Peak splitting with a quadrupole mass filter operated in the second stability region

Peak splitting or structure has been studied for a quadrupole mass filter operated in the second stability region with Mathieu parameters (a,q) ≈ (0.02.7.55). Two sources of peak splitting are considered and modeled theoretically: nonlinear resonances caused by field imperfections and ion collection effects caused by the periodic properties of ion motion in the quadrupole field. The conditions for the appearance of the nonlinear resonances and ion collection effects are derived and presented in terms of the β variables which determine the frequencies of ion oscillation. Comparisons of calculated peak structure to experimental peak shapes show that ion collection effects dominate, at least for the experimental conditions reported here. It is also shown that neither nonlinear resonances nor ion collection effects can distort the peak at high resolution.     

Inductively coupled plasma mass spectrometry with a quadrupole mass filter operated in the third stability region

An inductively coupled plasma mass spectrometer system is described in which the quadrupole mass filter is operated in the third stability region with Mathieu parameters (a, q)=(3, 3). Operation at the upper tip of this region is found to give generally better sensitivity and resolution than operation at the lower tip. A limiting resolution at half height of 4000 at m/z 59 is possible with operation at the upper tip. This resolution is insufficient to separate atomic ions from molecular ions of the same nominal mass except in favorable cases. However, operation at moderate resolution (R _1/2=500 to 1000) is found to give very high abundance sensitivity (>10⁷). The results suggest that the third stability region may be advantageous for specialized applications of inductively coupled plasma mass spectrometry.     

Ion source emittance influence on the transmission of a quadrupole operated in the second stability region

The variation of transmission (T) with resolution (R) has been calculated for a quadrupole mass filter operated in the second stability region with Mathieu parameters q=7.547 and a=0 to 0.02995. The fringing fields at the entrance to the quadrupole, which can be strongly defocusing, and which can dramatically reduce the acceptance, have been included in the calculation. Even in the absence of fringing fields, at a resolution of 10,000 the acceptance in the x and y directions is less than 2 × 10^?4 πr ₀ ⁴ f ², which is about 10^?3 of the acceptance in the first stability region at low resolution. Because the source emittance can strongly effect the T(R) behavior, the calculation of ion transmission has been done for two source emittances that correspond to different degrees of focusing of ions into the quadrupole. The T(R) characteristics for two realistic source emittances give behavior markedly different from the decrease in acceptance with increasing resolution which previously has been used as a measure of the quadrupole transmission. Comparisons of the calculated transmission losses with increasing resolution to earlier experimental results obtained with an inductively coupled plasma source show good agreement provided an emittance which corresponds to ions being tightly focused into the quadrupole is used. The calculation demonstrates that up to a resolution at half height of 7000 in the experiment, the transmission losses were a result of the decreasing quadrupole acceptance. At higher resolution the experimental transmission was limited by either the residence time of the ions in the quadrupole or the rod quality. It is also shown that the strong defocusing effects of the fringing fields at the entrance of the quadrupole can be largely overcome by accelerating the ions through these fields and then decelerating the ions in the quadrupole.     

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.     

Homotopy analysis method to study a quadrupole mass filter

The homotopy analysis method (HAM) is applied to study the behavior of a hyperbolic rods of quadrupole mass filter and a sinusoidal potential form V_ac cos(Ωt). Numerical computation method of a 20th‐order HAM is employed to compare the physical properties of the confined ions with fifth‐order Runge–Kutta method. Also, comparison is made for the first stability region, the ion trajectories in real time, the polar plots, and the ion trajectory in x ? y plan. The results show that the two methods are fairly similar; therefore, the HAM method has potential application to solve linear and nonlinear equations of the charge particle confinement in quadrupole field. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Coupling of a Rydberg electron capture ion source with a quadrupole mass filter

The coupling of a Rydberg electron capture ion source with a Nermag R10-10H quadrupole mass filter is described. Details are given of the addition to this instrument of a creation cell for atoms excited in Rydberg states. Within the Nermag ion source, such atoms allow attachment of electrons of well-defined thermal energy. SF(6) was used for optimization of the main experimental parameters (gas pressures and voltages applied to the electrodes). The procedure by which Rydberg electron attachment was confirmed is described. A polychlorobiphenyl compound was used to illustrate the performance of this ionization technique. Ion formation was observed in the absence of fragmentation.     

An improved model of the fringing fields of a quadrupole mass filter

The fringing field region of a quadrupole mass filter is modelled using an iterative finite difference technique to solve Laplace's equation for the electrostatic potential. The results are used to formulate an expression f(z) such that the electrostatic potential of the fringing field, F(x, y, z, t) may be written in the form F(x, y, z, t) = f(z) φ(x, y, t), where φ(x, y, t) is the hyperbolic field of the quadrupole. The function f(z) is expressed in the form f(z) = 1 - exp {- az - bz²}), where a and b are constants and z is in units of r_O, where 2r_O is the spacing of the quadrupole rods. The effect of the distance from the quandrupole rods to the end plate of the quadrupole mass filter, d on f(z) is investigated and the results presented show that for d < 0.125 r_O the function f(z) does not alter significantly.     

Comparison of ion coupling strategies for a microengineered quadrupole mass filter

The limitations of conventional machining and assembly techniques require that designs for quadrupole mass analyzers with rod diameters less than a millimeter are not merely scale versions of larger instruments. We show how silicon planar processing techniques and microelectromechanical systems (MEMS) design concepts can be used to incorporate complex features into the construction of a miniature quadrupole mass filter chip that could not easily be achieved using other microengineering approaches. Three designs for the entrance and exit to the filter consistent with the chosen materials and techniques have been evaluated. The differences between these seemingly similar structures have a significant effect on the performance. Although one of the designs results in severe attenuation of transmission with increasing mass, the other two can be scanned to m/z = 400 without any corruption of the mass spectrum. At m/z = 219, the variation in the transmission of the three designs was found to be approximately four orders of magnitude. A maximum resolution of M/DeltaM = 87 at 10% peak height has been achieved at m/z = 219 with a filter operated at 6 MHz and constructed using rods measuring (508 +/- 5) microm in diameter.     

Properties and performance of a quadrupole mass filter used for resonance ionization mass spectrometry

The performance of commercial quadrupole mass spectrometers (QMS) with a number of imperfections, as compared to the ideal hyperbolic geometry, has been characterized using the computer simulation program version 6.0. The analysis of simulated QMS geometries focuses primarily on modeling of the internal potential, the study of field deviations, and the influence of finite length on performance of the QMS. The computer simulation of ion trajectories in the QMS field yields predictions for optimum working conditions and provides estimates for the resolving power and the maximum isotopic abundance sensitivity. Experimental measurements that confirm these expectations are presented. Optimization of the geometry and various operational parameters of the QMS is an important step in the development of a system for highly selective ultratrace determination using laser-based resonance ionization mass spectrometry.     

Use of region II of the a/q stability diagram for fast scanning of a linear quadrupole mass spectrometer

For evaluation as a detector for high-speed gas chromatography, a linear quadrupole mass spectrometer was operated in rf only mode by using Region II (a = 0; 7.514 < q < 7.580) of the Mathieu a/q stability diagram. The available power supply and the diameter of the quadrupole rods of the mass spectrometer placed an upper mass limit of ～ m/z 93. Scan rates of 1000 scans/s were obtained with mass spectral peaks resolved over an 80-u range The m/z 91 and 92 ions produced from the electron ionization of toluene are resolved with an R _1/2 of 135. A potential difference between the source and the quadruple mass filter of up to 1000 V was used to accelerate ions into the quadrupole. Broadening of mass-to-charge ratio peaks results from the time constant of the signal amplification rather than the small number of rf cycles the ions experience. The expected loss of sensitivity relative to Region I is observed, and the problem of mass aliasing is discussed.     

Influence of realistic fringing fields on the acceptance of a quadrupole mass filter

The modifications of the x and y acceptances of a quadrupole mass filter due to the influence of realistic fringing fields are calculated using the phase space dynamics approach for a range of ion axial velocities. The results are compared to those obtained from the conventional linear fringing field approximation and experimental data; significant differences are apparent. The quadrupole acceptances are found to be only weakly dependent on the spacing between the quadrupole rod ends and the entrance aperture plate.     

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.     

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.     

Origin of mass shifts in the quadrupole ion trap: dissociation of fragile ions observed with a hybrid ion trap/mass filter instrument

A novel hybrid tandem mass analyzer, coupling a quadrupole ion trap with a quadrupole mass filter, has been constructed to permit mass analysis of ions ejected from the ion trap. The initial application of this instrument is the investigation of the origin of mass shifts in the ion trap due to ion fragility. We hypothesize that fragile ions undergo mass shifts, characterized by peak fronting, due to early ejection from the quadrupole ion trap. As these ions come into resonance with the ejection frequency, they gain kinetic energy, collide with buffer gas molecules and thus can dissociate to produce fragment ions. These fragment ions will not be stable within the ion trap as they are situated past the stability boundary at q(z) = 0. 908. Consequently the fragment ions are ejected prematurely. This results in an apparent mass shift due to peak fronting. The experiments reported here clearly document the production of fragment ions as the origin of mass shifts during the resonant ejection of fragile ions. Copyright 2000 John Wiley & Sons, Ltd.     

Molecular structure of fulvic acids by electrospray with quadrupole time-of-flight mass spectrometry

Characterisation of the molecular structure of aquatic fulvic acids (FA) has been performed using a quadrupole time-of-flight (Q-TOF) mass spectrometer equipped with an electrospray ionisation interface. Molecular masses centred around 450 Da and sinusoidal spectral distributions have been obtained for all fulvic acids. Tandem mass spectrometry (MS/MS) experiments showed losses of 18 Da (H(2)O) and 44 Da (CO(2)), and possible molecular structures were determined for the first time to our knowledge. A methodology is reported for evaluating the average elemental composition of FA from high-resolution mass spectra by processing post-acquisition data calculations using molecular size distributions and atomic compositions of ions. The results are found to be consistent with elemental analysis data.     

Influence of the 6th and 10th spatial harmonics on the peak shape of a quadrupole mass filter with round rods

The influence of the ratio of the rod radius, r, to field radius, r(0), on the peak shape for a linear quadrupole mass filter constructed with round rods has been investigated. The expansion of the potential in multipoles, phi(N),Phi(x, y) = sum(infinity)(N=0)A(N)phi(N)/r(N)(0) has been considered, and the peak shape and resolution have been determined by numerical calculation of ion trajectories in quadrupoles with different ratios, r/r(0). Geometries that make the dodecapole term (A(6)) zero (r/r(0) = 1.14511) do not give the best performance because the contribution of the 20-pole term, A(10), must be considered. The optimum ratio is r/r(0) approximately 1.13. With this ratio the dodecapole term (A(6)) is ca. 1 x 10(-3), but its effects are partially compensated by the A(10) term which has similar magnitude, but opposite sign.     

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.