Quadrupole hyperbolic quadrupoles

Figure 2.15. Schematic of a quadrupole analyzer, (a) A hyperbolic cross-section (b) cross-section of cylindrical rods (c) the operating principle of a quadrupole mass filter. The x-direction pair of rods acts like a high pass filter so ion C (with low m/z) is not allowed through, and the y-direction pair of rods acts like a low pass filter and takes care of ion A (with high m/z). Only ion B having an m/z in the stable range is allowed through the quadrupole mass filter for subsequent detection. Reprinted from A. Westman-Brinkmalm and G. Brinkmalm (2002). In Mass Spectrometry and Hyphenated Techniques in Neuropeptide Research, J. Silberring and R. Ekman (eds.) New York John Wiley Sons, 47-105. With permission of John Wiley Sons, Inc.

A linear quadrupole mass analyzer consists of four hyperbolically or cyclindrically shaped rod electrodes extending in the z-direction and mounted in a square configuration (xy-plane, Figs. 4.31, 4.32). The pairs of opposite rods are each held at the same potential which is composed of a DC and an AC component. 

Fig. 4.31. Cross section of a quadrupole (a) for the cyclindrical approximation and (b) for the hyperbolic profile of the rods. The electric field is zero along the dotted lines, i.e., along the asymptotes in (b). (a) Courtesy of Waters Corp., MS Technologies, Manchester, UK.

Theoretically, each electrode should have a hyperbolic cross section for optimized geometry of the resulting quadrupole field, and thus for optimized performance. [103,104] However, cyclindrical rods are often employed instead, for ease of manufacture. By adjusting the radius of the rods carefully (r = 1.1468ro), a hyperbolic field may be approximated. [113] However, even slight distortions of the ideal quadrupole field either from interference with external fields or due to low mechanical precision or inadequate shape of the device cause severe losses of transmission and resolution. [114] The expected advantages of hyperbolic rods [115] have been demonstrated by ion trajectory calculations [110,116] circular rods cause a reduction in macromotion frequency because of an increased residence time of the ions in close vicinity to the rods this in turn means reduced resolution. 

Brubaker, W.M. Comparison of Quadrupole Mass Spectrometers With Round and Hyperbolic Rods. J. Vac. Sci. Technol 1967,4, 326. 

Gibson, J.R. Taylor, S. Prediction of Quadrupole Mass Filter Performance for Hyperbolic and Circular Cross Section Electrodes. Rapid Commun. Mass Spectrom. 2000,14, 1669-1673. 

A quadrupole mass analyzer is made of four hyperbolic or circular rods placed in parallel with identical diagonal distances from each other. The rods are electrically connected in diagonal. In addition to an alternating radiofrequency (RE) potential (V), a positive direct current (DC) potential (U) is applied on one pair of rods while a negative potential is applied to the other pair (Fig. 1.17). The ion trajectory is affected in x and y directions by the total electric field composed by a quadrupolar alternating field and a constant field. Because there is only a two-dimensional quadrupole field the ions, accelerated after ionization, maintain their velocity along the z axis. 

Fig. 1.17 The quadrupole mass analyzer is formed by four circular or hyperbolic rods placed in parallel. O Quadrupolar potential.

Quadrupoles are comprised of four metal rods, ideally of hyperbolic cross section, arranged as shown in Fig. 5.4. A combination of radiofrequency (RF) and direct current (DC) voltages are applied to each pair of rods, which creates an electric field within the region bounded by the rods. Depending on the RF/DC ratio, the electric field between the rods will allow ions in a narrow m/z range to pass, typically 0.8 m/z —just how narrow will depend on a number of factors which influence the resolution. Hence, by changing the RF/DC ratio in a controlled manner, the quadrupole can be... 

Fig. 8.1.1 Simple illustrations of a various mass spectrometers, a The triple-quadrupole tandem mass spectrometer (top panel). The middle set of quadrupoles are part of the collision cell (CC) and do not perform mass separation. MSI and MS2 indicate the first and second quadrupole mass separation devices, respectively. The bold arrow shows the path of ions, b Ion-trap mass spectrometer (middle left). The charged sections of the ion trap are not elliptical as drawn, but rather hyperbolic. The diagram is also two-dimensional, whereas the ion trap is three-dimensional. The ion path is such that ions enter the device and are trapped until a specific voltage ejects these ions, c Time of Flight mass spectrometer with a Reflectron (middle left). Ions are separated by the time it takes to pass through the instrument. The Reflectron improves/focuses the ions, d Hybrid Tandem mass spectrometer (bottom). The diagram shows that a quadrupole instrument can be combined with a different type of mass spectrometer, forming a tandem hybrid instrument...

Improved separation behaviour is observed in quadrupole analyzers with hyperbolic rods (see Figure 3.9). The quadrupole field is produced by four parallel hyperbolic electrodes, whereby Equations 3.16-3.17 can be applied. 

Figure 3.9 Quadrupole mass analyzer with hyperbolic-shaped rods. A potential of + 0 is applied to the electrodes in the x direction and — 0 to the electrodes in the direction. The potential at the centre is zero. Equipotential contours have a hyperbolic shape.

Quadrupole Hyperbolic, Mo Binary gold coated ceramic, producing hyperbolic field Mo rods with prepost filters Stainless steel rods locked into ceramic mounts, producing hyperbolic field... 

Figure 16.9—Representation of a quadrupole. Notice the pairing of oppositely charged electrodes. This experimental design requires high-precision machining of the hyperbolic electrodes. To the right a series of equipotential hyperbolic lines in the central part of the quadrupole is shown.

An ideal quadrupole field can be generated using four parallel electrodes (Z, = 5 to 20 cm) which have a hyperbolic cross-sectional field at their interior (Fig. 16.9). The electrodes are coupled in pairs and a potential difference U is applied across the pairs. If the distance between two opposite electrodes is 2 r0, then the potential d> within the xy plane of the quadrupole will be given by ... 

Figure 22-13 Quadrupole mass spectrometer. Ideally, the rods should have a hyperbolic cross section on the surfaces that face one another.

If we examine the magnetic held from such a quadrupolar device, we will hnd that the held along the central axis is exactly zero and increases linearly to a maximum value at each pole face. (The pole tips should be hyperbolic surfaces to conform to the shape of the magnetic held, although cylindrical pole tips are often used for ease of manufacture.) Quadrupole magnets are thus characterized by the gradient of the magnetic held, dB/dr, where r is a radial coordinate and... 

The quadrupole mass analyzer is much smaller and cheaper than a magnetic sector instrument. A quadrupole setup (seen schematically in Figure 1.10) consists of four cylindrical (or of hyperbolic cross-section) rods (100-200 mm long) mounted parallel to each other, at the corners of a square. A complete mathematical analysis of the quadrupole mass analyzer is complex but we can discuss how it works in a simplified form. A constant DC voltage modified by a radio frequency voltage is applied to the rods. Ions are introduced to the tunnel formed by the four rods of the quadrupole in the center of the square at one end to the rods, and travel down the axis. 

Quadrupole analysers [2,3] are made up of four rods of circular or, ideally, hyperbolic section (Figures 2.4 and 2.5). The rods must be perfectly parallel. 

Quadrupole instrument made up of the source, the focusing lenses, the quadrupole cylindrical rods and the detector. Ideally, the rods should be hyperbolic. Reproduced (modified) from Kienitz H., Massenspektrometrie, Verlag Chemie, Weinheim,... 

Quadrupole with hyperbolic rods and applied potentials. The equipotendal lines are represented above, on the left. 

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