Demonstration of a Nested Electrostatic Linear Ion Trap for Flexibility in Selecting Analyzer Figures-of-Merit

Abstract

An electrostatic linear ion trap (ELIT) is used to trap ions between two ion mirrors with image current detection by central detection electrode. Transformation of the time-domain signal to the frequency-domain via Fourier transform (FT) yields an ion frequency spectrum that can be converted to a mass-to-charge $\left(m/z\right)$ scale. Injection of ions into an ELIT from an external ion source leads to a time-of-flight ion separation that ultimately determines the range of $m/z$ over which ions can be collected from a given ion injection step. The $m/z$ range is determined both by the length of the ELIT and by the distance of the ELIT entrance from the ion source. A longer ELIT leads to a wider $m/z$ range while a shorter ELIT, under equivalent conditions, leads to higher resolving power due to increased ion frequencies. Hence, there is an inherent trade-off between the two important analyzer figures-of-merit of $m/z$ range and resolving power based on the length of the ELIT. In this work, we demonstrate a nested ELIT arrangement, referred to herein as an NELIT, that allows for the selection of one of two possible ELIT lengths within a single array of plates while employing a common detection electrode. While a range of ELIT lengths are possible, in principle, the geometry described herein leads to an effective length ratio of 2.40 for the two traps in the NELIT.

Graphical Abstract

INTRODUCTION

Electrostatic linear ion traps (ELITs) using image current detection and Fourier transform techniques for the simultaneous measurement of $m/z$ and $z$ have been developed for the mass determination of one or several individual ions in charge detection mass spectrometry.^1,2,3 ELITs have also been used for $m/z$ determination involving large numbers of ions,^4,5,6 in analogy with other forms of mass analysis. The ELIT shares some of the same characteristics of the highly commercially successful Orbitrap^™ mass analyzer^7,8 as they are both electrostatic ion traps and therefore share the same fundamental relationship between ion frequency and $m/z$. The ELIT, however, lacks a central trapping electrode, like the spindle electrode of the Orbitrap^™, to provide trapping in x- and y-dimensions but rather relies on overlapping focal distances of the ion mirrors to minimize ion loss in the x- and y-dimensions as well as the ion bunching phenomenon to facilitate long storage times in the z-dimension.^9,10,11,12

An ELIT is fundamentally simple to fabricate, as it is comprised of a series of appropriately spaced flat plates with apertures and a central detector electrode. It is, therefore, relatively straightforward to construct a home-built mass spectrometer capable of moderate-to-high resolving power. Furthermore, the linear geometry of the ELIT enables several potentially useful experiments. For example, the ability to capture and release ions from the ELIT from and to an external quadrupole linear ion trap (QLIT) allows for non-destructive MS/MS experiments.¹³ The geometry also readily allows for mass analysis via either FT techniques using the central pick-up electrode, closed-loop multi-reflectron time-of-flight (MR-TOF)¹⁴ using a channel-plate detector behind one of the mirrors, or both.¹⁵ The MR-TOF aspect of the experiment enables, via appropriately-timed control of the voltages applied to the ion mirrors, referred to as mirror switching, high resolving power ion isolation (e.g., 38,000 FWHM)¹⁶ and simultaneous ion isolation of ions of disparate $m/z$ ratios.¹⁷ The linear geometry of the ELIT also allows for the use of more than one detector to increase resolving power,¹⁸ facilitates photodissociation at turning points in the ion mirrors,¹⁹ and allows for surface-induced dissociation at a surface behind an ion mirror via mirror switching with recapture of the products.^20,21

ELITs designed for MR-TOF experiments^22,23,24,25 generally have lengths on the order of 1–2 m to mitigate the racetrack effect²⁶ associated with closed-loop MR-TOF measurements. In the case of the FT experiment in an ELIT, on the other hand, ion lapping does not compromise $m/z$ measurement as it is based on frequency, rather than time of flight. In this regard, for a fixed ion energy, a shorter ELIT will lead to higher frequencies and, hence, higher resolving power. We individually built and compared the performance of two ELITs of lengths 6.67 and 13.34 cm, respectively.²⁷ As expected, the resolving power of the shorter ELIT was greater than that of the longer ELIT but the $m/z$ range of the short ELIT was narrower than that of the longer ELIT. In this work, we constructed an analyzer structure that consists of a short ELIT nested within a longer ELIT that both share a common detector. This ‘trap-in-a-trap’ geometry, referred to as a nested ELIT (NELIT), allows for the selection between an ELIT with a wider $m/z$ range with a lower resolving power and a shorter ELIT that has a narrower $m/z$ range and higher mass resolving power.

EXPERIMENTAL SECTION

Materials:

Nitrobenzene-¹⁵N (98% isotopic purity) was acquired from Cambridge Isotope Laboratories, Inc. (Tewksbury, MA USA). Perfluoro(methyldecalin) (PFMD, technical grade, 80%) was purchased from Sigma-Aldrich (St. Louis, MO, USA). Perfluoro(1,3-dimethylcyclohexane) (PDCH, technical grade, 90%) was obtained from Thermo Fisher Scientific (Waltham, MA, USA). All compounds were used as received, and stock aliquots were prepared at their respective concentrations for use in subsequent experiments.

Instrumentation and experimental sequence:

Experiments were performed on a home-built platform (see Figure 1) with many of the components in common with previously described versions of the instrument.^1,28 The key difference in this platform is the NELIT analyzer described below. Pulsed (2 ms/PFMD and PDCH and 20 & 100 ms/Nitrobenzene) atmospheric sampling glow discharge ionization (ASGDI)²⁹ was used to generate anions for this study. Anions from the ion source were transmitted via several DC lenses, an RF-only quadrupole (0.816 MHz, 358 V_p-p, SCIEX, Framingham, MA, USA), and a DC turning quadrupole (Extrel, Pittsburgh, PA) into a quadrupole linear ion trap (QLIT) (0.816 MHz, 358 V_p-p, SCIEX, Framingham, MA, USA). A pulsed valve (Series 9, Miniature Calibrant Valve, Parker, Mayfield Heights, OH, USA) was opened for 2 ms to admit N₂ into the QLIT 100 ms prior to the ionization pulse to facilitate capture and cooling of the injected ions and removal of much of the gas prior to injection of ions into the NELIT. A set of LINAC II electrodes³⁰ present in the QLIT allowed for the concentration of the ions near to the exit of the QLIT through an applied axial DC voltage with increasingly repulsive potential field as the ions are pushed towards the exit lens. This “ion bunching”^9–12 forces the ion cloud down to a tight packet with reduced spatial distribution due to the LINAC field potential extending further into the trap center moving axially. After accumulation of the ions into the QLIT, the entire rod set was lifted to −1500 V over a period of 160 ms with a 5 ms hold time for packet compression due to a 5 V DC reduction in the $\text{ML5}$ negative potential, which allowed the ions to move closer to the $\text{ML5}$ lens for subsequent release into the NELIT.¹⁶ Along with the rod-set lift, the LINAC was lifted to −200 V and the ML4 lens was lifted to −1510 V. A phase lock circuit was used to trigger the injection of the ion packet into the NELIT and the start of data collection at a zero crossing of the trapping RF so that a consistent ion energy was sampled.

Figure 1.

Schematic representation of a Fourier transform nested electrostatic linear ion trap- (NELIT) instrument. The outer trap lenses are depicted in green while the inner trap lenses are depicted in orange. The pressures indicate the base pressures in the relevant regions. The pressure in the analyzer region is 8.9 × 10⁻¹⁰ - 2 × 10⁻⁹ torr during the analysis because the base pressure is not fully reached after the pulsed admission of the bath gas to the trapping quadrupole.

A nested two-trap NELIT system was constructed with a smaller, inner trap spaced within a larger, outer trap. Following initial modeling of multiple dual trap configurations in SIMION v8.1 (Adaptas Scientific Instrument Services, Palmer, MA, USA), the analyzer was assembled using commercially available parts from Kimball Physics (Wilton, NH, USA). The configuration consisted of 8 lenses (OL#) for the outer trap and 8 lenses for the inner trap (IL#). The lenses were aligned with non-conducting ceramic rods and spacers to hold them at a fixed distance apart. There was a pick-up electrode for charge detection centered in the middle of a shielded and grounded region between IL4 and IL5. Initial SIMION modeling showed significant fringe fields between the closest outer lens (OL4) and the associated neighboring inner lens (IL1) (also IL8 and OL5). The fringe fields were minimized via the addition of an additional lens to the IL1 and IL8 lenses, held at the respective potentials of IL1 and IL8. The first lens of whichever trap was being used (OL1 or IL1) was held at a relatively low value to allow ions released from the QLIT to enter the ELIT. A delay between the release of ions and the restoration of the voltage for ion storage on OL1 or IL1 determined the $m/z$ range of the respective ELIT (see below).

Potentials for outer trapping were as follows: OL1 = OL8 =−1680.2 V_DC, OL2 = OL7 = −1176 V_DC, OL3 = OL6 = −815 V_DC, OL4= OL5 = +1991 V_DC, IL1 = IL8 = −212 V_DC. All other inner lenses were grounded. OL1 low was set to −830 VDC for initial ion entrance into the outer trap and prior to gating this lens to - 1680.2 VDC upon ion entrance. For inner trapping, the potentials were as follows: IL1 = IL8 = −1917 VDC, IL2 = IL7 = −1261.8 VDC, IL3 =IL6 = −908 VDC, IL4 = IL5 = +1978.1 VDC. IL1 low was set to −972 VDC for initial ion entrance into the inner trap and prior to gating this lens to −1917 VDC upon ion entrance. Note that all potentials are negative with this setup for trapping of ASGDI generated anions. The instrument can indeed be used with positive potentials and trapping of cations generated via another ionization method such as nESI.

Components for charge-sensitive detection were described previously.³¹ For detection, the signal was amplified via a charge sensitive preamplifier (A250, Amptek Inc., Bedford, MA, USA) and passed through a high-pass filter (Model 3945, Krohn-Hite Corporation, Brockton, MA, USA) with a gain of unity and a low cut-off frequency of 50 mHz. Digitization was accomplished at a rate of 10 MS/s via a PCI-based digitizer (CS1621, 16-bit, Gage Applied Technologies, Lanchine, Quebec, CA).⁷ Transient data was collected with LabView 2015 (National Instruments, Austin, TX). A custom program was written in Python for FFT processing of the time domain signal³² and output display of the spectrum as a function of $m/z$.

RESULTS AND DISCUSSION

The relationship between resolving power, ELIT length, ion kinetic energy, and acquisition time.

The following development provides an estimate of the roles of length and ejection voltage on the resolving power of an ELIT. The underlying assumptions are introduced with the relevant equations. Note that, by virtue of the fact that ions pass through the detector twice per full cycle, the measured frequency, ${\text{f}}_{\text{meas}}$, is twice the frequency of a full cycle, ${\text{f}}_{\text{cycle}}$, or, equivalently, ${\text{f}}_{\text{meas}}$ is the frequency of one-half cycle.

The measured frequency in Hz, ${\text{f}}_{\text{meas}}$, in an electrostatic ion trap is related to the inverse square root of $m/z$, i.e.:

$$f_{meas}=\frac{1}{2\pi }k\sqrt{\frac{z}{m}}$$ (1)

where $\text{k}$ is a constant related to the instrument geometry and operating conditions (see below) and $1/2\pi$ is the conversion from angular frequency to frequency in Hz. The relationship between $m/z$ and ${\text{f}}_{\text{meas}}$, therefore, is:

$$\frac{m}{z}={\left(\frac{1}{2\pi }\right)}^2\frac{k^2}{f_{meas}^2}$$ (2)

This relationship can be re-written as:

$$m={\left(\frac{1}{2\pi }\right)}^2\frac{z{k}^2}{f_{meas}^2}$$ (3)

Logarithmic differentiation of (3) with respect to ${\text{f}}_{\text{meas}}$ leads to (see supplemental information for a stepwise description of this proces):

$$\frac{1}{m}\frac{dm}{d{f}_{meas}}=\frac{-2z{\left(2\pi \right)}^{-2}{k}^2{f}_{meas}^{-3}}{z{\left(2\pi \right)}^{-2}{k}^2{f}_{meas}^{-2}}=-\frac{2}{f_{meas}}$$ (4)

The relationship between mass resolving power, $\text{R}$, and the frequency resolution, therefore, is:

$$R=\frac{m}{dm}=-\frac{f_{meas}}{2d{f}_{meas}}$$ (5)

In the low-pressure limit and in the absence of dephasing, the uncertainty in the measurement of ${\text{f}}_{\text{meas}}$, ${\text{df}}_{\text{meas}}$, is inversely related to the observation (or acquisition) time, ${\text{T}}_{\text{acq}}$, i.e.:

$$T_{acq}\propto \frac{1}{d{f}_{meas}}$$ (6)

Hence, combining (1), (5) (dropping the negative sign) and (6), assuming ${\text{T}}_{acq}{\text{=1/df}}_{\text{meas}}$, we can write the maximum mass resolving power, ${\text{R}}_{\text{max}}$, as:

$$R_{max}=\frac{1}{\pi }k\sqrt{\frac{z}{m}}{T}_{acq}$$ (7)

The frequency of one-half cycle given by (1) can be estimated from the average velocity of an ion divided by the length of one-half cycle, as estimated by the length of the $\text{ELIT}$, ${\text{D}}_{\text{X,ELIT}}$, where $\text{X}$ refers to either the outer (O) ELIT or inner (I) ELIT:

$$f_{meas}=\frac{v_{avg}}{D_{X,ELIT}}$$ (8)

The kinetic energy of the ion, $\text{KE}$, injected into the $\text{ELIT}$ as a result of a voltage difference, $\Delta \text{V}$, is given by:

$$KE=ze\Delta V=\frac{1}{2}m{v}^2$$ (9)

The velocity of the fully accelerated ion is:

$$v=\sqrt{\frac{2ze\Delta V}{m}}$$ (10)

Taking the velocity of the ion as it is injected into the trap, as given by (9), as an estimate of ${\text{v}}_{\text{avg}}$, and substituting into (8) gives an estimate for ${\text{f}}_{\text{meas}}$:

$$f_{meas}\approx \frac{\sqrt{\frac{2ze\Delta V}{m}}}{D_{X,ELIT}}$$ (11)

Substituting (6), again assuming ${\text{T}}_{acq}{\text{=1/df}}_{\text{meas}}$, and (11) into (5) yields:

$$R_{max}\approx \frac{\sqrt{2ze\Delta V}}{D_{X,ELIT}}\sqrt{\frac{z}{m}}{T}_{acq}$$ (12)

Note that the use of (10) over-estimates ${\text{v}}_{\text{avg}}$ because it does not account for the deceleration of the ions in the mirrors while ${\text{D}}_{\text{X,ELIT}}$ overestimates the length of one-half cycle because the ions turn around before they reach the last electrode of each of the mirrors. Furthermore, (12) does not take into account any uncertainties in ion frequencies that can arise from a distribution of injected ion energies, differences in distances due, for example, to an angular distribution, power supply instabilities, etc. Hence, in addition to the approximations mentioned above, (12) assumes the only source of uncertainty in frequency to be the inverse of the acquisition time (relation (6)).

Trap lengths and resolving powers in the NELIT

Relation (12) shows that resolving power can be expected to increase with the square root of the ion kinetic energy, with the inverse of the length of the ELIT, and with the acquisition time, at least in the low pressure limit. For most FT-based instruments, the most straightforward means for increasing resolving power is to increase ${\text{T}}_{\text{acq}}$. However, increasing ${\text{T}}_{\text{acq}}$ increases the total overall path-length, which places a premium on achieving ultra-high vacuum, and reduces the spectral acquisition rate. An alternative for increasing resolving power is to increase the ion kinetic energy.³³ This approach can reduce the spectral acquisition rate by reaching the same number of cycles in a shorter ${\text{T}}_{\text{acq}}$. The use of higher potentials, however, can eventually lead to electrical breakdown and issues with fast voltage switching.³⁴ Reducing the length of the ELIT leads to an increase in frequency for the same path length but reduces the $m/z$ range using our current approach to injecting ions into the ELIT (see below). The trade-off between resolving power and $m/z$ range motivated this work, which involves the incorporation of two nested ELITs of different length.

The distance of one-half cycle, which is close to the physical length of the $\text{ELIT}$, can be estimated by rearranging (11) to give:

$$D_{X,ELIT}\approx \frac{\sqrt{\frac{2ze\Delta V}{m}}}{f_{meas}}$$ (13)

The effective lengths of the nested ELITs can therefore be estimated from the measured frequencies of ions stored in the respective traps. Table 1 lists ${\text{f}}_{\text{meas}}$ values acquired at ${\text{T}}_{\text{acq}}=100-500\text{ms}$ and $\Delta \text{V}\text{=}\text{1500}\text{V}$ for several representative ions stored in the outer and inner traps, respectively, along with the ${\text{D}}_{\text{X,ELIT}}$ values determined from (13). The effective lengths of the inner and outer ELITs are 8.24 ± 0.01 cm and 19.77 ± 0.83 cm, respectively, with an outer/inner trap dimension ratio of 2.40. Figure 2 provides a mass spectrum collected using the outer trap for a mixture of PFMD and PDCH as an illustration of the origin of much of the experimental data provided in Table 1 for the outer trap.

Table 1.

Measured fundamental frequencies of a variety of anions and the corresponding calculated trap lengths (Equation (13)) for the outer and inner traps in the NELIT.

	Outer trap			Inner trap
$Ion(nominal\text{m}/\text{z})$	sample size	$f_{meas}\left(Hz\right)$	$D_{O,ELIT}\left(cm\right)$	sample size	$f_{meas}\left(Hz\right)$	$D_{I,ELIT}\left(cm\right)$
[C6H515NO2]−• (124)	8	219848 ± 9428	21.96	5	586363 ± 18	8.23
[PDCH-CF3•]− (331)	43	152020 ± 28	19.44	32	358842 ± 119	8.24
[PDCH-F•]− (381)	43	141694 ± 32	19.44	32	334453 ± 113	8.24
[PDCH]−• (400)	43	138283 ± 25	19.44	32	326428 ± 93	8.24
[PFMD-CF3•]− (443)	8	131225 ± 4	19.47	7	310264 ± 10	8.23
[PFMD-CF2]−• (462)	8	128502 ± 6	19.47	7	303706 ± 276	8.24
[PFMD-F•]− (493)	8	124412 ± 8	19.46	7	294114 ± 15	8.23
[PFMD]−• (512)	8	122063 ± 6	19.47	7	288590 ± 22	8.23
		Mean ± σ	19.77 ± 0.83		Mean ± σ	8.24 ± 0.01

Figure 2.

Mass spectrum ions derived from a mixture of PDCH and PFMD generated from a 2 ms pulse of an ASGDI source and stored in the outer trap of the NELIT. The most abundant ions correspond to [PFMD]^−•, [PFMD-F•]⁻, [PFMD-CF₂]^−•, [PFMD-CF₃•]⁻, [PDCH]^−•, [PDCH-F•]⁻and [PDCH-CF₃•]^.−. At $\text{m/z}<\text{200}$ second and third harmonics of these ions can be observed.

In order to characterize resolving power ($\left(\text{m/z}\right)\text{/(Δ}\left(\text{m/z}\right)$, FWHM) mass spectra were collected using acquisition times of 100 – 400 ms for both the inner and outer traps. Figure 3 provides plots of resolving power versus acquisition time for the molecular anion of PDCH $\left(m/z400\right)$ for both the inner (orange data points) and outer (green data points) traps. In both cases, resolving power increases nearly linearly with acquisition time, although some non-linearity is apparent at longer acquisition times with the inner trap. We noted that under 400 ms, ion frequencies did not change beyond +/− 1 Hz but greater deviations were noted beyond 400 ms. This usually indicates an issue with power supply stability. However, at the pressures present in the NELIT during acquisition, the low pressure limit does not strictly apply, which would lead to a roll-over in resolving power with acquisition time.³⁵ In any case, the relative ratio of the resolving powers for the two traps follow the inverse ratio of the trap lengths, as expected, due to the role of trap length on determining ion frequency at constant ion kinetic energy (relation (12)).

Figure 3:

Mass resolving power ($\left(m/z\right)/(\Delta \left(m/z\right)$, FWHM) as a function of acquisition time. Replicates of n = 4 – 8 for each time point were collected. Horizontal demarcations indicate resolving power at FWHM for 200 and 400 ms transient trapping times for both inner and outer traps.

Anions derived from PDCH from both the inner (orange) and outer (green) traps at an acquisition time of 200 ms are plotted as a function of frequency in the top trace of Figure 4. Several harmonics fall within the plotted frequency range for the outer trap while only the first and second harmonics are apparent for the ions stored in the inner trap. The peak shapes for the molecular anion in the inner and outer traps are plotted together on the $m/z$ scale in the plot at the bottom of the figure. A measured resolving power improvement of 2.23 was noted in using the inner trap, which is roughly 2.4 times smaller than the outer trap.

Figure 4.

Anions derived from PDCH from the inner (orange) and outer (green) traps on the frequency scale using a 200 ms acquisition time. (top) Peak shapes of the PDCH molecular anions stored in the inner (orange) and outer (orange) traps.

Platform dimensions and $m/z$ range:

The delay time between release of ions from the trapping quadrupole through $\text{ML5}$ and the time at which the entrance mirror voltage is gated up to trap injected ions, referred to as the gate time, ${\text{t}}_{\text{g}}$, determines the $m/z$ range of an $\text{ELIT}$ experiment.²⁷ Release of ions from the trapping quadrupole initiates a separation of ions based on their times-of-flight. The gate time is the drift time and, hence, establishes the high $m/z$ limit for those ions too slow to reach the entrance ion mirror before the gate closes and the low $m/z$ limit for those ions that are so fast that they can enter and leave the trap before the gate closes (see the Figure 4 and insert to Figure 5). The approximate $m/z$ range of an $\text{ELIT}$ using the mirror switching approach for capturing injected ions can therefore be predicted using the basic equations for time-of-flight. Taking the gate time as the drift time, the time-of-flight for an ion is given by the drift distance, $\text{D}$, divided by the ion velocity (see relation (10)):

$$t_g=\raisebox{1ex}{$D$}\!\left/ \!\raisebox{-1ex}{${\left[\frac{2ze\Delta V}{m}\right]}^{\frac{1}{2}}$}\right.$$ (14)

Figure 5.

Schematic diagram showing the NELIT from the point of release of ions from the trapping quadrupole, $\text{ML5}$. The red arrow shows the relevant distances for determining the $m/z$ ratio range for the inner trap and the blue arrows show the relevant distances for determining the $m/z$ ratio range for the outer trap. The table summarizes the relevant distances measured by collecting mass spectra of PDCH as a function of gate time, ${\text{t}}_{\text{g}}$.

The drift distance is therefore,

$$D=t_g{\left[\frac{2ze\Delta V}{m}\right]}^{\frac{1}{2}}$$ (15)

The drift distances for the ions at the low, ${\text{D}}_{\text{low}}$, and high, ${\text{D}}_{\text{high}}$, ends of the $m/z$ range, respectively, are given by:

$$D_{low}=t_g{\left[\frac{2ze\Delta V}{m_{low}}\right]}^{\frac{1}{2}}$$ (16)

and

$$D_{high}=t_g{\left[\frac{2ze\Delta V}{m_{high}}\right]}^{\frac{1}{2}}$$ (17)

Taking the ratio of ${\text{D}}_{\text{low}}{\text{/D}}_{\text{high}}$ and solving for ${\text{m}}_{\text{high}}{\text{/m}}_{\text{low}}$ yields:

$$\frac{m_{high}}{m_{low}}={\left[\frac{D_{low}}{D_{high}}\right]}^2$$ (18)

The distance of flight for the high $m/z$ limit is the distance between $\text{ML5}$ and $\text{XL1}$, $\text{D}\left(\text{ML5-XL1}\right)$, where $\text{X}\text{=}\text{O}\text{or}\text{I}$. The distance of flight for the low $m/z$ ion can be approximated as the sum of $\text{D}\left(\text{ML5-XL1}\right)$ and twice ${\text{D}}_{\text{X,ELIT}}$. In general, the $m/z$ range ratio is approximated by:

$${\left(\frac{m_{high}}{m_{low}}\right)}_X={\left(\frac{D\left(ML5-XL1\right)+2D_{X,ELIT}}{D\left(ML5-XL1\right)}\right)}^2$$ (19)

The $m/z$ range ratio is determined solely by the relevant distances $\text{D}\left(\text{ML5-XL1}\right)$ and ${\text{D}}_{\text{X,ELIT}}$. The high and low $m/z$ limits to the $m/z$ range are also determined by the ion kinetic energy and the gate time. The upper $m/z$ limit is given by:

$${\left(\frac{m}{z}\right)}_{high,X}=\frac{2e\Delta V{t}_g^2}{{\left(D_{ML5}-D_{XL1}\right)}^2}$$ (20)

and the low $m/z$ limit is given by:

$${\left(\frac{m}{z}\right)}_{low,X}=\frac{2e\Delta V{t}_g^2}{{\left(\left(D_{ML5}-D_{XL1}\right)+2D_{X,ELIT}\right)}^2}$$ (21)

By acquiring mass spectra as a function of ${\text{t}}_{\text{g}}$, it is possible to measure the times that ions appear in the mass spectrum, which is a measure of the $\text{D}\left(\text{ML5-XL1}\right)$, as well as the times that they disappear, which is a measure of the time-of-flight for $\text{D}\left(\text{ML5-XL1}\right){\text{+2D}}_{\text{X,LIT}}$. A series of mass spectra of ions derived from PDCH were collected as a function of ${\text{t}}_{\text{g}}$. For ions initially appearing in the spectrum, the ${\text{t}}_{\text{g}}$ at half-maximum peak signal was taken to determine $\text{D}\left(\text{ML5-XL1}\right)$ while for ions disappearing from the spectrum, the ${\text{t}}_{\text{g}}$ at half-maximum was taken to determine $\text{D}\left(\text{ML5-XI1}\right){\text{+2D}}_{\text{X,ELIT}}$. The results were then used to determine the $m/z$ range ratio using relation (19). Figure 5 shows a schematic of various distances within the NELIT, the specific distances used to determine the $\text{m/z}$ range ratio (blue and red arrows), and a table summarizing the relevant distance measurements and resulting $\text{m/z}$ range ratios. The $\text{m/z}$ range ratio of the outer trap is determined to be roughly 38 whereas that for the inner trap is roughly 5. The roughly 7-fold decrease in the $\text{m/z}$ range ratio in going from the outer trap to the inner trap is due both to the shorter trap length and to a longer flight path to reach OL3 versus OL1. The latter condition arises from the use of a common detector for both ELITs in the NELIT, which requires the entrance lens of the inner trap (IL1) to be further from $\text{ML5}$ than the entrance lens of the outer trap (OL1).

Plots of ${\left(m/z\right)}_{high}$ and ${\left(m/z\right)}_{low}$ determined using relations (20) and (21) and the distances shown in the table of Figure 5 for the outer (green) and inner (orange) traps, respectively, are shown in Figure 6. The ratio of the $\text{m/z}$ ranges for the outer/inner traps is approximately 7.6. The insert illustrates the separation of ions based on different times-of-flight from $\text{ML5}$ to the respective entrance gates, OL1 or IL1, as well as the further separation once the ions are within the NELIT analyzer.

Figure 6.

Upper (dashed lines) and lower (solid lines) limits to the $m/z$ ranges for the outer (green) and inner (orange) traps of the NELIT as a function of ${\text{t}}_{\text{g}}$ as determined using relations (20) and (21).

CONCLUSIONS

This work demonstrates a nested ELIT (NELIT) analyzer configuration that provides flexibility in resolving power and $m/z$ range without requiring the replacement of an ELIT of one length for another of a different length. In this case, the effective outer ELIT length is 2.40 x larger than that of the inner ELIT. No apparent compromise was noted in the performance of either ELIT due to the presence of the electrodes of the other ELIT. Previous work had demonstrated that a shorter ELIT provides greater resolving power at the expense of $m/z$ range. An analogous trade-off is also observed with the NELIT but with a greater relative loss in $m/z$ range with the NELIT due to the use of a common pick-up electrode, which leads to a greater distance from the trapping quadrupole to the inner trap entrance. The $m/z$ range ratio, i.e. the ratio of the high $m/z$ limit to that of the low $\text{m/z}$ limit, is roughly 7.6x smaller with the inner trap (roughly a factor of five for the inner trap versus a ratio of 38 for the outer trap). However, variation of the gate time provides a high degree of flexibility in choosing the $m/z$ range itself (e.g., $\text{m/z}\text{20–100}$, $m/z100\text{-}500$, etc.). We note that similar time-of-flight discrimination effects also apply to other some other analyzer types, such as orthogonal acceleration time-of-flight and FT-ion cyclotron resonance. Techniques that allow for controlled release of ions from a trapping quadrupole such that high $m/z$ ions are ejected first, followed by low $m/z$ ions leading to a temporal focus at the analyzer have been reported^36,37 and might be considered in this scenario to mitigate the effect of using a shorter ELIT. We note, however, that the shorter trap could be used in a zoom-in mode, in which case the $m/z$ range is less of an issue. We also note that there are other variations of nested ELIT analyzers that might be considered in, for example, altering the degree to which higher harmonics are observed, which might also be considered for enhancing mass resolving power.

Supplementary Material

Logarithmic differentiation for the NELIT.

Highlights:

• Two electrostatic ion trap analyzers can be nested to yield two analyzers within a single device.

• Each analyzer described herein was operated in frequency-measurement mode (i.e., Fourier transformation of time-domain signals obtained using image current measurement)

• The shorter analyzer gives greater resolving power

• The longer analyzer allows for a wider m/z range

• The performance of each analyzer, in terms of resolving power and m/z range, can be anticipated via simple equations based on first principles.