Quadrupole mass analyzer with hyperbolic rods

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.

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. 

Quadrupole mass analyzers consist of four parallel metal rods which are either round-shaped or ideally have a hyperbolic section. Ion separation is realized by applying an alternating electrical fleld to the four rods with each pair of adjacent rods having the opposite signs of the potential. The potential applied to two opposite rods is a superposition of a constant potential U and an alternating potential V cos mt (Eq. (5.1)). The other two opposite rods bear the potential . co describes the angular frequency and equals Inv when v is the frequency of the applied radio frequency field t is the time. 

Quadrupole Mass Filters Quadrupole mass analyzers consist of four electrodes, ideally of hyperbolic rods, that are accurately positioned in a radial array. For practical as well as economic reasons, most quadrupole mass filters have employed electrodes of circular cross section. A potential is applied to one pair of diagonally opposite rods consisting of a DC voltage and an rf voltage. To the other pair of rods, a DC voltage of opposite polarity and an rf voltage with a 180° phase shift are applied. The ion motion under the influence of this two-dimensional (2D) field can be described mathematically by the solutions to the second-order linear differential equation, known as Mathieu equation, from which the Mathieu parameters, and can be derived as... 

The linear quadrupole mass analyzer is a mass filter. It consists of four hyperbolic rods that are placed parallel in a radial array. Opposite rods are charged by a positive or negative DC potential Uat which an oscillating radiofrequency voltage Vo cos cor is superimposed. The latter successively reinforces and overwhelms the DC field. Ions are introduced into the quadrupole field by means of a low accelerating potential, typically only a few volts. The ions start to oscillate in a plane perpendicular to the rod length as they traverse through the quadrupole filter. The trajectories of the ions of one particular m/z are stable. These ions are transmitted toward the detector. Ions with other m/z have unstable trajectories and do not pass the mass filter because the amplitude of their oscillations becomes infinite. Ions of different m/z can consecutively be transmitted by the linear quadrupole filter toward the detector when the DC and AC potentials are swept, while their ratios and oscillation frequencies are kept constant. 

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.

Quadrupole mass filter A mass analyzer that uses a stm-cture of four colinear rods of hyperbolic cross section (energized with a combination of DC and rf fields) that creates trajectory oscillations in low-kinetic-energy ions passing through the rods. At a particular set of DC and rf values, only ions of one mass maintain a stable trajectory that allows passage through the mass Alter. 

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