The Linear Quadrupole

A linear quadrupole mass analyzer consists of four hyperbolically or cylindrically shaped rod electrodes extending in the z-direction and mounted in a square configuration (xy-plane. Figs. 4.25, 4.26). The pairs of opposite rods are each held at the same potential which is composed of a DC and an AC component. 

In case of an inhomogeneous periodic field such as the above quadrupole field, there is a small average force which is always in the direction of the lower field. The electric field is zero along the dotted lines in Fig. 4.25, i.e., along the asymptotes in case of the hyperbolic electrodes. It is therefore possible that an ion may traverse the quadrupole without hitting the rods, provided its motion around the z-axis is stable with limited amplitudes in the Jty-plane. Such conditions can be derived from the theory of the Mathieu equations. 

Note The Mathieu functions were originally derived in 1868 by Emile Leonard Mathieu, a French mathematician, to describe the vibrations of elliptical drumheads. It turned out that they are also useful to treat quadrupole mass filters and several other physical phenomena. 

For a given set of U, V, and ro the overall ion motion can result in a stable trajectory causing ions of a certain m/z value or m/z range to pass the quadrupole. Ions oscillating within the distance 2ro between the electrodes will have stable trajectories. These are transmitted through the quadrupole and detected thereafter. The path stability of a particular ion is defined by the magnitude of the RF voltage V and by the ratio U/V. 

By plotting the parameter a (ordinate, time invariant field) vs. q (abscissa, time variant field) one obtains the stability diagram of the two-dimensional quadrupole field. This reveals the existence of regions where i) both x- and y-trajectories are stable, ii) either x- or y-trajectories are stable, and Hi) no stable ion motion occurs 

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Principle. The cylindrical quadrupole ion trap is based on the same principle as the quadrupole mass filter, but the geometry is different (Fig. 2.16). The cylindrical QIT, or Paul trap, was developed almost simultaneously with the quadrupole mass filter [232, 233]. Recently, a variant of the theme has emerged, the linear quadrupole ion trap [236], which is a device built like a quadrupole mass filter with extra trapping end electrodes for the axial direction. Under stable conditions, ions moving around inside such traps will ideally continue to do that forever. 

Geometries composing of an oaTOF as MS2 bear the advantage that advanced TOFs offer accurate mass measurements close the the accuracy of magnetic sector instruments. Currently, QqTOF systems can be regarded as the commercially most successful hybrid. While the linear quadrupole serves as MSI in MS/MS experiments, it is operated in RF-only mode when tandem MS is not intended, because... 

Essentially, the ion storage trap is a spherical configuration of the linear quadrupole mass filter. The operations, however, differ in that the linear filter passes the sorted ions directly through to the detector, whereas the ion trap retains the unsorted ions temporarily within the trap. They are then released to the detector sequentially by scanning the electric field. These instruments are compact (benchtop), relatively inexpensive, convenient to use, and very sensitive. They also provide an inexpensive method to carry out GC/MS/MS experiments (Section 2.2.7) (GC is gas chromatography). 

Figure 5.8 Instrumental configurations of the plasma source ion trap (PSIT) (a) PSITI utilizes a linear quadrupole for ion transport and mass filtering, (b) PSIT II uses direct injection of ions into the trap (without the linear quadrupole transfer/selection optics). (Barinaga, C. Eiden . C., Alexander, M. L. and Koppenaal, D. W., Fresenius. J. Anal. Chem., 355, 487(1996). Reproduced by permission of Springer Sciences and Business Media.)...

The ion trap is a 3D analog of the linear quadrupole. Two of the rods form the end-cap electrodes, whilst the other pair of rods is bent round to form the doughnut-shaped ring electrode (Fig. 12). 

The ion trap works on a similar principle to the linear quadrupole. Oscillating RF and DC voltages are applied to the electrodes. These voltages create a quadrupolar field in the ion trap, and ions can be retained in stable trajectories in this field. The force acting upon the ions in the trap is directly proportional to the distance of the ions from the center of the ion trap. Therefore the quadrupolar field acts to store the ions as a packet at the center of the trap. For an ion to be retained in the ion trap it needs to have a stable trajectory in both the axial (z) and radial (r) directions. Whether the ion is stable in one or both of these directions is given by the solutions to the Mathieu equation previously used to describe ion motion through the linear quadrupole with the reduced Mathieu parameters ... 

The quadrupole ion trap is a three dimensional analogue of the linear quadrupole mass analyzer [71,72]. It consists of a cylindrical ring electrode and two end-cap electrodes. Both end-cap electrodes contain a whole for injecting and ejecting ions into and out of the ion trap (Fig. 8.11). A relatively high pressure of helium damping gas (about 0.1-0.4 Pa) is present in the ion trap in order to kinetically cool the trapped... 

Both atomic and metal oxide ions were observed in initial investigations. Ions with low metal oxide or hydroxide bond energies resulted in the detection of only the bare metal ions. For elements with strong oxide bond energies, metal oxides were observed. By utilizing the preselection capability of the linear quadrupole, it was determined that the metal oxides were not originating from the ion... 

The quadrupole ion trap is a three-dimensional (3-D) analog of the linear quadrupole [33]. It consists of two end-cap electrodes with hyperbolic cross sections and one ring electrode located between the end caps (Figure 7-5B). The RF voltage is applied to the ring electrode and the ground potential is normally operated on the end caps. A rotationally symmetric electric... 

Quadrupole ion trap mass analyzers merge the trapping characteristics of the ICR with the physical principles of the linear quadrupole mass analyzer. Quadrupole ion traps produce time-dependent spectra with excellent sensitivity and tandem mass spectrometry capabilities, but unlike the ICR they provide these ion trapping characteristics with physically smaller and considerably less expensive instrumentation, giving them a reputation as a powerful and accessible tool for both qualitative and quantitative mass spectrometry [43-47]. The capability of quadrupole ion traps to be configured with either internal and external ionization sources has expanded their utility for modem analytical applications [48—52]. 

The first idea was to build a trap from the linear quadrupole mass filter structure but, rapidly, the properties of multi-pole potentials were exploited also. For a quadrupole linear trap, the RF electric field [19] is transverse to the z-axis of the ion trap near this axis, the time potential, ( ), in the x- and y-directions can be expressed by... 

In 1989 the Nobel Prize in physics was shared by Wolfgang Paul (for development of the three-dimensional quadrupole ion trap as an extension of the linear quadrupole mass filter) and Hans Dehmelt (for spectroscopic studies of ions suspended in ion traps of various kinds, including the Paul trap) the Nobel award lectures (Paul 1990 Dehmelt 1990) incidentally also provide accounts of their work that are interesting historically and also lucid and accessible to nonexperts. Other early work on development of the same general principles for ion trapping (Good 1953 Wuerker 1959) should also be... 

The other common mass analyzer is the linear quadrupole. This mass analyzer consists of four cylindrical rods oriented in a square arrangement as shown in Figure 7.7. Radiofrequency (RF) and direct-current (DC) potentials are applied... 

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