Hyperbolic quadrupole rods

A recent development for the improved mass resolution of quadrupole analysers has been published and commercialized for a SIM technique in MS/MS named H-SRM (< 0.4 Da) or U-SRM (< 0.2 Da), selected reaction monitoring by using enhanced mass resolution. Hyperbolic quadrupole rods of a true hyperbolic pole face, high-precision four-section design with a rod length of 25 cm length... 

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.

Fig. 8 Schematic of a tandem quadrupole MS/MS instrument. A tandem quadrupole MS/MS instrument consists of two quad-rupole MS filters, MSI and MS2, separated by a collision cell. Each quadrupole MS filter consists of four cylindrical or hyperbolic shaped rods. A unique combination of direct current (dc) potential and radiofrequency (rf) potential is applied to each pair of rods (one pair 180° out of phase with the other). A mass spectrum results by varying the voltages at a constant rf/dc ratio. A variety of scan modes (e.g., full scan, product ion, precursor ion, neutral loss) provide unique capabilities for quantitative and qualitative structure analysis. (Courtesy of Micromass, Manchester, UK.)...

The operation of the QIT is based on the same physical principle as the quadrupole mass spectrometer described above. Both devices make use of the ability of RF fields to confine ions. However, the RF field of an ion trap is designed to trap ions in three dimensions rather than to allow the ions to pass through as in a QMF, which confines ions in only two dimensions. This difference has a significant unpact on the operation and limitations of the QIT, The physical arrangement of a QIT is different from that of a QMF. If an imaginary axis is drawn through the y-axis of the quadrupole rods, and the rods are rotated around the axis, a solid ring with a hyperbolic inner surface results from the x-axis pair of rods. 

Developed in the early 1980s, quadrupole-based systems represent approximately 85% of all ICP mass spectrometers used today. This design was the first to be commercialized, and as a result, today s quadrupole ICP-MS technology is considered a very mature, routine trace element technique. A quadrupole consists of four cylindrical or hyperbolic metallic rods of the same length and diameter. They are typically made of stainless steel or molybdenum and sometimes coated with a ceramic coating... 

Figure 2.177 Ion transmission of round and hyperbolic quadrupole systems (resolving power ag. ion transmission), first documented investigation by Brubaker (1968) (two curves left round rods two curves right hyperbolic rods).

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. 

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... 

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. 

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

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,... 

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