Cylindrical quadrupoles

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. 

Quadrupoles. The quadmpole mass filter (16,17), which became available commercially in 1967, consists of four cylindrical rods having circular or, more recentiy, hyperboHc cross sections, arranged with their centers on the perimeter of a circle of radius Tq. Figure 2 is a schematic diagram of a... 

In contrast, the second term in (4.6) comprises the full orientation dependence of the nuclear charge distribution in 2nd power. Interestingly, the expression has the appearance of an irreducible (3 x 3) second-rank tensor. Such tensors are particularly convenient for rotational transformations (as will be used later when nuclear spin operators are considered). The term here is called the nuclear quadrupole moment Q. Because of its inherent symmetry and the specific cylindrical charge distribution of nuclei, the quadrupole moment can be represented by a single scalar, Q (vide infra). 

Remarkably, only one nuclear constant, Q, is needed in (4.17) to describe the quadrupole moment of the nucleus, whereas the full quadrupole tensor Q has five independent invariants. The simplification is possible because the nucleus has a definite angular momentum (7) which, in classical terms, imposes cylindrical symmetry of the charge distribution. Choosing x, = z as symmetry axis, the off-diagonal elements Qij are zero and the energy change caused by nuclear... 

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.

We may arrive at this conclusion another way. In Table 13.6 the components xx —yy)/2, xy, xz, and yz are zero indicating that the quadrupole field is cylindrically symmetric about the z-axis. The axial moment around the x- or j-axis is... 

ISI sector electrostatic energy spectrometer Einzel cylindrical lens Quadrupole... 

In the quadrupole mass analyzer, focusing electrodes direct and accelerate the ionized fragments into a mass filter consisting of four cylindrical electrodes in a vacuum. Tire cylindrical electrodes establish a combination radio-frequency and direct-current electrical field that permits only those ions with a specific, selected mass-to-charge ratio to pass all the way through the filter. The rest of the ions impact die electrodes and do not travel to the exit. Varying the electrical field allows ions with other masses to pass through the filter. 

No general analytical method is possible for obtaining the eigenstates and eigenvalues of in case (1), while case (2) belongs to pure quadrupole resonance. We shall consider the usual high-field case in which Jfz p take t] = 0 for simplicity (which assumes a field gradient of cylindrical symmetry), and denote... 

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 HREELS, Auger electron spectroscopy (AES) and thermal desorption spectrometry (TDS) experiments were carried out in a UHV chamber described previously.6 Briefly, the chamber was equipped with a HREELS spectrometer for vibrational analysis, a single-pass cylindrical mirror analyzer for AES measurements and a quadrupole mass spectrometer for TDS measurements. The HREELS spectra were collected in the specular direction with an incident energy of 3.5 eV and with a spectroscopic resolution of 50-80 cm-1. The TDS data were obtained by simultaneously monitoring up to 16 masses, with a typical heating rate of about 1.5 K s-1. 

Here % specify the transformation from coordinate system j to system i. In Equation 3 only Dq q (Qdm) varies with the molecular motion. Since amphiphilic liquid crystalline systems generally are cylindrically symmetrical around the director Dq q (nDM) = 0 if qf 0. If it also is assumed that a nucleus stays within a domain of a given orientation of the director over a time that is long compared with the inverse of the quadrupole interaction, one now obtains for the static quadrupole hamiltonian... 

QIT The quadrupole ion trap (QIT) utilizes a cylindrical ring and two end-cap electrodes to create a three-dimensional (3D) quadrupolar field for mass analysis. These instruments are capable of selectively trapping or ejecting ions and are often used for the sequential fragmentation and analysis experiments of product ion MS/MS. Also known as a 3D trap due to the configuration (March, 1997). 

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... 

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. 

For nuclear systems with a suitable cylindrical symmetry, the quadrupole interaction energy, Ey, is given by [143]... 

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