of a dark core can be seen (panel C). The extent of charge exchange can be monitored through the growth of this dark core over time.

Figure 2. A side view schematic representation of the two experimental set-ups employed, differing in the length of the fieldfree flight region, with the relevant distances specified. The top apparatus is employed with the DIT; the lower apparatus is utilized with the DCT. A MCP detector is employed in both instances.

the position of the third (grounded) TOF-MS electrode and the length of the free-flight region. This is because two distinct reaction chambers with different dimensions and applications are employed, one ultimately for combining the ion trap with a Stark decelerator and the second for combination with a quadrupole velocity selector.2,23 An effusive beam of calcium atoms is nonresonantly ionized (using 355 nm photons from a frequency-tripled Nd:YAG laser, 10 Hz, ∼5 mJ/pulse) at the trap center, producing a cloud of Ca+ ions. A 397 nm diode laser (cw, ∼100 μW) excites the 4s 2 S1/2 → 4p 2P1/2 transition in 40Ca+, with a second diode (866 nm, cw, ∼1 mW) returning population lost to the dark 3d 2 D3/2 state to the main cycle. In this way, 40Ca+ ions are laser cooled and a Coulomb crystal is formed. Bidirectional cooling is achieved by reflecting the cooling lasers back along the trap axis. The fluorescence emitted by laser-cooled Ca+ ions is focused by a magnification lens into a charge-coupled device (CCD) camera, returning a two-dimensional image of the Coulomb crystal in real time. As described previously,19 the reaction of Ca+ with H2O and D2O is examined in the DIT and DCT, to probe the mass resolution of the methodology and the optimal operating parameters. H2O and D2O are introduced to the reaction chamber sequentially, through separate high-precision leak valves, yielding tricomponent Coulomb crystals composed of Ca+, CaOH+, and CaOD+ ions. A second reaction system is examined in the DCT, where the Ca+ ions act as spectator ions, playing no direct role in the reaction but acting to sympathetically cool the ionic reactants and products into the crystal. Xenon is introduced to the reaction chamber through a high-precision leak valve and is ionized at the DCT trap center using a (2 + 1) REMPI (resonance-enhanced multiphoton ionization) scheme at 249.6 nm (10 Hz, ∼1 mJ/pulse). The resulting Xe+ ions are sympathetically cooled into the Coulomb crystal. The incorporation of Xe+ ions into the crystal manifests as a flattening and elongation of the fluorescing Ca+ framework, as the heavier Xe+ ions form a dark outer shell. This can be observed as the change between the first two experimental images provided in Figure 3. To confirm that Xe+ reactant ions are cleanly incorporated into the crystal, we eject bicomponent Ca+/Xe+ crystals for mass-sensitive detection. Figure 4 shows one such bicomponent crystal and the corresponding TOF trace; laser-cooled 40Ca+ ions arrive at 5.84 μs, with a broader Xe+ peak centered at around 10.5 μs. The absence of any other peaks indicates that

Figure 4. Bicomponent Ca+/Xe+ crystal (inset), with the accompanying experimental TOF trace recorded following ejection of the crystal. The peaks at 5.85 and 10.5 μs indicate the presence of 40Ca+ and Xe+ ions (respectively) in the Coulomb crystal. A peak can be seen just above the baseline at 6.17 μs, indicating the presence of one or two 44 Ca+ ions. The absence of any additional peaks in the TOF trace confirms that there are no other species present.

there are no impurity ions present. The width of the Xe+ peak arises primarily from the natural isotopic abundance of the xenon isotopes, which include 128Xe (natural abundance of 1.92%), 129Xe (26.44%), 130Xe (4.08%), 131Xe (21.18%), 132Xe (26.89%), 134Xe (10.44%), and 136Xe (8.87%). (The REMPI laser line width of ∼0.06 cm−1 is insufficiently narrow for isotope-selective ionization.) The Xe+ peaks are not fully resolved; a high mass-to-charge ratio (3.3 times that of 40Ca+) means that Xe+ ions are less strongly confined to the trap center, residing in an outer shell around the Ca+ core. Xe+ ions thus exhibit a larger spatial distribution and are not as effectively translationally cooled as cotrapped species with a mass-to-charge ratio closer to that of 40Ca+. The Coulomb crystals formed in this work are fairly large, containing typically a few hundred ions. As such, the average ion energydominated by the driven RF motionis on the order of 1−10 K for Ca+, 8−11 K for CaOH+/CaOD+, and 10− 15 K for Xe+. Lighter species, such as ammonia ions, reside at the trap center and thus exhibit lower average ion energies of 1−2 K. 12451

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four isotopologues of the ammonia cation: NH3+, NH2D+, NHD2+, and ND3+. In addition to the 17−20 u mass peaks, two side peaks can be seen at masses 21 and 22 u. These minor peaks indicate the presence of a small number of ammonium ions, formed by secondary reactions involving H- or D-addition from neutral ammonia molecules to trapped ammonia ions, for example ND3 + ND3+ → ND2 + ND4+. As noted above, the presence of ions at masses 17−22 u could not be discerned from the crystal images alone, as all of these ions are found in the dark inner core. A detailed measurement and analysis of the reaction rates for this system are currently underway in our laboratory.

Crystals are ejected from the ion trap at a series of reaction times to investigate the rate of ion−molecule reactions. In this way, the resulting TOF spectra provide a snapshot of the composition of a Coulomb crystal after a given reaction time. As the TOF-MS technique is destructive, numerous repeats of this crystal loading and ejection process must be undertaken to gain a complete picture of the reaction as a function of time. Following the formation of bicomponent Ca+/Xe+ crystals, neutral ammonia reactant molecules (partially deuterated ammonia containing all four isotopologues: NH3, NH2D, NHD2, and ND3, 5% seed ratio in xenon carrier gas) are supersonically expanded into the chamber through a pulsed valve. Charge exchange reactions between Xe+ and the ammonia mixture, for example Xe+ + ND3 → Xe + ND3+, occur at partial pressures of up to 1 × 10−9 mbar. At a given reaction time, crystals are ejected from the trap for masssensitive detection. The Xe+ + ammonia reaction system is an interesting test case for a number of reasons. First, Xe+ ions are sympathetically cooled into the crystal (and do not fluoresce), thus the number of reactant ions is not easily ascertained from the crystal images. Second, there are multiple product ions formed, which all reside in the dark inner core and cannot be distinguished from analysis of the crystal images alone. Finally, while the reactions are exothermic, the depth of the DCT is sufficient for all product ions to be trapped. Accompanying each TOF trace is a series of experimental crystal images, as displayed in Figure 3: the initial Ca+-only crystal, a bicomponent Ca+/Xe+ crystal (representing the crystal composition at t = 0), and a series of images depicting the growth of a dark inner core of product ions as a function of reaction time. The final image in the series is recorded immediately prior to ejection of the crystal, and the mass of each constituent ion and relative ion numbers can be established from the corresponding TOF trace (see Figures 4 and 5). The TOF-MS methodology thus enables the relative numbers of each ammonia product ion to be discerned. The four main peaks centered at ∼4.1 μs indicate the presence of

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SIMULATIONS Methods. To establish the trajectories of ions ejected from a linear Paul trap into a TOF tube and onto a detector, the fields and dimensions of the experimental apparatus must first be defined. Two experimental set-ups are utilized, as discussed above and depicted schematically in Figure 2. Each experimental apparatus is drawn in SIMION,24 enabling the Laplace equation to be numerically solved and the electric fields calculated. The resulting fields are incorporated into the simulation program, which uses a Velocity-Verlet algorithm25,26 to propagate ion trajectories. The ion positions and velocities within the Coulomb crystal are imported from a custom-written molecular dynamics (MD) Coulomb crystal simulation program, which equilibrates the crystallized ions under the cooling, trapping, repulsive and heating forces. Either digital RF fields19 or conventional cosine RF fields are employed to confine ions within the trap. Experimental ejection waveforms, with a nonzero rise time of up to 160 ns and other minor imperfections, are included in the crystal simulation and ejection trajectory programs to accurately model the experimental ejection process. The forces experienced by each ion, arising from the electric potential gradient and explicit ion−ion repulsion, are calculated at each time step, and the ions are moved by Velocity-Verlet integration of the equations of motion. Trajectories are propagated until all ions strike a surface, either the front plate of the MCP detector, an electrode, or a side wall. The location of each ion as a function of time is output, enabling one to visualize the ejection process, as depicted in Figure 6. Simulated arrival times for ions of a given mass are in quantitative agreement with experimental ion arrival times, for all species considered. This is achieved with the inclusion of a small static offset in the simulations, attributed to delays between the triggering and response of electronic components. To replicate the experimentally observed instrument response, and thus ensure that the simulated mass resolution is accurate, every ion reaching the detector is assumed to generate a Gaussian voltage response. Each Gaussian is centered at the simulated ion arrival time, and the Gaussian responses arising from each detected ion are summed. A standard deviation of σ = 1.7 × 10−8 s best describes the experimental response observed in the TOF spectra, reproducing the experimental mass resolution. Nondamped Cosine Trap: The Effects of Ringing on Detection Efficiency. A complication with using the ion trap electrodes as repeller and extractor plates arises when the RF trapping fields are switched off. The effect of ringing noise superimposed on the ejection pulses is investigated here−as occurs when resonant circuits are employed and cosine RF trapping voltages are not damped or given time to decay.

Figure 5. Experimental TOF trace recorded following the ejection of a crystal midway through the charge exchange reaction between Xe+ and ammonia, with the crystal image recorded immediately prior to ejection inset. The series of peaks centered at ∼4.1 μs indicate the presence of four isotopologues of ammonia: NH3+, NH2D+, NHD2+, and ND3+, with minor contributions from ammonium ions (NH4+, NH3D+, NH2D2+, NHD3+, and ND4+) also evident. The 40Ca+ peak is located at 5.85 μs, with a shoulder peak at 6.17 μs indicating the presence of a small number of 44Ca+ ions. The unreacted Xe+ ions can be seen at 10.5 μs. 12452

DOI: 10.1021/acs.jpca.5b07919 J. Phys. Chem. A 2015, 119, 12449−12456

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Figure 6. Electric potentials generated when repeller and extractor voltages are applied to the ion trap; electrodes are depicted from the side view, along with the trajectories (moving from left to right) of 200 ejected Ca+ ions, in the longer TOF tube apparatus. Positive potentials appear in red, negative potentials in blue, and ion trajectories in green. Ions are trapped using digital RF waveforms, with Vrf = 51 V, Udc = 1 V, Ωrf = 2 π × 1.3 MHz, and τ = 0.21. Repeller and extractor voltages of 223 V and 97 V (respectively) are applied for ion ejection.

dependent on experimental parameters such as the ejection voltages and TOF apparatus dimensions. Further difficulties arise when one considers the ejection of multicomponent crystals. For example, species with higher mass-to-charge ratios spend more time in the acceleration regions. As such, species of different mass are subject to different phases of the decaying trapping fields superimposed on the ejection pulses. To overcome these detection efficiency challenges, and remove the dependence on the RF phase at the instant of ejection, we have explored two different techniques. As detailed previously, digital RF trapping fields are not resonantly driven, and so can be switched off cleanly (i.e., with no residual ringing noise on the ejection pulses).19 Alternatively, as described in this work, the cosine RF trapping fields can be actively damped prior to the application of ejection pulses. Through the use of experimental waveforms in the simulations, it is evident that detection efficiency in the DCT is independent of the phase of the RF cycle upon ejection, and with both the DIT and DCT is insensitive to minor imperfections in the ejection pulses. The TOF-MS detection efficiency of both the DIT and the DCT is near-unity; almost every ion (>99%) reaches the detector in all crystals simulated. It should be noted, however, that there are limitations to the simulations and thus potential sources of ion loss that are not explicitly considered (see Supporting Information). Factors Affecting Mass Resolution. Effects of Residual Ringing with the DCT. While the cosine RF trapping fields are damped prior to the application of ejection voltages in the DCT, a small amount of ringing noise remains on the ejection pulse (see Figure 1). A series of Ca+ crystals containing 150− 250 ions are simulated with the shorter TOF apparatus and DCT to establish the effect of two features of the damped cosine experimental waveforms on the mass resolving power: the residual ringing on the ejection pulse, and the 1.26 μs decay of the cosine trapping voltages before the ejection pulses are applied. When waveforms with no ringing on the ejection pulse (but all other features left unchanged from the experimental waveforms) are utilized in the simulations, there is a 20 ± 2% improvement in the mass resolving power. This suggests that more effective damping of the cosine RF trapping fields before the application of ejection voltages would yield enhanced mass resolution in the resulting spectra. As the confining RF waveforms decay during the 1.26 μs damping time, Coulombic repulsion between neighboring ions can begin to increase ion−ion separation. However, given the relative magnitudes of the (decaying) confining trapping forces and ion−ion repulsive forces, and the short decay time, any increase in the size of the crystal is marginal. As such, simulations indicate that there is a minimal increase in the spatial distribution of ions at the point of ejection. Accordingly,

Simulations show that this ringing severely limits detection efficiency; ions are deflected away from the detector due to the instantaneous field component perpendicular to the ejection axis. The detection efficiency is therefore highly sensitive to the phase of the trapping field upon ejection, as can be seen in Figure 7 for a simulated 200-ion Ca+ Coulomb crystal. While high detection efficiency can be demonstrated when ejection is performed at selected phases in the RF cycle, this is highly

Figure 7. The number of ions reaching the detector when using nondamped cosine RF trapping waveforms is dependent on the phase of the waveform when the ejection pulses are applied. The amplitude of the cosine trapping waveforms is shown above, where a phase factor of 1 is equal to 2π in radians. The detection efficiency for a series of simulated 200-ion Ca+ Coulomb crystals (with Ωrf = 2 π × 3.81 MHz, Vrf = 147 V and Udc = 2.7 V, in the shorter flight tube) ejected at 30 different phases in the RF cycle are shown below, for two sets of repeller and extractor voltages: 305 V and 176 V (dashed line), and 220 V and 97 V (solid line). It can be seen that the number of ions reaching the detector is dependent on both the phase of the RF waveform upon ejection and the magnitude of the ejection voltages. 12453

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The Journal of Physical Chemistry A the 6 ± 3% decrease in mass resolving power arising from the delay in the application of ejection fields while damping the cosine RF fields is a minor effect when balanced against the much improved detection efficiency with damping (outlined above). One could thus optimize the mass resolving power of the DCT by finding the damping time that best balances these two considerations; preventing any substantial increase in the size of the crystal, while allowing the RF voltages to decay sufficiently to minimize residual ringing on the ejection pulses. Impact of Crystal Size on Mass Resolving Power. Simulations quantitatively reproduce the experimental trend in mass resolving power with Ca+ ion number, as depicted in Figure 8. The mass resolving power decreases with increasing

resulting TOF traces, facilitating a quantitative analysis of the crystal components at a given reaction time. The importance of selecting optimal repeller and extractor voltages can be seen in the series of simulated TOF traces presented in Figure 9. To optimally resolve the CaOH+ and CaOD+ peaks in the shorter flight tube apparatus, one should apply repeller and extractor voltages of 300 V and 250 V (respectively) for our geometry of ion trap. When suboptimal ejection voltages are selected, the CaOH+ and CaOD+ peaks are less separated in time and can become split. Splitting of the CaOD+ mass peak, for example, arises from ions initially nearer the repeller getting too much of an acceleration kick, and overtaking the CaOD+ ions initially closer to the detector. The effect is illustrated in Figure 9, where CaOD+ ions contributing to the earlier component of the split peak (at 7.07 μs) are colored black, and those arriving later (at 7.09 μs) are colored red. The effect is independent of the magnitude and direction of the ion velocity at the point of extraction. For optimal mass resolution, it is thus important to establish the appropriate repeller and extractor voltages for each species of interest. In this way, ejection voltages can be selected to maximize the separation between nearby peaks of interest, enhancing the resolving power in this mass region. It is also worth noting that the reflectron principle could be adopted to improve mass resolution, where a reversing field is added after the field-free region.27 Ions with greater kinetic energy penetrate further into the reversing field and thus take longer to turn around, allowing all ions of a given mass to converge in time at the detector. A well-designed reflectron apparatus with stable and uniform fields can improve mass resolution by several orders of magnitude over conventional Wiley−McLaren mass spectrometry. This would more than compensate for the loss of mass resolving power through the use of nonplanar electrodes (see Supporting Information). The presence of multiple “heavy” ionic species sympathetically cooled into the crystal (for example, CaOH+ and CaOD+) can affect the mass resolution achievable for a given species. This effect is most marked for the heaviest species that get pushed further from the trap center and hence exhibit a greater spread of transverse positions (see Supporting Information). Spatial Mapping of Coulomb Crystals. Despite the use of nonplanar electrodes, the shape of the crystal is somewhat spatially preserved on the detector. This can be clearly seen in Figure 10, in which the positions of ion strikes on the MCPs are shown for prolate, spherical, and oblate crystals. This interesting result is achieved without any corrective or focusing lenses in the apparatus. It is likely that this spatial mapping of Coulomb crystals could be greatly enhanced by the inclusion of corrective lenses. For example, Bethlem and co-workers successfully compensated for astigmatism arising from nonplanar electrodes using a series of corrective planar electrodes with horizontal and vertical slits.28 With the inclusion of corrective electrodes, alongside the addition of a phosphor screen and CCD camera, one could potentially observe the 2D spatial distribution of a given species within a Coulomb crystal on the detector. This would be very valuable, as currently only the host Ca+ ions (or other laser-cooled species) can be directly observed through fluorescence. One is effectively blind to the positions of the nonfluorescing ions within the crystal, relying on MD simulations and changes in the crystal morphology to infer the locations of “dark” ions. Hence the prospect of spatially mapping crystals, with mass-sensitive and positionsensitive detection, is an exciting one.

Figure 8. Mass resolving power of the TOF-MS approach detailed in this work with the longer flight tube apparatus and DIT, as a function of the number of Ca+ ions in the Coulomb crystal. Experimental conditions are set out in Figure 6, with digital trapping fields and extraction voltages of 223 V (repeller) and 97 V (extractor). Experimental results are shown as black diamonds, with simulations in red. The reduction in mass resolving power with increasing crystal size is attributed to the increased spread of ion positions in larger crystals.

ion number, as there is a greater spread of initial positions (and ion velocities) in larger crystals. With further optimization of the repeller and extractor voltages, simulations suggest the TOF-MS method could achieve m/Δm of, for example, 120 for up to 200 Ca+ ions in the longer flight tube apparatus, adopting repeller and extractor voltages of 223 V and 210 V (respectively). Interestingly, mass resolution is independent of whether digital or damped cosine RF trapping fields are employed prior to the application of ejection voltages, within the approximate ±5% uncertainty in the simulated mass resolving power. Simulations (see Supporting Information) indicate that more oblate crystals, achieved by increasing the end-cap voltages, have lower mass resolution because of the greater transverse spread of the ion positions in the crystal. Optimizing Mass Resolving Power with Multicomponent Crystals. Extending our analysis to multispecies crystals to complement experimental investigations, crystals containing up to 200 ions with masses of 17−59 u are simulated using digital trapping fields and the longer flight tube.19 Larger crystals of up to 700 ions with masses of 17−136 u are simulated using damped cosine fields and the shorter flight tube apparatus. As previously reported,19 the reaction between Ca+ and two deuterated isotopologues of water, H2O and D2O, has been examined experimentally in the DIT TOF-MS apparatus. The CaOH+ and CaOD+ products ions can be resolved in the 12454

DOI: 10.1021/acs.jpca.5b07919 J. Phys. Chem. A 2015, 119, 12449−12456

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Figure 9. Simulated TOF spectra are shown on the left, for multicomponent crystals containing 100 Ca+, 50 CaOH+, and 50 CaOD+ ions over the 6.8−7.4 μs range of interest. For all traces, the repeller voltage is 300 V; extractor voltages range from 200−250 V. The split in the CaOD+ peak with repeller and extractor voltages of 300 V and 200 V (respectively), as seen in the lowest (black) trace, arises from the excess acceleration imparted to ions closer to the repeller. This can be seen in the right panel, where the positions and velocity vectors of the CaOD+ ions in the crystal are shown: ions contributing to the earlier portion of the split peak are colored black, and those with a later arrival time are colored red. Ions are ejected to the right. Damped cosine trapping fields are employed, with Ωrf = 2 π × 3.81 MHz, Vrf = 147 V and Udc = 2.7 V, in the shorter flight tube.

When comparing the performance of the DIT with the DCT, equivalent detection efficiency and mass resolving power are observed. However, under our operating parameters, the DIT has a shallower trap depth (1.21 eV) than the DCT (1.36 eV). As derived in ref 19, the secular trap depth is dependent on the time-varying pseudopotential, the static end piece potential, and a coefficient term, c. For a conventional linear Paul trap with cosine RF fields, such as the DCT, c = 0.5. In the DIT, c is dependent on τ, the fractional pulse width. When τ = 0.293, c = 0.5 and the depth of the DIT is equivalent to that of the DCT. Because of design constraints, we are restricted to operating the DIT with τ = 0.25, in addition to employing a lower Vrf, Udc, and ωrf than typically adopted for the DCT. As the dimensionless stability parameters, a and q, are also dependent on Udc, Vrf, and ωrf, the operating limitations of our DIT have the dual effect of lowering the trap depth and restricting the region of the stability diagram the DIT can operate in. Should these operating restrictions be overcome, the increased flexibility of the DITarising from the ability to instantaneously switch off the trapping fields for an arbitrary length of timewould recommend it over the DCT. For example, the DIT would allow trapped species to be photoexcited in the absence of external fields. Considering the current restrictions, the deeper DCT offers increased versatility in terms of the range of ion−molecule reactions that can be studied. Combined with recent experimental results, simulations clearly illustrate the power of TOF-MS to quantitatively identify the masses and abundances of all ions within a Coulomb crystal at the point of ejection. This will enable the investigation cold ion−molecule reaction rate coefficients with unprecedented precision and accuracy.

Figure 10. The final positions of 100 Ca+ ions striking the MCP detector are shown, as a function of crystal shape. In all instances, damped cosine RF trapping fields are employed with Ωrf = 2 π × 3.81 MHz. The prolate crystal, A, is formed with Vrf = 147 V and Udc = 2.7 V; the spherical crystal, B, is formed with Vrf = 80 V and Udc = 2.7 V; and the oblate crystal, C, is formed with Vrf = 75 V and Udc = 5 V.

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CONCLUSIONS The sensitivity of TOF-MS detection for Coulomb-crystallized ions is demonstrated through a combination of experimental results and extensive modeling. Simulations describing the ejection of Coulomb crystals for TOF-MS analysis aid our understanding of the ion ejection process, identifying loss mechanisms and establishing optimal operating parameters. Even with cylindrical repeller and extractor electrodes, a good mass resolving power (m/Δm on the order of 100 for up to 200-ion Ca+ crystals) is demonstrated, more than adequate for examining most reactions of interest. 12455

DOI: 10.1021/acs.jpca.5b07919 J. Phys. Chem. A 2015, 119, 12449−12456

Article

The Journal of Physical Chemistry A

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07919. Additional details arising from the simulations. These set out the detection limitations of the simulations and also examine the role that the cylindrical electrodes, crystal shape, and multiple components have on the resulting TOF-MS mass resolution (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.P.S. acknowledges financial support from the EPSRC under Grants EP/G00224X/1 and EP/1029109. B.R.H. is grateful for support from the Royal Commission for the Exhibition of 1851 and the Marie Curie Career Integration Grant Scheme (PCIG13-GA-2013-618156). T.P.S., B.R.H., and L.S.P. acknowledge support from the Marie Curie Initial Training Network Scheme (COMIQ, FP7-GA-607491). The authors thank Mr. A. D. Smith for his contribution to the trajectory simulation code. Metadata associated with this work can be accessed through the Oxford Research Archive, at DOI: 10.5287/bodleian:dr26xx430.

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REFERENCES

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DOI: 10.1021/acs.jpca.5b07919 J. Phys. Chem. A 2015, 119, 12449−12456