Principle of the Linear Quadrupole

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. 

As an ion enters the quadrupole assembly in z-direction, an attractive force is exerted on it by one of the rods with its charge actually opposite to the ionic charge. If the voltage applied to the rods is periodic, attraction and repulsion in both the X- and y-directions are alternating in time, because the sign of the electric force also changes periodically in time. If the applied voltage is composed of a DC 

In case of an inhomogenous 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. 4.31, 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 xy-plane. Such conditions can be derived from the theory of the Mathieu equations, as this type of differential equations is called. Writing Eq. 4.24 dimensionless yields 

For a given set of U, V and co 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. 

Overall, the quadmpole analyzer rather acts as a mass filter than as a momentum (B sector) or energy (ESA) spectrometer hence the widespread use of the term quadmpole mass filter. 

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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]. 

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