Quadrupole potential well

From Figure 49.2, it can be seen that the quadrupole assembly provides a potential well to contain the ions in their journey along the main quadrupole axis. The potential well of the quadinpole has not very steep sides and, compared with steep-sided hexapoles or higher -poles or ion tunnels, the quadrupole is not as efficient as the others in containing ions inside the rod assembly. 

The difference between the Markov model lineshapes and those from the Smoluchowski model is particularly pronounced when the diffusion coefficient is of the order of the quadrupole coupling constant. In the limit of large diffusion coefficients, the two models converge, and in the limit of low diffusion coefficients, the spectra are dominated by small-amplitude oscillations within potential wells, which can be approximately modelled by a suitable Markov model. This work strongly suggests that there could well be cases where analysis of powder pattern lineshapes with a Markov model leads to a fit between experimental and simulated spectra but where the fit model does not necessarily describe the true dynamics in the system. 

In the following we will limit the discussion to the case where only one quadrupole nucleus is present in the molecule. Ethylenimine will be used as an example in all numerical calculations. As mentioned above, the nucleus has a small positive prolate shaped quadrupole moment. If the potential well at the equilibrium position of the nucleus lacks spherical symmetry, the nucleus will tend to align itself with respect to the molecular frame as depicted in Fig. III. 17. 

Thermo Einnigan linear ion trap In the Thermo Einnigan instrument shown in Figure 3, an ion beam from an electrospray source is directed through a heated capillary, two successive rod arrays, a front lens, and into a linear ion trap composed of three sections of quadrupole hyperbolic rod arrays with Zo = 4 mm. Radial confinement of ions is effected by the trapping potential well in the center section and axial confinement by dc potentials applied to the front and rear lenses. The basic design of the linear... 

The effective well depth in a Paul trap is another concept that is frequently met in the literature. The hyperboloid shapes of the electrodes were chosen so as to produce an ideal quadrupole electric field when an RF potential is applied to the ring electrode and the two end cap electrodes are grounded. Such a field in turn produces a (truncated) parabolic potential well (V a r or z ) for the confinement of ions (recall that the field strength Ej = dV/dr and similarly for z) thus hyperboloid shapes were chosen because the motions of particles in parabohc potential wells is a very well understood problem in mechanics. The wells are truncated at the physical boundaries of the trap to define well depths for the electrical potential given by ... 

Key among these are quadrupole based instruments, single quadrupoles and triple quadrupoles as well as the closely related quadrupole ion trap instruments (3D and 2D ion traps). Their widespread use in trace quantitative analyses has been facilitated by the fact that these instruments can also be readily coupled to GC and/or LC because of inherent features of the mass analyzer fields, i.e. they operate at or near ground potential. 

A time of flight (TOP) mass spectrometer has several distinct advantages over quadrupoles, namely, high ion transmission efficiencies at all mass ranges very high data rates simplicity of design, construction and repair and adaptability to most pulse type ionization sources. A TOP instrument was also modified for use with a SI source [29]. The author claimed that formation of a potential well within the ionization region to trap ions prior to acceleration improved sensitivity without any apparent loss in resolution. 

The electrodes in Figure 2 are truncated for practical purposes but, in theory, they extend to infinity and meet the asymptotes shown. The electrode geometries are defined so that, when an RF potential is applied to the ring electrode with the end-cap electrodes grounded, a near-ideal quadrupole field is produced, which creates a parabolic potential well for ion confinement. Figure 3. As shown in Figure 3, the potential well in the axial directioims of depth D, while that in the radial direction D ] since 2Dr, the potential well resembles more a flower vase than a bowl. 

M possesses a nonzero dipole moment, g. [If M has no dipole moment but a nonzero quadrupole moment, Q, then the asymptotic form of the potential is a charge-quadrupole interaction, V(r) -Q/r. ] The M -l-e potential well in Figure 4(a) is much shallower than that for M" " -l-e, consistent with the observation that IPs for neutral atoms and molecules are large compared to EAs. As such, the anion typically possesses few (if any) bound Rydberg states. ... 

The adsorptives were modelled using the 12-6 potential model with the parameters given in Tabie 1, where e , and e, o are the potential well depths and hard sphere diameters for the adsoibate and adsorbate adsorbent potentiais respectiveiy. Ciearly this is less satisfactory for than for Ar since, in spite of the fact that free rotation is to be expected to reduce the quadrupole effects in the bulk phase above 40K, it is not necessarily the case that this also applies to the adsorbate. This reservation seems to be borne out by the results reported below. Nevertheless it has proved valuable here to be able to compare two similar models which differ only in their molecular parameters. Because of its particular combination of molecular size and interactions the Ar-graphite system is difficult to model with precision at the temperature of interest. A useful touchstone for evaluating model potentials is provided by the liquid to incommensurate solid transition exhibited by this system at 77.5K. It is also of interest in the present context to know how porosity affects this transition. 

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