Calculating the fragmentation process in quadrupole ion traps

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Highlights

  • Exact calculations of trajectory changes after ion dissociation.

  • Higher trapping efficiency at higher excitation q-value.

  • Calculation of resulting collisional temperatures.

  • Calculated fragment-ion signal-intensity discrimination.

Abstract

The present theoretical study calculates the consequences of an ion dissociating in a quadrupole field, describing both 3D and linear ion traps. The dissociation induces a change in q-stability parameter, resulting in fragment ions abruptly changing their trajectories. This includes a change in oscillation amplitude and mean-square velocity, i.e., effective collisional temperature. While the first one can lead to ions being lost to the electrodes, the latter one can be used to determine how likely fragment ions are to be further excited. During the collisional focusing process, ions can endure internal heating, just like during the injection process. The difference here is that fragment ions start this process with already elevated internal energies. The process is calculated by making use of the well-known phase-space ellipses. It is shown that fragment ions of lower m/z in average decrease their oscillation amplitude and are thus better trapped. Only very light ions close to the LMCO have a high chance of being lost. However, lighter fragment ions in average start with higher mean-square velocities than the precursor was assumed to need to have to induce dissociation, suggesting further collisional heating. Despite the harsh collisional environment m/z ratios close to the LMCO in average have to endure, a small percentage of these ions drastically decrease their oscillation amplitude, not requiring any collisional focusing. Fragment ions of higher m/z in average increase their oscillation amplitudes, however, their low velocities make further internal heating unlikely. The used calculations have been uploaded to Github: https://github.com/NeugebauerT/ion-trap.

Introduction

P.H. Dawson [1] and J.F.J. Todd were already early on one of the first and few scientists who saw the large potential of the phase-space ellipses that had been mathematically introduced to the mass spectrometry literature by M. Baril and A. Septier [2,3]. These phase-space ellipses can be derived from G.W. Hill's well-known solution [4,5] to the Mathieu equation [[6], [7], [8]] and had also already been shown by Paul and coworkers [9]. They can be used to exactly characterize the strictly speaking aperiodic trajectories in quadrupole fields. Further, they allow to simplify the complicated mathematics behind the solution to Mathieu's equation to basic geometric calculations of points on ellipses. Therefore, it is no surprise that we chose this same method to systematically investigate the collision-induced resonant excitation process in quadrupole ion traps. Dawson was already in extracts describing the phenomenon that happens at the moment an ion dissociates in the time and position dependent electric field, thereby changing its mass-to-charge ratio and with that its q-value [10]. This can result in a drastic change in trajectory and lead to fragment ions hitting the electrodes, although having mass-to-charge ratios laying in the stable area of the stability diagram. In addition to that, we use a recently presented similar method of obtaining these space-space ellipses as a second reference method [11,12].

The exact motivation for this investigation is to determine the observed trends in terms of ion loss ratios and especially reached velocities to allow predictions about possible consecutive excitation events. The collision harshness in the quadrupole ion trap and thus resulting fragmentation mass spectra are depending on the reached oscillation amplitude of the ions during the resonant excitation process. While by changing the way we apply auxiliary resonant excitation voltages, we can vary the way an ion increases its oscillation amplitude until it eventually dissociates, the change calculated here, caused by the change in q-value, cannot be influenced. This change is purely based on the change in mass-to-charge ratio at the moment of dissociation in the still identic oscillating electric field.

It will be first shown with the simple pseudopotential well-depth equation [13,14] that the only two important parameter describing the ions' velocity function in quadrupole ion traps is their q-stability parameter and the oscillation amplitude ions have. The velocity then determines the collision harshness described in the center-of-mass collision energy, which can further be converted into an effective collisional temperature [11,15]. As the excitation q-parameter may be chosen the same for any precursor ion, allows an ion independent characterization of the collision induced dissociation process. The mathematical consequences of the change in q upon dissociation are calculated in two ways that both build up on the same solution to Mathieu's equation. The first approach is geometric and thereby facilitates the understanding of the calculations. The second approach is very compact, also serving directly as a tool for verification. The results are followed by a short discussion of the made assumptions.

Section snippets

Theory

Before the exact solution to Mathieu's or Hill's equation will be used, very important principles are demonstrated, which also need to be understood to follow the actual calculations. These principles can already be shown with the well-known pseudopotential well approximation [13,14].

According to the literature, the pseudopotential well depth is given by:eD¯zqeV08with e being the charge of an electron, D¯z the pseudopotential (typically only used one-dimensionally for the z-direction, i.e.,

Calculating the fragmentation process

The essence of the following calculations is visualized in Fig. 3 and Fig. 4. It will be investigated now, how the oscillation amplitude zmax is affected, when the stability parameters abruptly change, which represents the ion's dissociation.

Discussion

In order to compare different fragmentation LMCO settings or fragmentation q-values, the oscillation amplitude zmax was adjusted for each q-value in order to result in the same root-mean-square velocity z˙RMS (here 1554.8 m/s) or effective collisional temperature Teff (here 700 K). This includes the assumption that these trajectories with slightly different velocity probability distributions [12,38] but equal vRMS and almost exactly equal z˙max3z˙RMS [12,36], result in the same reaction

Conclusion

Two ways have been presented of how to calculate the change in trajectory that happens at the moment an ion dissociates in the electric field of a quadrupole ion trap. During the resonant excitation process we can intentionally change the way we increase the oscillation amplitude to induce dissociation by manipulating excitation waveforms. The change in oscillation amplitude calculated here, however, cannot be influenced. Most important, resulting oscillation amplitudes can only be decreased by

Additional information

The shown calculations have also been uploaded to Github in form of a script in the Python programming language: https://github.com/NeugebauerT/ion-trap.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (46)

  • M. Splendore et al.

    A simulation study of ion kinetic energies during resonant excitation in a stretched ion trap

    Int. J. Mass Spectrom. Ion Process.

    (1996)
  • K.G. Asano et al.

    Thermal dissociation in the quadrupole ion trap: ions derived from leucine enkephalin

    Int. J. Mass Spectrom.

    (1999)
  • A. Colorado et al.

    An empirical approach to estimation of critical energies by using a quadrupole ion trap

    J. Am. Soc. Mass Spectrom.

    (1996)
  • B.A. Collings

    Fragmentation of ions in a low pressure linear ion trap

    J. Am. Soc. Mass Spectrom.

    (2007)
  • S.A. McLuckey et al.

    Protonated water and protonated methanol cluster decompositions in a quadrupole ion trap

    Int. J. Mass Spectrom. Ion Process.

    (1991)
  • Y. Wang et al.

    The non-linear ion trap. Part 3. Multipole components in three types of practical ion trap

    Int. J. Mass Spectrom. Ion Process.

    (1994)
  • Y. Wang et al.

    The non-linear resonance ion trap. Part 2. A general theoretical analysis

    Int. J. Mass Spectrom. Ion Process.

    (1993)
  • J. Franzen

    The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

    Int. J. Mass Spectrom. Ion Process.

    (1994)
  • J.F.J. Todd et al.

    An appreciation of the scientific researches of Dr Peter H. Dawson

    Rapid Commun. Mass Spectrom.

    (2019)
  • M. Baril et al.

    Piégeage des ions dans un champ quadrupolaire tridimensionnel à haute fréquence

    Rev. Phys. Appl.

    (1974)
  • R.E. March

    Quadrupole ion traps

    Mass Spectrom. Rev.

    (2009)
  • G.W. Hill

    On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon

    Acta Math.

    (1886)
  • C. Wilson

    The Hill-Brown Theory of the Moon's Motion: its Coming-To-Be and Short-Lived Ascendancy (1877-1984)

    (2010)
  • Cited by (0)

    Based in part on work originally submitted by T. S. Neugebauer as a thesis in partial fulfillment for the doctoral degree at the Friedrich-Alexander-Universität Erlangen-Nürnberg.

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