Computer simulation of single-ion trajectories in paul-type ion traps

A simple numerical simulation model can elucidate the key factors for designing a miniaturized ion trap mass spectrometer

BACKGROUND

Miniature ion trap mass spectrometer enables mass-to-charge ratio analysis of ions via quadrupole field in a low vacuum environment. It plays an important role in on-site detection due to its portability and specificity. In order to gain a deeper understanding of the analysis mechanism of miniature ion trap mass spectrometers, a quadrupole MS ion trajectory numerical simulation model (QITNS) is established in this paper for ions trajectory calculation under the action of quadrupole field, exciting field and neutral gas molecule collision. Compared with the existing methods, the model in this paper is simpler and more direct, which effectively explored the effects of dipole excitation and quadrupole excitation on ion manipulation under high background pressure.

RESULTS

The simulation results demonstrate that high RF amplitude, low auxiliary AC amplitude and quadrupole excitation can effectively improve the isolation resolution. Besides, it clarified the difference between the analysis mechanism of ion trap mass spectrometers under high background pressure (above 13.332 Pa) and absolute vacuum conditions. The relevant results are consistent with the conclusions of previous experiments and other theories, proving the applicability and accuracy of the proposed calculation model and solution method.

SIGNIFICANCE

This research bears the guiding significance for further understanding the mechanism of quadrupole mass spectrometry as well as designing and developing miniature mass spectrometers.

The Resonant Excitation Process in Commercial Quadrupole Ion Traps Revisited

The collision-induced resonant excitation process in real quadrupole ion traps is revisited theoretically and experimentally by explicitly including in the discussion the influence of higher order potential impurities. This includes mainly the dependence of the secular oscillation frequency f_ion on the ion's oscillation amplitude z_max. Due to frequency calibration, commercial ion traps use excitation frequencies f_exc that are higher than the theoretical secular oscillation frequency f_ion. This may lead to switching in frequency order between f_exc and f_ion that can allow ions to stay longer in on-resonance. It is also found that there is a most efficient but also a harshest excitation frequency, which are not identical. These phenomena are explained and described with a simple harmonic oscillator model and precise numerical calculations, using the trajectory simulation program ITSIM 5.0. Experimental MS² have been performed with the thermometer ion leucine-enkephalin, which are then in line with expectations from the trajectory calculations. The important difference to the existing literature is that, here, overexcitation is characterized by the observed a₄/b₄ fragment-ion ratio, while the fragmentation efficiency was kept constant. By slightly increasing the excitation frequency one can obtain drastically different effective collisional temperatures. This knowledge gives even commercial ion traps, without instrument adjustments, the possibility of producing energetically versatile fragment ion spectra. It is also shown that the damped driven harmonic oscillator cannot be used as a simplified model of the motion during the resonant excitation process in real ion traps.

Study of In-Trap Ion Clouds by Ion Trajectory Simulations

Gaussian distribution has been utilized to describe the global number density distribution of ion cloud in the Paul trap, which is known as the thermal equilibrium theory and widely used in theoretical modeling of ion clouds in the ion traps. Using ion trajectory simulations, however, the ion clouds can now also be treated as a dynamic ion flow field and the location-dependent features could now be characterized. This study was carried out to better understand the in-trap ion cloud properties, such as the local particle velocity and temperature. The local ion number densities were found to be heterogeneously distributed in terms of mean and distribution width; the velocity and temperature of the ion flow varied with pressure depending on the flow type of the neutral molecules; and the "quasi-static" equilibrium status can only be achieved after a certain number of collisions, for which the time period is pressure-dependent. This work provides new insights of the ion clouds that are globally stable but subjected to local rf heating and collisional cooling. Graphical Abstract ᅟ.

Fourier transform ion cyclotron resonance (FT ICR) mass spectrometry: Theory and simulations

Fourier transform ion cyclotron resonance (FT ICR) mass spectrometer offers highest resolving power and mass accuracy among all types of mass spectrometers. Its unique analytical characteristics made FT ICR important tool for proteomics, metabolomics, petroleomics, and investigation of complex mixtures. Signal acquisition in FT ICR MS takes long time (up to minutes). During this time ion-ion interaction considerably affects ion motion and result in decreasing of the resolving power. Understanding of those effects required complicated theory and supercomputer simulations but culminated in the invention of the ion trap with dynamic harmonization which demonstrated the highest resolving power ever achieved. In this review we summarize latest achievements in theory and simulation of FT ICR mass spectrometers.

A membrane introduction mass spectrometer utilizing ion-molecule reactions for the on-line speciation and quantitation of volatile organic molecules

RATIONALE

The ability of membrane introduction mass spectrometry to quantitatively resolve low molecular weight volatile organic compounds (VOCs) such as benzene, toluene, ethylbenzene and xylene (BTEX) using electron ionization (EI) can be compromised by isobaric interferences. This work focuses on reducing isobaric interferences with ion-molecule reactions in a portable quadrupole ion trap mass spectrometer for the analysis of VOCs.

METHODS

EI was used to produce reagent ions from precursors (chloroform, methyl iodide, trichloroethylene or chlorobenzene) that were continually infused into the helium acceptor phase upstream of the membrane introduction mass spectrometry (MIMS) sampling interface. The reagent ions were selectively stored in the ion trap, and then allowed to react with target VOC analytes in air samples via ion-molecule reactions within the trap storage volume. A variety of reaction times were examined (50-5000 ms), and the resulting product ions were analyzed in positive ion mode.

RESULTS

The detection limits achieved were comparable with those obtained using EI (low ppbv), and in some cases better than for EI coupled with tandem mass spectrometry (MS/MS). For the VOCs studied, isobaric interferences were greatly reduced or eliminated using chloroform as a reagent gas. The predominant ionization mechanism was via adduct formation, although charge transfer and hydride abstractions were also observed. An internal standard was shown to be effective at correcting for signal changes due to consumption of reagent ions when complex mixtures were sampled.

CONCLUSIONS

Ion-molecule reactions were exploited to eliminate isobaric interferences that are often encountered in direct, real-time analysis strategies for atmospheric VOC mixtures. The use of a continuously infused internal standard will improve quantitative results in field applications where analyte concentration and sample complexity may be wide ranging.

Computer Modeling of an Ion Trap Mass Analyzer, Part I: Low Pressure Regime

We present the multi-particle simulation program suite Computational Ion Trap Analyzer (CITA) designed to calculate the ion trajectories within a Paul quadrupole ion trap developed by the Jet Propulsion Laboratory (JPL). CITA uses an analytical expression of the electrodynamic field, employing up to six terms in multipole expansion and a modified velocity-Verlet method to numerically calculate ion trajectories. The computer code is multithreaded and designed to run on shared-memory architectures. CITA yields near real-time simulations with full propagation of 26 particles per second per core. As a consequence, a realistic numbers of trapped ions (100+ million) can be used and their trajectories modeled, yielding a representative prediction of mass spectrometer analysis of trace gas species. When the model is compared with experimental results conducted at low pressures using the conventional quadrupole and dipole excitation modes, there is an excellent agreement with the observed peak shapes. Owing to the program's efficiency, CITA has been used to explore regions of trapping stability that are of interest to experimental research. These results are expected to facilitate a fast and reliable modeling of ion dynamics in miniature quadrupole ion trap and improve the interpretation of observed mass spectra. Graphical Abstract ᅟ.

Realistic modeling of ion-neutral collisions in quadrupole ion traps

In this study, three ion-neutral collision models have been discussed and compared, including the Langevin, the hard-sphere and the mixed collision models. With the pseudo-potential approximation, analytical expressions of ion secular motions with the hard-sphere and mixed collision models have been obtained for the first time. Through numerical simulations and theoretical calculations, it is found that the mixed collision model could be used as a general description of ion-neutral collisions under different conditions. Langevin collision model is a good description of low energy collisions between small ions and neutrals, while hard-sphere collision model could be used to describe high energy collisions and/or ions with higher masses (larger physical sizes). These analytical expressions of ion motion decay profiles enable the creation of direct relationships between time-domain image currents with ion collision cross sections.

Theoretical calculations for mass resolution of a quadrupole ion trap reflectron time-of-flight mass spectrometer

We have developed a theoretical method of predicting the mass resolution for a quadrupole ion trap reflectron time-of-flight (QIT-reTOF) mass spectrometer as a function of the spatial and velocity distributions of ions, voltages applied to the electrodes, and dimensions of the instrument. The flight times of ions were calculated using theoretical equations derived with an assumption of uniform electric fields inside the QIT and with the analytical description of the potential including the monopole, dipole, and quadrupole components. The mass resolution was then estimated from the flight-time spread of the ions with finite spatial and velocity distributions inside the QIT. The feasibility of the theoretical method was confirmed by the reasonable agreement of the theoretical resolution with the experimental one measured by varying the extraction voltage of the QIT or the deceleration voltage of the reflectron. We found that the theoretical resolution estimated with the assumption of the uniform electric fields inside the QIT reproduced the experimental one better than that with the analytical description of the potential. The possible applications of this theoretical method include the optimization of the experimental parameters of a given QIT-reTOF mass spectrometer and the design of new instruments with higher mass resolution.

Calculation of coupled secular oscillation frequencies and axial secular frequency in a nonlinear ion trap by a homotopy method

In this paper the homotopy perturbation method is used for calculation of the frequencies of the coupled secular oscillations and axial secular frequencies of a nonlinear ion trap. The motion of the ion in a rapidly oscillating field is transformed to the motion in an effective potential. The equations of ion motion in the effective potential are in the form of a Duffing-like equation. The homotopy perturbation method is used for solving the resulted system of coupled nonlinear differential equations and the resulted axial equation for obtaining the expressions for ion secular frequencies as a function of nonlinear field parameters and amplitudes of oscillations. The calculated axial secular frequencies are compared with the results of Lindstedt-Poincare method and the exact results.

Quadrupole ion traps

The extraordinary story of the three-dimensional radiofrequency quadrupole ion trap, accompanied by a seemingly unintelligible theoretical treatment, is told in some detail because of the quite considerable degree of commercial success that quadrupole technology has achieved. The quadrupole ion trap, often used in conjunction with a quadrupole mass filter, remained a laboratory curiosity until 1979 when, at the American Society for Mass Spectrometry Conference in Seattle, George Stafford, Jr., of Finnigan Corp., learned of the Masters' study of Allison Armitage of a combined quadrupole ion trap/quadrupole mass filter instrument for the observation of electron impact and chemical ionization mass spectra of simple compounds eluting from a gas chromatograph. Stafford developed subsequently the mass-selective axial instability method for obtaining mass spectra from the quadrupole ion trap alone and, in 1983, Finnigan Corp. announced the first commercial quadrupole ion trap instrument as a detector for a gas chromatograph. In 1987, confinement of ions generated externally to the ion trap was demonstrated and, soon after, the new technique of electrospray ionization was shown to be compatible with the ion trap.

Ion trap mass analysis at high pressure: a theoretical view

The mass-selective manipulation of ions at elevated pressure, including mass analysis, ion isolation, or excitation, is of great interest for the development of mass spectrometry instrumentation, particularly for systems in which ion traps are employed as mass analyzers or storage devices. While experimental exploration of high-pressure mass analysis is limited by various difficulties, such as ion detection or electrical discharge at high-pressure, theoretical methods have been developed in this work to study ion/neutral collision effects within quadrupole ion traps and to explore their performance at pressures up to 1 Torr. Ion trapping, isolation, excitation, and resonance ejection were investigated over a wide pressure range. The theoretically calculated data were compared with available experimental data for pressures up to 50 mTorr, allowing the prediction of ion trap performance at pressures more than 10 times higher.

Model for ion injection into a quadrupole ion trap to assess the distribution of initial conditions of confinement

A pulsed ion-injection mode for a quadrupole ion trap is described. Switched direct current (d.c.) potentials are applied to the source and trap electrodes to inject the ions into the trap and slow them down. The injection time is sufficient to ensure a steady distribution of the injected ions at the beginning of the confinement. An elementary uni-dimensional model is detailed giving the axial positions and velocities of the ions injected into the trap. The ion distribution in phase space, the number of injected ions and the number of injected ions that will be trapped are also given. These expressions depend on ion position and velocity at the creation, applied potentials and spatial location of the source and trap electrodes. This model is validated by comparing simulation and experimental results. For this purpose the number of confined ions is plotted versus the slowing-down potentials applied on the ring and the upper end-cap of the trap. The size of the area of removable ions in the source is deduced from these results.

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle-in-cell approach

Using a 'Particle-In-Cell' approach taken from plasma physics we have developed a new three-dimensional (3D) parallel computer code that today yields the highest possible accuracy of ion trajectory calculations in electromagnetic fields. This approach incorporates coulombic ion-ion and ion-image charge interactions into the calculation. The accuracy is achieved through the implementation of an improved algorithm (the so-called Boris algorithm) that mathematically eliminates cyclotron motion in a magnetic field from digital equations for ion motion dynamics. It facilitates the calculation of the cyclotron motion without numerical errors. At every time-step in the simulation the electric potential inside the cell is calculated by direct solution of Poisson's equation. Calculations are performed on a computational grid with up to 128 x 128 x 128 nodes using a fast Fourier transform algorithm. The ion populations in these simulations ranged from 1000 up to 1,000,000 ions. A maximum of 3,000,000 time-steps were employed in the ion trajectory calculations. This corresponds to an experimental detection time-scale of seconds. In addition to the ion trajectories integral time-domain signals and mass spectra were calculated. The phenomena observed include phase locking of particular m/z ions (high-resolution regime) inside larger ion clouds. A focus was placed on behavior of a cloud of ions of a single m/z value to understand the nature of Fourier transform ion cyclotron resonance (FTICR) resolution and mass accuracy in selected ion mode detection. The behavior of two and three ion clouds of different but close m/z was investigated as well. Peak coalescence effects were observed in both cases. Very complicated ion cloud dynamics in the case of three ion clouds was demonstrated. It was found that magnetic field does not influence phase locking for a cloud of ions of a single m/z. The ion cloud evolution time-scale is inversely proportional to magnetic field. The number of ions needed for peak coalescence depends quadratically on the magnetic field.

Ion trajectory simulation for electrode configurations with arbitrary geometries

A multi-particle ion trajectory simulation program ITSIM 6.0 is described, which is capable of ion trajectory simulations for electrode configurations with arbitrary geometries. The electrode structures are input from a 3D drawing program AutoCAD and the electric field is calculated using a 3D field solver COMSOL. The program CreatePot acts as interface between the field solver and ITSIM 6.0. It converts the calculated electric field into a field array file readable by ITSIM 6.0 and ion trajectories are calculated by solving Newton's equation using Runge-Kutta integration methods. The accuracy of the field calculation is discussed for the ideal quadrupole ion trap in terms of applied mesh density. Electric fields of several different types of devices with 3D geometry are simulated, including ion transport through an ion optical system as a function of pressure. Ion spatial distributions, including the storage of positively charged ions only and simultaneous storage of positively/negatively charged ions in commercial linear ion traps with various geometries, are investigated using different trapping modes. Inelastic collisions and collision induced dissociation modeled using RRKM theory are studied, with emphasis on the fragmentation of n-butylbenzene inside an ideal quadrupole ion trap. The mass spectrum of 1,3-dichlorobenzene is simulated for the rectilinear ion trap device and good agreement is observed between the simulated and the experimental mass spectra. Collisional cooling using helium at different pressures is found to affect mass resolution in the rectilinear ion trap.

Prediction of collective characteristics for ion ensembles in quadrupole ion traps without trajectory simulations

Fundamental aspects are presented of a two-temperature moment theory for quadrupole ion traps developed via transformation of the Boltzmann equation. Solutions of the moment equations correspond to changes in the ensemble average for any function of ion velocity, because the Boltzmann equation reflects changes to an ion distribution as a whole. The function of primary interest in this paper is the ion effective temperature and its behavior during ion storage and resonance excitation. Calculations suggest that increases in ion effective temperature during resonance excitation are due primarily to power absorption from the main RF trapping field rather than from the dipolar excitation signal. The dipolar excitation signal apparently serves mainly to move ions into regions of the ion trap where the RF electric field, and thus ion RF heating, is greater than near the trap center. Both ideal and non-ideal ion trap configurations are accounted for in the moment equations by incorporating parameterized variables a and q , which are modified versions of the commonly used forms for the DC and AC ring voltages, and b and d , which are new forms that account for the voltages applied to the endcaps. Besides extending the applicability of the moment equations to non-ideal quadrupole ion traps, the modified versions of the parameterized variables can have additional utility. Calculation of the spatial dependence of ion secular oscillation frequencies is demonstrated as an example.

Simulations of ion trapping in a micrometer-sized cylindrical ion trap

We have performed detailed SIMION simulations of ion behavior in micrometer-sized cylindrical ion traps (r0 = 1 microm). Simulations examined the effects of ion and neutral temperature, the pressure and nature of cooling gas, ion mass, trap voltage and frequency, space-charge, fabrication defects, and other parameters on the ability of micrometer-sized traps to store ions. At this size scale voltage and power limitations constrain trap operation to frequencies about 1 GHz and rf amplitudes of tens of volts. Correspondingly, the pseudopotential well depth of traps is shallow, and thermal energies contribute significantly to ion losses. Trapping efficiency falls off gradually as qz approaches 0.908, possibly complicating mass-selective trapping, ejection, or quantitation. Coulombic repulsion caused by multiple ions in a small-volume results in a trapping limit of a single ion per trap. If multiple ions are produced in a trap, all but one ion are ejected within a few microseconds. The remaining ion tends to have favorable trapping parameters and a lifetime about hundreds of microseconds; however, this lifetime is significantly shorter than it would have been in the absence of space-charge. Typical microfabrication defects affect ion trapping only minimally. We recently reported (IJMS 2004, 236, 91-104) on the construction of a massively parallel array of ion traps with dimensions of r0 = 1 microm. The relationship of the simulations to the expected performance of the microfabricated array is discussed.

Kinetic theory of radio frequency quadrupole ion traps. I. Trapping of atomic ions in a pure atomic gas

A kinetic theory based on the Boltzmann equation is developed for the trapping of atomic ions in a radio-frequency quadrupole ion trap containing enough neutral atoms that ion-neutral collisions cannot be ignored. The collisions are treated at the same level of sophistication and detail as is used to deal with the time- and space-dependent electric fields in the trap. As a result, microscopic definitions are obtained for the damping and stochastic forces that originate from such collisions. These definitions contrast with corresponding phenomenological terms added ad hoc in previous treatments to create damped Mathieu and Langevin equations, respectively. Furthermore, the theory indicates that either collisional cooling or heating of the ions is possible, depending upon details of the ion-neutral mass ratios and interaction potential. The kinetic theory is not dependent on any special assumptions about the electric field strengths, the ion-neutral interaction potentials, or the ion-neutral mass ratio. It also provides an ab initio way to describe the ion kinetic energies, temperatures, and other properties by a series of successive approximations.

Determination of dioxins/furans and PCBs by quadrupole ion-trap gas chromatography-mass spectrometry

The versatility and sensitivity of the quadrupole ion trap tandem mass spectrometer has been applied to the determination of polychlorodibenzo-p-dioxins (PCDDs) and polychlorodibenzofurans (PCDFs), and of polychlorinated biphenyls (PCBs). A brief introduction to the theory of ion confinement in a quadrupole ion trap permits discussion of ion trajectory stability, mass-selective ion ejection, the frequencies of ion motion, and the role of resonant excitation of ion motion. The tandem mass spectrometric examination of PCDDs and PCDFs eluting and co-eluting from a gas chromatographic column is described. Illustrative examples are given of the analysis of field samples containing PCDDs and PCDFs. A comparison is presented of the performance of each of a quadrupole ion trap tandem mass spectrometer, a triple stage quadrupole mass spectrometer, and a sector instrument of relatively high mass resolution for the determination of PCDDs and PCDFs. This comparison is made with respect to instrument tuning, calibration plots, detection limits, ion signals at low concentration, relative response factors, ionization cross-sections, and the examination of field samples. The application of quadrupole ion trap tandem mass spectrometry to the examination of PCBs is focused upon those PCB congeners that have the greatest toxicity. 39 congeners of the total of 209 PCB congeners have been identified as having the greatest toxicities. Chemical ionization has been used for the determination of co-eluting congeners #77 and #110 where the toxicity of the former is much greater than that of the latter. An analytical protocol, based on the variation of molecular ion fragmentation according to the degree (or absence) of chlorine ortho-substitution, has been proposed for distinguishing between toxic and nontoxic PCB congeners.

Simulation of ion trajectories in a quadrupole ion trap: a comparison of three simulation programs

An attempt has been made to compare the performance, design and operation of three simulators, ISIS, ITSIM and SIMION-3D, when applied to the calculation of ion trajectories in a quadrupole ion trap. For the simulation of the trajectory of a single ion in a collision-free system, the calculated spatial trajectory components, kinetic energies and secular frequencies from the three simulators were virtually identical. It is concluded that, despite the various approaches to electrode design, calculation of fields, integration methods and ion generation tactics, there is a remarkable degree of consistency among the products of the simulators when dealing with collision-free conditions. The results of the ion injection simulations under collisional conditions were indicative of the complexity that can be introduced into the simulations with little effort. Random effects such as collisions of ions with He buffer gas and accumulated calculation errors together with the different collision model settings and the different approaches to field calculation are thought to have contributed to the somewhat minor differences in trapping efficiency. SIMION is the simulator of choice for the simulation of ion trajectories in hybrid instruments and in custom-designed assemblies of electrodes; and ITSIM would appear to be the best choice on the basis of computational speed for running multiparticle simulations and user friendliness. Both ISIS and ITSIM are adept at providing detailed information of collision events. Copyright 1999 John Wiley & Sons, Ltd.

Article

The quadrupole ion trap mass spectrometer is of great interest for chemical analysis. Nevertheless, negative ion studies using in situ ionization (negative ions created inside the ion trap) are difficult and limited. This paper describes the difficulties that occurred during negative ion analysis when using a commercial gas chromatography quadrupole ion trap mass spectrometer (GC/MS) system. Detection problems, due to simultaneous trapping of both positive and negative ions, are explained by the large kinetic energies of the ejected ions. Negative ion formation, produced by electron capture, is limited by the fundamental RF field, which imparts high kinetic energy to the electrons, precluding the possibility that the electrons will reach the thermal energies needed for electron capture processes. In addition, simultaneous confinement of negative and positive ions affects the recorded mass spectra. Space charge potentials that exist inside the ion trap (due to the ionization conditions necessary to detect negative ions) induce the destabilization of positive ions at higher m/z ratios, while negative ions in the same m/z range are stabilized. Moreover, loss of resolution and decalibration could occur for negative ions when they are ejected in the presence of positive ions with higher m/z ratios. At the very least, ion-ion reactions could limit the observation of negative ions. The understanding of these phenomena, viz. detection, formation, and simultaneous confinement, will permit the proposal of solutions for negative ion analysis with quadrupole ion trap mass spectrometers using in situ ionization.Key words: mass spectrometry, quadrupole ion trap, negative ion, perfluorotributylamine, space charge.

Extended theoretical considerations for Mass resolution in the resonance ejection mode of quadrupole Ion Trap Mass Spectrometry

Proceeding from the pseudopotential-well approximation for ion motion in a quadrupole ion trap, mathematical expressions are derived to describe the excitation amplitude of an ion packet at a given mass-to-charge ratio. Ion-neutral collisions are incorporated to describe the damping of ion trajectories and to describe the distribution of individual ion trajectories about a mean amplitude for the ion packet. The rate of increase of the amplitude during scanning is related to expressions that describe the amplitude dispersion of the ions at the time of ejection from the trap, which is operating in a resonance ejection scanning mode to describe the temporal line width of the ejected ion packet. The temporal line width is related to mass resolution under a number of different scanning conditions. Included in the discussion are considerations of the effect on resolution of the resonance excitation voltage, temperature, pressure, noise, and buffer-gas composition. An expression for the maximum possible resolution at high ion mass-to-charge ratios is developed, and these results are compared to an existing theoretical construction. The expressions derived under the pseudopotential-well approximation are further extended to high q z values and compared to experimental data previously published by two other researchers.