Linear quadrupoles in mass spectrometry

We consider the case of a quadrupole mass spectrometer (QMS) in which a static magnetic field is applied axially in the z-direction along the length of the mass filter. The theoretical approach assumed in the model is that the QMS contains hyperbolic rods as electrodes and that the magnetic field acts over the full length of the mass filter assembly. Initial experimental results with argon and helium for a low-resolution instrument confirm the predicted theoretical trends. The analysis also predicts for which values of operating parameters an enhancement of the instrument resolution is achieved when an axial magnetic field is applied. The model predicts instrument resolution R Ͼ3000 for a QMS with a 200 mm long mass filter via application of an axial magnetic field. Attributes of the QMS such as versatility, accuracy, low cost, mass range, and sensitivity have ensured that it has been deployed in a wide range of applications, varying considerably from the modest residual gas analyzer to high-performance mass spectrometer for chemical analysis of simple and complex molecules, e.g., when used in conjunction with gas chromatography [7,8]. Different applications have different requirements for resolution, sensitivity, and stability.There have been many analytical predictions of the behavior of QMS. Dawson used matrix methods to calculate ion transmission for various scan lines and various apertures both with and without fringing fields, based on maximum ion displacements for mass filters [9]. Later research describes the performance of the QMS more comprehensively by solving the Mathieu equation in two dimensions for an infinitely long mass filter [2]. Batey showed that some features of the behavior of the QMS could be predicted by tracing the motion of ion through the mass filter [10]. Muntean used the matrix method to develop a computer simulation program to model ion transmission through the filter by calculating ion trajectories in radio frequency (rf) only quadrupoles [11]. More examples of such types of analytical work include the modeling of ion transmission through the filter by calculating ion trajectories in exactly determined hyperbolic quadrupole fields [12], the effects of rf frequency, phase and magnitude on the performance of QMS [13], and the effects of initial ion energy and quadrupole rod length on transmission percentage of ions through the mass filter along with the effects of aperture parameters [14]. Some workers have developed computational methods to determine the trajectories of large number of ions in QMS; their computer program generates large number of ions (at least 10 5 ions injected into the quadrupole model at each point on the mass scale), thus providing a detailed computer simulation for both hyperbolic and circular rods [15,16]. Douglas and Konenkov have used numerical calculations to investigate the influence of electrode radius r to field radius r 0 , which is referred to as (r/ r 0 ) on the peak shape for a linear QMF constructed with round rods [17]. Other workers have used com...

Section: F Irst Described By W Paul and H Steinwedel Inmentioning

confidence: 99%

Effect of an axial magnetic field on the performance of a quadrupole mass spectrometer

Syed

Sreekumar

Brkić

et al. 2010

“…Addition of these field distortions might be expected to cause conventional mass analysis, done by scanning the applied direct current (DC) and radio frequency (rf) voltages so that ions cross the tip of the first stability diagram [1], to deteriorate. Nevertheless, mass analysis with quadrupoles with added octopole [13] or hexapole [14] fields has been found to be possible in some cases, provided the positive DC is applied to the x rods so that the Mathieu parameter a, (eq 5 below) is positive for positive ions.For mass analysis, linear quadrupoles can also be operated with islands of stability [4,[15][16][17][18][19][20]. Islands of stability, separated by bands of instability, are formed in a stability region when auxiliary quadrupole excitaAddress reprint requests to D. J. Douglas,…”

mentioning

confidence: 99%

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

Zhao

Xiao

Douglas

2010

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 Ͻ 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 Ͼ 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. In some instruments, a quadrupole operated as a linear ion trap (such as Q3 in a triple quadrupole mass spectrometer) must also be capable of mass analysis [9].In general, the potential of a linear quadrupole with field distortions can be written as [10]where x and y are Cartesian coordinates, r 0 represents the distance from the central axis to an electrode for an ideal quadrupole and otherwise is a normalization factor, Re͓f͑x ϩ iy͔͒ is the real part of the complex function f(x ϩ iy), i 2 ϭ Ϫ1, A N is the dimensionless amplitude of a multipole (2N-pole), and (t) is a timedependent voltage applied to the electrodes. An ideal linear quadrupole has A 2 ϭ 1 and all other multipoles zero. A practical linear quadrupole usually has A 2 Ϸ 1, and other higher order multipole amplitudes in the range 10 Ϫ5 to 10 Ϫ3 [2-4]. Methods of adding an octopole field of 2% to 4% [11], i.e., A 4 ⁄A 2 ϭ 0.02 Ϫ 0.04, and a hexapole field [12] of up to 12% (A 3 ⁄A 2 Յ 0.12) to linear quadrupoles constructed from round rods have been described. (Hexapole and octopole fields are the next two higher multipoles after the quadrupole in the expansion of eq 1.) A hexapole field is added by rotating the two y rods towards an x rod through a small angle . The amplitude of the hexapole, A 3 , is approximately proportional to . This method also adds other higher multipoles, including an octopole field [12]. Addition of these field distortions might be expe...

“…The mass window is scanned by simultaneously ramping the DC and rf voltages along a constant a/q line to obtain a constant resolving power across the mass range as follows from Equation (5) [16]. Because V is increased to select a higher value of m/z, the maximum well depth also increases as described by Equation (2), resulting in improved sensitivity at constant resolving power.…”

Section: Resultsmentioning

confidence: 99%

Computational Analysis of Quadrupole Mass Filters Employing Nontraditional Waveforms

Brabeck

Reilly

2016

Abstract. Quadrupole mass filters using non-sinusoidal driving potentials present exciting opportunities for new functionality. Predicting figures of merit like resolving power and transmission efficiency helps characterize these emerging devices. To this end, matrix methods of solving the Hill equation of ion motion are employed to calculate stability diagrams and pseudopotential well depth maps in the a,q plane for arbitrary waveforms. The theoretical resolving power and well depth of digital, trapezoidal and sinusoidal mass filters are compared. Simplified expressions for digital mass filter operation are presented.