Experimental Characterization of Secular Frequency Scanning in Ion Trap Mass Spectrometers
Secular frequency scanning is implemented and characterized using both a benchtop linear ion trap and a miniature rectilinear ion trap mass spectrometer. Separation of tetraalkylammonium ions and those from a mass calibration mixture and from a pesticide mixture is demonstrated with peak widths approaching unit resolution for optimized conditions using the benchtop ion trap. The effects on the spectra of ion trap operating parameters, including waveform amplitude, scan direction, scan rate, and pressure are explored, and peaks at black holes corresponding to nonlinear (higher-order field) resonance points are investigated. Reverse frequency sweeps (increasing mass) on the Mini 12 are shown to result in significantly higher ion ejection efficiency and superior resolution than forward frequency sweeps that decrement mass. This result is accounted for by the asymmetry in ion energy absorption profiles as a function of AC frequency and the shift in ion secular frequency at higher amplitudes in the trap due to higher order fields. We also found that use of higher AC amplitudes in forward frequency sweeps biases ions toward ejection at points of higher order parametric resonance, despite using only dipolar excitation. Higher AC amplitudes also increase peak width and decrease sensitivity in both forward and reverse frequency sweeps. Higher sensitivity and resolution were obtained at higher trap pressures in the secular frequency scan, in contrast to conventional resonance ejection scans, which showed the opposite trend in resolution on the Mini 12. Mass range is shown to be naturally extended in secular frequency scanning when ejecting ions by sweeping the AC waveform through low frequencies, a method which is similar, but arguably superior, to the more usual method of mass range extension using low q resonance ejection.
KeywordsIon motion Simulations Miniature mass spectrometer Tandem mass spectrometry Higher order fields Collision-induced dissociation Ion ejection
The four experimental parameters that determine the stability of an ion in a quadrupolar field are thus (1) the amplitude of the dc potential, (2) the frequency of the applied fundamental rf waveform, (3) the radius of the device, and (4) the rf amplitude.
In a quadrupole mass filter , ions are selected for detection by mass selective stability , wherein the amplitudes of the rf and DC are increased while either keeping their ratio constant (constant resolution) or changing their ratio slightly to increase resolving power with mass and maintain unit resolution. With this method, ions of consecutive masses are successively brought to the apex of the Mathieu stability diagram, causing all other ions to become unstable. If the ramp of the rf and DC components is linear, time domain current or voltage data are linearly related to m/z. That is, m/z is directly proportional to the rf/DC amplitude.
By contrast, quadrupole ion traps operate on the basis of mass selective instability . In this technique, typically no DC component is used (U = au = 0), placing all ions on the q axis of the Mathieu stability diagram. The rf amplitude is ramped linearly as a function of time, causing ejection of ions of increasing m/z as they are brought successively to the ejection point (q = 0.908). The ions detected are thus those that are unstable, whereas only stable ions are detected in a conventional quadrupole mass filter. Since m/z is directly proportional to the rf amplitude, the time domain data correspond directly to the mass spectrum. Resonance ejection is a similar scan mode in which a “hole” is created on the q axis of the stability diagram by also applying a small supplementary dipolar AC voltage to eject ions whose secular frequencies match the frequency of the applied AC signal . As before, the rf is ramped, causing ions’ secular frequencies to change; when ions of particular m/z come into resonance with the frequency of the applied AC, these ions are mass-selectively ejected.
Alternative methods of scanning quadrupoles and ion traps exist but are uncommon. Scanning the frequency of the fundamental rf is a variant on the mass-selective instability scan that has been performed by only a few groups. The first report of rf frequency scanning demonstrated advantages for analysis of high mass ions , and subsequent reports demonstrated frequency scanning in a quadrupole mass filter with ions ranging in size from mass 176 Da  to microparticles . Frequency scanning has also been reported in specially designed digital ion traps, which do not have rf amplitude scan capabilities but which have demonstrated exceptionally fast scan rates while maintaining reasonable resolution (unit resolution for a 100 Hz scan rate, peak widths FWHM ~2.0 Th for a 1000 Hz scan rate) [12, 13, 14]. These scan methods simplify the electronics, but there remain problems of nonlinearity in mass calibration (save for the linear calibration described in ref. ), unexpected peaks, and poor mass resolution . As a result, traditional rf amplitude sweeps have remained the favored method of ion trap operation. It is also theoretically possible to sweep the size of the device (r0), but this is impossible in practice .
Thus we see that an ion’s secular frequency, for low au and qu, is inversely proportional to m/z. This is not a strictly accurate relationship throughout a,q-space, but it is a reasonable approximation in the range of values for which Equation 9 applies. This is important because it complicates mass calibration. In order to convert from the time domain to the mass domain, each time point must be converted to an excitation frequency dependent upon the scan parameters and electronic triggers. Each frequency is then converted to a value of beta and subsequently to a qu value using an iterative algorithm because beta is a continuing fraction in terms of qu. The qu value is then used to convert to mass, giving the ejected ion mass as a function of time. Thus, in contrast to the simple linear calibration in rf amplitude scanning, there is no analytical equation available to calibrate mass in secular frequency scanning. Nonetheless, a calibration procedure is demonstrated in ref. .
To date, secular frequency scanning has been mentioned in patents [25, 26] and review papers  but has only been performed sparingly. Welling and co-workers used this method, which they termed “secular scanning”, to obtain higher resolution mass spectra when compared to q scanning in a linear ion trap (the resonance was quadrupolar over a limited mass range and with slow frequency scanning) , Roth and coworkers used secular frequency scanning in a linear trap for mass selective excitation , and the Austin group at Brigham Young University used it to scan ions out of the halo ion trap [29, 30, 31]. Note that in the case of the halo trap, the geometry of the device necessitated the use of AC frequency scanning because simulations indicated that a conventional rf amplitude ramp would cause ions to collide with the electrodes and ceramic holders instead of being ejected out the apertures in the electrodes. However, AC scanning has yet to be systematically characterized despite some clear advantages, particularly the fact that the high amplitude, high frequency rf signal is kept constant, which greatly simplifies the electronics since strictly linear rf ramps, which are difficult to generate, are no longer needed. This feature is particularly appealing for miniature instruments [32, 33]. More importantly, precursor ion scans using a single ion trap [34, 35] can be performed by exciting ions of successive masses as a function of time using a low amplitude dipolar signal while a chosen product ion is ejected by applying a second high amplitude constant frequency AC signal at the product ion’s secular frequency. This capability would appear to mark a significant step forward in ion trap mass spectrometry, bringing single ion trap capabilities closer to those of the widely used triple quadrupole. The performance of a triple quadrupole is much superior but in some applications the small size and simplicity may favor use of an ion trap. These extended ion trap capabilities demand an understanding of the underlying principles, particularly those of secular frequency scanning, in order to improve the performance of precursor scans in single ion traps.
In this paper, we show that secular frequency scans can be carried out using either a miniature rectilinear ion trap mass spectrometer or a commercial linear ion trap. We also characterize the effect of scan direction, scan rate, rf amplitude, rf frequency, AC amplitude, and pressure on the spectra, and demonstrate facile mass range extension compared with conventional rf amplitude sweeps at low q. “Black holes” occurring at nonlinear resonance points are also investigated.
Frequency scanning experiments were performed using the Mini 12  miniature rectilinear ion trap (RIT)  mass spectrometer and a benchtop Thermo LTQ XL linear ion trap (Thermo Scientific, San Jose, CA, USA) in the positive ion mode. The former was chosen to assess the effect of higher order fields and higher pressures, whereas the LTQ exhibits higher performance. The rectilinear ion trap uses electrodes with rectangular cross sections, in contrast to the hyperbolic cross sections of the commercial LTQ. The rf is applied to the y electrodes, while the AC and other waveforms are applied in a dipolar fashion to the x electrodes, which have slits for ion ejection.
Secular frequency scans were performed by outputting a swept frequency sinusoidal waveform of 0.5–10 Vp-p (peak to peak) over a range of 10–500 kHz in a scan lasting 300–800 ms, unless otherwise specified, from a Sony Tektronix AFG320 arbitrary function generator (Beaverton, OH, USA). In the case of the Mini 12, two channels were used to produce a dipolar (180° out of phase) waveform that was applied to the x electrodes after passage through a low pass frequency filter with a cutoff frequency of 500 kHz. Data were recorded using the data system of the Mini 12 . The function generator was triggered on a high frequency kilohertz AC waveform of ~7 Vp-p output from the Mini AC waveform board in a 1 ms segment just prior to the mass scan. Unless otherwise specified, all scans were performed using a constant rf amplitude of 6000 digital-to-analog converter (DAC) units (~195 V0-p) and 0.999 MHz frequency, corresponding to a lower mass/charge cutoff of ~98 Thomson (Th). Note that DAC units and rf and AC amplitudes are directly proportional.
Using the LTQ, secular frequency scans were performed by replacing the resonance ejection waveform generated from the analog board with the same swept frequency waveform as just described. The function generator was triggered at the start of the mass scan using the triggers included in the LTQ Tune diagnostics menu. The rf frequency was tuned to 1.1995 MHz, and the change in rf amplitude built into the Thermo system was minimized by performing “Ultrazoom” scans over the period of the AC frequency scan. Ultrazoom scans occur at a rate of 27 Da/s. This small change in rf amplitude slightly changes resolution, depending on scan direction, but otherwise has a minimal effect on the spectra. The lower mass cutoff (lmco or LMCO) was typically set at 100–200 Th at the beginning of the scan. The LTQ’s data system was used to collect data (~2700 points per s). Unless otherwise specified, all AC scans were linear forward frequency sweeps from low to high frequency (high mass to low mass).
Ions studied in both traps were generated by nanoelectrospray ionization (nESI) at ~2000 V. In the case of the Mini 12, ions were gated into the mass analyzer for ~12 ms, followed by a ~500 ms ion cooling period. The standard Ultrazoom scan function was used in the LTQ.
Simulations were performed in ITSIM 6.0  using a 2010 MacBook Pro (2.4 GHz Core i5, 3 GB usable RAM, 32-bit Windows 10). One hundred ions of each m/z were generated at the start of the simulations with a Gaussian distribution of positions about the center of the trap but zero velocity in x, y, and z. The frequency, but not amplitude, of the supplementary AC waveform applied to the simulated rectilinear trap was ramped linearly (in a forward or reverse direction) versus time while the main trapping rf amplitude and frequency were kept constant. Simulated scan times were shortened to ~3 ms in order to decrease computational time. In order to compensate for the shorter scan time, higher AC amplitudes were used. Collisions were simulated using a hard-sphere collision model at 4 mTorr helium.
Didodecyldimethylammonium bromide and EPA 508.1 herbicide mix (a mixture of alachlor, butachlor, simazine, atrazine, metolachlor, and hexachlorocyclopentadiene) were purchased from Sigma Aldrich (St. Louis, MO, USA, and Bellefonte, PA, USA, respectively). Hexadecyltrimethylammonium bromide was purchased from Tokyo Chemical Industry Co. (Tokyo, Japan). Benzylhexadecyldimethylammonium chloride was purchased from JT Baker Chemical Co. (Phillipsburg, NJ, USA). Ultramark calibration solution (4.5 ppm caffeine, 2 ppm MRFA, and 0.0005% Ultramark 1621 in ACN:MeOH:H2O 2:1:1 with 0.5% acetic acid) was purchased from Thermo Fisher (Rockford, IL, USA). All reagents were initially dissolved in either HPLC grade methanol (MeOH) or deionized water and then diluted in 50:50 MeOH:H2O with 0.1% formic acid to obtain their final concentrations, which were generally 1–10 ppm.
Results and Discussion
The secular frequency scans over a frequency range of 10–500 kHz, swept from low to high frequency with an amplitude of 3 Vp-p (Mini 12) and 1 Vp-p (LTQ), are shown in Figure S3 for a sample of three tetraalkylammonium ions (2–6 ppm) along with the equivalent resonant ejection spectra using the Mini 12 (simulated results shown in (b) and the LTQ (d)-(f). Peak widths are quite broad (~2 ms FWHM) in the RIT, likely due to the low pressure in the trap and the presence of higher order fields, whereas the LTQ shows much sharper peaks (~1 ms FWHM). The spectrum obtained from the LTQ when converted to the mass domain (Figure S3e), indicated peak widths of ~2–3 Da. Preliminary experiments using an approximately linear mass scan on a cylindrical ion trap showed the ability to resolve bromine isotopic peaks, despite the imperfect geometry (Figure S4). Under more optimal conditions where the rf amplitude is increased (LMCO = 200 Th), peak widths approaching unit width can be obtained using the LTQ, as discussed later. Resolution decreases with increasing mass due to the nonlinear spacing of ion secular frequencies in terms of mass.
In general, reverse frequency sweeps (forward mass scans) result in up to 50% higher signal compared with forward frequency sweeps on the Mini 12, and resolution in the reverse sweep is also significantly better.
The same effect of scan direction on mass spectra is observed in conventional rf scans with resonance ejection . Owing to nonlinear fields, ion frequencies shift upward toward the ejection point in a forward resonance ejection scan (low mass to high mass), resulting in an increase in sensitivity and resolution; the opposite effect is observed for the reverse rf amplitude sweep since the secular frequency shifts away from the working point . See Figure S6 for reproduced resonance absorption curves of n-butylbenzene, which show the increase of ion secular frequency at higher AC amplitudes (i.e., in regions with more prominent higher order fields). The effect is much less pronounced on the LTQ since its rods are hyperbolic rather than rectangular .
Note that nonlinear fields cause absorption spectra to shift to higher frequencies only for a positive octopole or other even higher order contribution, as is present in the Mini 12 . A positive octopole increases field strength, particularly near the electrodes, which causes ion frequencies of motion to increase correspondingly. The opposite occurs for a negative octopole component. For traps with a negative octopole component, higher resolution and sensitivity would be obtained in the forward frequency sweep.
A rather minor but interesting and unexpected effect of scan direction is illustrated by the red boxes in Figure 1. The relative spacing between the indicated peaks is identical to the spacing between the main peaks in the spectrum, which indicates that the same ions are being ejected at different frequencies. As we will show later, these frequencies correspond to higher order parametric resonances, which are observed despite using dipolar excitation. In the forward sweep, these resonances, of which there are many as given by Equation 6, are encountered before the secular frequency. This could have both a detrimental and favorable effect on resolution and sensitivity. In the forward sweep, the ions would increase their amplitude as they encounter these higher order resonances, which may increase the rate of ejection when their secular frequencies match the AC frequency at a later point in time. However, this effect appears to be very small, likely due to collisional cooling during the long mass scan, so that resolution and sensitivity in forward frequency sweeps are always worse than in reverse sweeps. The parametric resonances are significantly weaker on the LTQ than on the Mini, which indicates that higher order fields play a role. Curiously, the parametric resonances also appear in reverse frequency sweeps, even though they are encountered after the secular frequency. However, secular frequency scanning, particularly with low AC amplitudes, is a relatively weak method of ejection, so a small population of ions is left over after their secular frequencies have already been matched. Thus, these ions are ejected at their parametric resonance frequencies instead.
The effect of scan rate on the spectra is shown in Figure S7. The scan rate was changed by altering the scan time on the function generator while keeping the scan range constant. The scan rate here is nonlinear since the AC frequency is swept linearly while ion secular frequencies follow an approximately inverse relationship (Equation 11). Nonetheless, decreasing the scan rate increases peak separation in time, which is an expected result since ions experience more rf cycles at or near resonance and since their resonance conditions are further separated in time, but it decreases signal intensity. A similar result is obtained in conventional rf amplitude scans; decreasing the scan rate increases resolution but also decreases S/N, the latter partly due to charge transfer to neutral gas molecules .
Experimental Ejection Frequencies for Ions in Figure 5, Indicating Ejection of Ions at Higher Order Parametric Resonances Despite Application of Only Dipolar Excitation
Experimental ejection time (ms)
Experimental ejection frequency (kHz)
Parametric frequency / experimental frequency
AC frequency (kHz)
K = 2 or dipolar
K = 2 or dipolar
K = 2 or dipolar
K = 4
K = 4
K = 4
K = 6
K = 6
K = 6, 8
K = 8
K = 10
K = 10
Although higher order dipolar resonances have not previously been reported, it is feasible that higher order parametric resonances are being excited due to the coupling of motion in the x and y dimensions, which is a direct result of higher order field components (e.g., hexapole and octopole) introduced by electrode imperfections, electrode truncation, non-ideal geometries, and misalignment. The calculated frequencies of ejection at the higher AC amplitudes corresponded to approximately one-half, one-third, one-fourth, and one-fifth of the secular frequency (Table 1), or equivalently one-fourth, one-sixth, one-eighth, and one-tenth of the parametric resonance frequency, which is indicative of higher order quadrupolar resonances (K > 1 in Equation 6). These resonances were not limited to the Mini 12; spectra on the LTQ also suffered from these added peaks if the amplitudes of the AC and rf were high enough (see Figure S9 and Table S1). Since the LTQ has hyperbolic rods compared with the rectangular cross sections in the RIT, the resonances were more difficult to observe, presumably because of weaker coupling of ion motion in x and y. For example, only with a very high LMCO of ~1000 Da were the parametric resonances observed on the benchtop instrument. Furthermore, the K = 4 resonances were the only ones observed in this case, which is further evidence for x,y-coupled motion as the cause.
In general, higher resonances can only be accessed with higher excitation amplitudes as illustrated in Figure S10, which is reproduced from Collings et al. This shows regions of the Mathieu stability diagram in which the higher order parametric resonances may be accessed. Since the parameter Q is directly proportional to the excitation amplitude and because K increases with Q, higher amplitudes are required for excitation at K > 1 resonances.
An alternative explanation for these findings is possible: electronic coupling between the AC and rf waveforms could accidentally introduce a small supplementary quadrupole field. The need for higher AC and rf amplitudes corroborates this explanation as well. However, though the rf and AC are coupled together electronically on the LTQ (i.e., the rf is applied to all four rods and the AC is applied only to one pair), this is not the case on the Mini 12. In the latter case, the rf is applied to one rod pair and the AC is applied to the other pair, so there ought to be no coupling between the two. Small perturbations in the sinusoidal excitation could also promote excitation at parametric resonances because of the introduction of higher harmonics. Nonetheless, the more likely cause is the higher order field components because of (1) the difference in the accessibility of these resonances on the two different instruments, (2) the observation of parametric resonances on both instruments with two different sets of electronics, and (3) the AC amplitude dependence observed on the Mini 12, which agrees with previous reports (Figure S10).
In any case, sensitivity and peak width appeared to be improved over that of the fundamental resonance, which has been reported previously [22, 23]. Higher resolution at higher order resonances may present an interesting alternative to mass spectral acquisition compared with the fundamental resonances. Furthermore, if the secular frequency scan were used for fragmentation, it may benefit from the higher order fields since ions will gain kinetic energy at several points during the mass scan (the secular frequency and the higher order parametric resonances), promoting more efficient collision-induced dissociation. The fragmentation would be fairly mass-selective in time, but different ions of the same mass would presumably fragment at several different times, leading to some overlap in the spectral intensities.
An advantage of secular frequency scanning over conventional rf scanning is mass range extension at low rf amplitudes. Mass range extension can also be accomplished in an ion trap by resonance ejection at a low q value, that is, at a low AC frequency, or by lowering the rf frequency . Figure S11 shows the secular frequency scan mass spectrum of a calibration solution of caffeine (m/z 195), the peptide MRFA (m/z 525), and Ultramark 1621 (m/z 1022–1922, every 100 Th). For reference, resonance ejection at an optimal q value was performed as well (Figure S12). As shown, the high mass Ultramark calibration ions can be detected at low rf amplitudes by using a relatively low amplitude AC waveform scanned through low frequencies using an appropriate scan time. Despite the closeness of their secular frequencies, the fast frequency scanning, and the large mass range, the Ultramark peaks are resolved in a linear frequency sweep, and their higher order resonances can even be observed using the Mini 12 with a 4 Vp-p AC amplitude (not shown). The same experiment on the LTQ is shown in Figure S11c and S11d. Ion intensity in the secular frequency scan with a LMCO of 1000 Th is double that in the resonance ejection scan with a LMCO of 50, though the latter is a shorter scan in terms of time and the scan rate is uniform, which contrasts with the secular frequency scan in which the scan rate increases with mass. When converted to the mass domain (not shown), the approximate resolution is ~2 Da FWHM (m/z 1422) for the secular frequency scan, but again resolution degrades with increasing mass. Mass range extension in this method is arguably superior to resonance ejection at low q for several reasons: in the latter case (1) ions are also ejected at q = 0.908, convoluting the mass spectrum, (2) higher rf amplitudes are required, (3) a linear rf amplitude ramp is needed, and (4) the entire mass spectrum is difficult to obtain because of the low mass cutoff imposed by the supplementary AC [this assumes ions below that cutoff are ejected from the trap prior to the mass scan, due to reason (1)].
Secular frequency scanning is an electronically simple alternative to conventional rf amplitude or frequency ramping, which has advantages in terms of access to ions of high mass. Initial results show poorer resolution, but this can be optimized by tuning the AC amplitude, rf amplitude (or rf frequency), and pressure, or by scanning at a constant rate. Higher order fields and non-optimal pressure also appear to contribute to peak broadening. Imperfect ion traps with large higher order field contributions, such as the Mini 12, through coupling of x- and y-motion of ions excited by a dipolar signal allow parametric excitation with observation of signals at a set of higher order parametric resonances. In normal dipolar secular frequency scan conditions, these processes do not make a large contribution to the mass spectra, but it is important to recognize their origin.
The authors thank Zane Baird and Adam Hollerbach for help with electronics and data collection, and Wolfgang Plass for the improved version of ITSIM 6.0. The authors also acknowledge discussions with Jae Schwartz (Thermo Fisher Scientific). This work was supported by NASA (grant IP 11033366).
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