Quadrupole mass filters with octopole fields

The performance of quadrupole mass filters with added octopole fields in the range 2.0-4.0% has been investigated. The added fields are much greater than those normally added to conventional rod sets by mechanical tolerances or construction errors. Quadrupole rod sets with added octopole fields were constructed with round rods by making one pair of rods greater in diameter than the other pair. For positive ions, resolution at half height of only about 200 is possible if the negative direct current (dc) output of the quadrupole power supply is connected to the smaller rods. If the positive dc output of the quadrupole power supply is connected to the smaller rods, the resolution improves dramatically; a resolution at half height of 5800 has been observed with a rod set with 2.6% added octopole field. For negative ions the best resolution is obtained with the polarity of the dc reversed, i.e. with the negative dc applied to the smaller rods. These findings are unexpected in view of the literature that argues that to obtain high mass resolution with quadrupole mass filters, higher order multipoles must be kept as small as possible. Numerical simulations of peak shapes agree qualitatively with experiments. Simulation of the boundaries of the first stability region for positive ions shows that when the positive dc is applied to the smaller rods, the addition of a 2.0% octopole field causes the boundaries to shift slightly but the boundaries are well defined, and the tip of the stability region remains sharp. When the positive dc is applied to the larger rods, the boundaries of the stability region move out and become diffuse. For instruments that require a rod set that can be used both as a linear trap and a mass filter, these rod sets may offer improved trap performance while still being capable of providing conventional mass analysis.     

Experimental investigation of mass analysis using an island of stability with a quadrupole with 2.0% added octopole field

We describe experimental investigations of mass analysis using an island of stability with a linear quadrupole with a 2.0% added octopole field. The island is formed by auxiliary quadrupole excitation. The experiments confirm the results of previous computer simulations (Konenkov et al., J. Am. Soc. Mass Spectrom. 2007; 18: 826-834). With the resolving direct current (dc) applied to the quadrupole so that the Mathieu parameter a > 0, conventional mass analysis with applied radio-frequency (rf) and dc and no auxiliary excitation is possible. In this case, use of an island of stability yields similar peak shape and resolution. However, with the polarity of the resolving dc reversed, so that a < 0, only very low resolution can be obtained; the added octopole prevents conventional mass analysis. By using a stability island when a < 0, the resolution is substantially improved. In this case the use of an island allows mass analysis under conditions where the added octopole field severely degrades conventional analysis. The experiments also confirm the position of the island predicted by the simulations.     

Mass analysis with islands of stability with linear quadrupoles incorporating higher order multipole fields

Mass analysis with islands of stability has been investigated with three linear quadrupole mass filters: two with 4% added hexapole fields constructed with equal diameter (quadrupole 4A) and unequal diameter (quadrupole 4B) rods, and a conventional round-rod quadrupole that has apparently been slightly damaged. Islands are formed by applying auxiliary quadrupole excitation. With the Mathieu parameter, a < 0, mass analysis with both quadrupoles with hexapole fields operated normally, i.e., without islands, gives only low resolution. A factor of 10 or more increase in resolution is possible with the use of stability islands. With a > 0, when quadrupole 4A is operated normally, peak shapes similar to that of a conventional quadrupole can be obtained at resolutions higher than 850. At lower resolutions, peaks are split. When quadrupole 4B is operated without islands, resolution up to 2000 is possible, but there are low mass tails and structure is formed on the peaks. With mass analysis with an island of stability, both quadrupoles 4A and 4B show peaks free of structure and without tails. Ion transmission is also improved with some operating conditions. With the conventional round-rod quadrupole, mass analysis with islands of stability increases the limiting resolution from 2500 to 4360. At a resolution of 2500, the transmission is increased by about two orders of magnitude. These results show that the use of islands of stability improves mass analysis with quadrupoles with distorted fields, and may, in the future, allow use of quadrupoles constructed with at least some lower mechanical tolerances.     

Linear quadrupoles with added hexapole fields

Linear quadrupoles with added hexapole fields are described. The shifts in ion oscillation frequency caused by the addition of a hexapole field are calculated within the effective potential model. Methods to construct linear quadrupoles with added hexapole fields with exact electrode geometries and with round rods are discussed. A quadrupole with added hexapole field can be constructed with round rods by rotating two rods (say the y rods) towards an x rod. Computer simulations are used to investigate the possibility of mass analysis with quadrupoles with added hexapole fields. We find that a quadrupole with an added hexapole field in the range 2-12% can provide mass analysis provided the dc is applied with the correct polarity and value. When a rod set is constructed with round rods, other multipoles in the potential degrade the peak shape, resolution and transmission. The largest of these after the quadrupole and hexapole are a dipole and octopole term. With round rod sets, the peak shape can be improved by using different diameters for the x and y rod pairs to minimize the octopole term in the potential and by injecting ions at the field center where the dipole term is zero. Calculations of the boundaries of the stability diagram for this case show the boundaries move out, relative to those of a pure quadrupole field, but remain sharp.     

Quadrupole mass filters with added hexapole fields

Conventional mass analysis has been investigated experimentally with six quadrupole mass filters with added hexapole fields; three with added hexapole fields of 4%, 8% and 12% with equal diameter rods, and three with added hexapole fields of 4%, 8% and 12% with unequal diameter rods to remove an added octopole field. Compared with conventional quadrupoles, these rod sets have very large field distortions. With the positive resolving dc applied to the y rods (Mathieu parameter ) only low resolution (10–100) and low transmission are seen. With the polarity reversed ( ) much higher resolution (≥1000) and transmission are possible. Increasing the magnitude of the added hexapole field decreases the limiting resolution at m/z 609. Removing the added octopole field increases the limiting resolution. In some cases structure is formed on the peaks. For a given scan line slope, U/V _rf , the resolution decreases as the amplitude of the added hexapole field increases. These results are consistent with changes to the stability diagrams, calculated here. With , adding a hexapole field causes the x stability boundary to move outward with all rod sets. With , the boundaries become diffuse and the tip of the stability diagram becomes rounded, limiting the resolution to ca. 10‐100. Where comparisons are possible, experiments show the rod sets with added hexapole fields have transmission 10–300 times less than a conventional quadrupole. Thus these quadrupoles are less useful for mass analysis than conventional quadrupoles. However, it is surprising, given the highly distorted fields, that some of the quadrupoles give resolution of 1000 or more. Copyright © 2010 John Wiley & Sons, Ltd.     

Mass selective axial ion ejection from linear quadrupoles with added octopole fields

Mass selective axial ejection of ions from linear quadrupoles with added octopole fields is described. Quadrupoles with 2.0% and 2.6% added octopole fields have been tested and compared with a conventional quadrupole. The effects of trapping ions at different q values, excitation voltage, scan direction, balanced and unbalanced rf voltages on the rods, and dc applied between the rods have been investigated. The highest scan speeds and best resolution are obtained with resonant excitation and ejection at high q (q = 0.8). With axial ejection, the quadrupole with a 2.0% added octopole field provides mass resolution and ejection efficiencies similar to a conventional rod set. Quadrupole, dipole, and simultaneous dipole-dipole excitation between the x and y rod pairs were compared, and no advantage was found with quadrupole or dipole-dipole excitation. The effects of scan speed were investigated and a resolution at half height of about 1600 is possible at scans speed up to 5000 Th/s.     

Quadrupole excitation of ions in linear quadrupole ion traps with added octopole fields

Modeling and experimental studies of quadrupole excitation of ions in linear quadrupole traps with added octopole fields are described. An approximate solution to the equations of motion of ions trapped in a quadrupole with added octopole and dodecapole fields, with quadrupole excitation and damping is given. The solutions give the steady-state or stationary amplitudes of oscillation with different excitation frequencies. Trajectory calculations of the oscillation amplitudes are also presented. The calculations show that there can be large changes in the amplitude of ion oscillation with small changes in excitation frequency, on both the low and high-frequency sides of a resonance. Results of experiments with quadrupole excitation of reserpine ions in linear quadrupole traps with 2.0%, 2.6%, and 4.0% added octopole fields are given. It is found that as the excitation frequency is changed, two resonances are generally observed, which are attributed to the motion in the x and y directions. The two resonances can have quite different intensities. Sudden jumps or sharp sided resonances are not observed, although in some cases asymmetric resonances are seen. The calculated frequency differences between the two resonances are in approximate agreement with the experiments.     

Ion excitation in a linear quadrupole ion trap with an added octopole field

Modeling of ion motion and experimental investigations of ion excitation in a linear quadrupole trap with a 4% added octopole field are described. The results are compared with those obtained with a conventional round rod set. Motion in the effective potential of the rod set can explain many of the observed phenomena. The frequencies of ion oscillation in the x and y directions shift with amplitude in opposite directions as the amplitudes of oscillation increase. Excitation profiles for ion fragmentation become asymmetric and in some cases show bistable behavior where the amplitude of oscillation suddenly jumps between high and low values with very small changes in excitation frequency. Experiments show these effects. Ions are injected into a linear trap, stored, isolated, excited for MS/MS, and then mass analyzed in a time-of-flight mass analyzer. Frequency shifts between the x and y motions are observed, and in some cases asymmetric excitation profiles and bistable behavior are observed. Higher MS/MS efficiencies are expected when an octopole field is added. MS/MS efficiencies (N(2) collision gas) have been measured for a conventional quadrupole rod set and a linear ion trap with a 4% added octopole field. Efficiencies are chemical compound dependent, but when an octopole field is added, efficiencies can be substantially higher than with a conventional rod set, particularly at pressures of 1.4 x 10(-4) torr or less.     

Dipole Excitation: A New Method for Mass Analysis with a Quadrupole Mass Filter

Trajectory calculations are used to investigate peak shapes and ion transmission with a proposed new method of mass analysis with a quadrupole mass filter. Dipole excitation is applied to either the x or the y electrodes, or both, to create bands of instability within the first stability region. With excitation between the y electrodes (near β _y ?=?0), ions are removed from the low mass side of a peak, and with ion excitation in x (near β _x ?=?1), ions are removed from the high mass side. The mass resolution can be approximately doubled with comparatively little loss in ion transmission. Ion motion in an ideal quadrupole field and in the field of a quadrupole constructed with round rods has been studied. With an ideal quadrupole field, excitation in y is found to give better peak shape and resolution than excitation in x. With quadrupoles constructed with round rods, excitation in y is found to remove ions from both the low and high mass sides of a peak. The additional higher order multipoles introduced to the quadrupole potential by the use of round rods couple the x motion to the y motion so that exciting the y motion also excites ions in x. Thus, only excitation in y is necessary. Both with an ideal quadrupole field and quadrupoles constructed with round rods, the resolution can be increased ca. ×2 with little loss of transmission.

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Graphical Abstract ?

     

Computational evaluation of mass filter acceptance and transmittance influenced by developing fields: An application of the plane method to investigate prefilter efficacy for rectangular wave operated mass filters

The acceptance of quadrupole mass filters is improved when the alternating current (AC) and direct current (DC) fields are developed separately. Physically, this is achieved when a short RF only quadrupole (prefilter) is situated directly ahead of the mass filter. The acceptance gained by a system operating with a prefilter can be observed as an increase in sensitivity over conventional operation. Frequency dynamic duty cycle based rectangular waveform driven (rectangular wave) mass filters, a recent development, currently do not operate with prefilters. Little is known about the influence of duty cycle changes on the acceptance of rectangular wave mass filters. The sensitivity gain seen by conventional systems operating with prefilters indicates that the sensitivity of duty cycle based rectangular wave systems should increase comparably. The objective of this work was to determine prefilter efficacy for nonspecific rectangular wave mass filter systems. In this work, the plane method of acceptance was used to model the change to the acceptance and transmittance of sine and rectangular waveform driven mass filters under different modes of field development. Both systems indicated a fourfold increase in sensitivity when the mass filtering DC or duty cycle was delayed.     

Linear quadrupoles with added octopole fields

Two methods of adding relatively small octopole fields to the main quadrupole field of quadrupoles and linear ion traps with cylindrical rods are investigated. The first, 'stretching' the quadrupole by moving two rods out from the axis, produces a combination of higher order fields with similar magnitudes in which the octopole field is not necessarily the greatest. The quadrupole field strength is changed significantly and a large potential appears on the axis. The second method uses rod pairs of different diameters. It adds octopole components of up to several percent while all other higher order fields remain small. An axis potential is also added, but it is only a few percent of the radio-frequency (RF) voltage and approximately equal to the strength of the octopole field. The axis potential can be removed by moving the larger rod pair out from the axis or applying unbalanced RF to the electrodes.     

Erratum to: Upper stability island of the quadrupole mass filter with amplitude modulation of the applied voltages

Modulation of the voltages applied to a quadrupole mass filter (QMF), either RF or RF and DC, leads to splitting of the stability region into islands of stability. The ion optical properties, such as transmission, resolving power and peak tails of the first upper stability islands have been investigated by numerical simulation of ion trajectories. The dependence of the location of this island on the amplitude of the modulation and the parameter ν=ω/Ω=Q/P where ω is modulation frequency, Ω is main angular radio frequency, and Q and P are integers, is calculated in detail. Different methods of adjusting the QMF resolution are examined. It is found that operation at the upper and lower tips of the stability islands created by amplitude modulation of the RF voltage is preferred, because of the technical simplicity of this method and a reduction of the required separation time. Amplitude modulation improves the performance of a QMF constructed with round rods, in comparison to perfect quadrupole fields. For example, with amplitude modulation of the RF, to reach a resolution of R_0.1=1200 requires only about 75 RF cycles of ion motion in a quadrupole field created by round rods.     

A novel tandem quadrupole mass analyzer

A new “tandem mass analyzer” is described. Two quadrupole mass filters are operated in series. Each is operated at low resolution and a small mass offset is introduced between the two quadrupoles so that the pair operate together to give higher resolution. The resolution of the tandem analyzer can be changed by changing the mass offset. The transmission is highest when the quadrupoles are operated as close together as possible with the poles aligned, with no intervening ion lens, and with the radio frequency (rf) voltages phase locked. A phase shift between the rf voltages applied to the quadrupoles also improves the ion transmission. For a given resolution the tandem analyzer has transmission comparable to that of a single quadrupole. Results obtained with operation of the quadrupoles in the first, second, and third stability regions are described. Operation in the third stability region is particularly advantageous because the tandem analyzer exhibits good abundance sensitivity on the low and high mass sides under conditions where a single quadrupole produces a long peak tail on at least one side. It is also shown that scattering losses in the tandem analyzer are about half of those of a conventional quadrupole. The results suggest that it may be possible to build a low cost tandem analyzer that has relatively poor mechanical precision and yet that produces satisfactory peak shape and resolution.     

The coupling effects of hexapole and octopole fields in quadrupole ion traps: a theoretical study

A theoretical method, the harmonic balance method, was introduced to study the coupling effects of hexapole and octopole fields on ion motion in a quadrupole ion trap. Ion motion characteristics, such as ion motion center displacement, ion secular frequency shift, nonlinear resonance curve and buffer gas damping effects, have been studied with the presence of both hexapole and octopole fields. It is found that hexapole fields have bigger impacts on ion motion center displacement, while octopole fields dominate ion secular frequency shift. Furthermore, the nonlinear features originated from hexapole and octopole fields could enhance or cancel each other, which provide us more space in a practical ion trap design process. As an example, an ion trap with improved performance was designed using a specific combination of hexapole and octopole fields. In this ion trap, a hexapole field was used to achieve efficient ion directional ejection, while an octopole field was added to correct the chemical mass shift and resolution degradation introduced by the hexapole field. Copyright © 2013 John Wiley & Sons, Ltd.     

Matrix methods for the calculation of stability diagrams in quadrupole mass spectrometry

The theory of the computer calculation of the stability of ion motion in periodic quadrupole fields is considered. A matrix approach for the numerical solution of the Hill equation and examples of calculations of stability diagrams are described. The advantage of this method is that it can be used for any periodic waveform. The stability diagrams with periodic rectangular waveform voltages are calculated with this approach. Calculations of the conventional stability diagram of the 3-D ion trap and the first six regions of stability of a mass filter with this method are presented. The stability of the ion motion for the case of a trapping voltage with two or more frequencies is also discussed. It is shown that quadrupole excitation with the rational angular frequency omega = Nomega/P (where N, P are integers and omega is the angular frequency of the trapping field) leads to splitting of the stability diagram along iso-beta lines. Each stable region of the unperturbed diagram splits into P stable bands. The widths of the unstable resonance lines depend on the amplitude of the auxiliary voltage and the frequency. With a low auxiliary frequency splitting of the stability diagram is greater near the boundaries of the unperturbed diagram. It is also shown that amplitude modulation of the trapping RF voltage by an auxiliary signal is equivalent to quadrupole excitation with three frequencies. The effect of modulation by a rational frequency is similar to the case of quadrupole excitation, although splitting of the stability diagram differs to some extent. The methods and results of these calculations will be useful for studies of higher stability regions, resonant excitation, and non-sinusoidal trapping voltages.     

Mass peak shape improvement of a quadrupole mass filter when operating with a rectangular wave power supply

Numeric experiments were performed to study the first and second stability regions and find the optimal configurations of a quadrupole mass filter constructed of circular quadrupole rods with a rectangular wave power supply. The ion transmission contours were calculated using ion trajectory simulations. For the first stability region, the optimal rod set configuration and the ratio r/r₀ is 1.110–1.115; for the second stability region, it is 1.128–1.130. Low‐frequency direct current (DC) modulation with the parameters of m = 0.04–0.16 and ν = ω/Ω = 1/8–1/14 improves the mass peak shape of the circular rod quadrupole mass filter at the optimal r/r₀ ratio of 1.130. The amplitude modulation does not improve mass peak shape. Copyright © 2009 John Wiley & Sons, Ltd.     

Upper stability island of the quadrupole mass filter with amplitude modulation of the applied voltages

Modulation of the voltages applied to a quadrupole mass filter (QMF), either RF or RF and DC, leads to splitting of the stability region into islands of stability. The ion optical properties, such as transmission, resolving power and peak tails of the first upper stability islands have been investigated by numerical simulation of ion trajectories. The dependence of the location of this island on the amplitude of the modulation and the parameter nu = omega/Omega = Q/P where omega is modulation frequency, Omega is main angular radio frequency, and Q and P are integers, is calculated in detail. Different methods of adjusting the QMF resolution are examined. It is found that operation at the upper and lower tips of the stability islands created by amplitude modulation of the RF voltage is preferred, because of the technical simplicity of this method and a reduction of the required separation time. Amplitude modulation improves the performance of a QMF constructed with round rods, in comparison to perfect quadrupole fields. For example, with amplitude modulation of the RF, to reach a resolution of R(0.1) = 1200 requires only about 75 RF cycles of ion motion in a quadrupole field created by round rods.     

Performance enhancements of mass selective axial ejection from a linear ion trap

Mass selective axial ejection (MSAE) of ions from a linear ion trap (LIT) takes advantage of the rf fringing fields at the end of the linear quadrupole to convert radial ion excitation into axial ejection. Ions gain radial amplitude via a mass selective resonance excitation process and are ejected axially over an electrostatic DC barrier. The extraction efficiency and resolution are determined by the length and shape of the extraction region in the vicinity of the exit aperture. In the work presented here, axial DC fields, created by auxiliary electrodes, were used to modify the shape of the trapping electrostatic fields along the quadrupole axis and to increase the density of the ions in the extraction region. Better confinement and ion cloud coherence increased the extraction efficiency and the spectral resolution. As a result, extraction efficiency can be increased by up to one order of magnitude at fast scan rates, i.e., 10 and 20 kTh/s, and a factor of 2–3 at the slower scan speed of 1 kTh/s. The length of the extraction region was also modified by application of a portion of the drive rf voltage to the end lens of the LIT. A comparison of the MSAE spectra at different scan rates and rf levels showed that extraction efficiencies increase at scan rates of 10 kTh/s or higher, with associated improvements in mass spectral peak widths.     

Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

In this article, the Poincare-Lighthill-Kuo (PLK) method is used to derive an analytical expression on the stability boundary and the ion trajectory. A multipole superposition model mainly including octopole component is adopted to represent the inhomogeneities of the field. In this method, both the motional displacement and secular frequency of ions have been expanded to asymptotic series by the scale of nonlinear term ε, which represents a weak octopole field. By solving the zero and first-order approximate equations, it is found that a frequency shift exists between the ideal and nonlinear conditions. The motional frequency of ions in nonlinear ion trap depends on not only Mathieu parameters, a and q, but also the percentage of the nonlinear field and the initial amplitude of ions. In the same trap, ions have the same mass-to-charge ratio (m/z) but they have different initial amplitudes or velocities. Consequently, they will be ejected at different time through after a mass-selective instability scan. The influences on the mass resolution in quadrupole ion trap, which is coupled with positive or negative octopole fields, have been discussed respectively.