Slow passage

FIGURE 2.9 (a) Ringing that occurs after a scan through resonance, (b) Ideal slow passage 

FIGURE 2.10 Typical (a) absorption mode and (b) dispersion mode signals. 

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Neither rapid sand nor mixed-media filters remove appreciable quantities of coUoidal particles without adequate pretreatment. Although it is widely beheved that filters are an effective barrier against unsafe water, the effluent may be as colored, as turbid, or as bacteriologicaHy unsafe as the water appHed. In contrast, slow sand filters requite no pretreatment, as the slow passage through the bed allows the particles to contact and attach to the schmut ecke. 

Dibutylcarbitol [di(ethyleneglycol)dibutyl ether] [112-73-2] M 218.3, b 125-130 /0.1mm, d 0.883, n 1.424. Freed from peroxides by slow passage through a column of activated alumina. The eluate was shaken with Na2C03 (to remove any remaining acidic impurities), washed with water, and stored with CaCl2 in a dark bottle [Tuck J Chem Soc 3202 1957]. 

If the rate of sweep through the resonance frequeney is small (so-called slow passage), a steady-state solution, in which the derivatives are set to zero, is ob-tained. The result expresses M,., and as funetions of cu. These magnetization components are not actually observed, however, and it is more useful to express the solutions in terms of the susceptibility, a complex quantity related to the magnetization. The solutions for the real (x ) and imaginary (x") components then are... 

In a continuous wave (CW) magnetic resonance experiment, the radiation field B is continuous and BQ is changed only slowly compared with the relaxation rates (so-called slow passage conditions). Thus a steady-state solution to eqns... 

The diaphragm prevents the diffusion of sodium hydroxide toward the anode. This wall allows for the slow passage of solution and the free passage of sodium ions. It is made of asbestos fibers supported on an iron screen. The anode solution level is maintained higher than in the cathode compartment to retard back migration. If sodium hydroxide built up near the... 

Cylinder, Recoil A cylinder with component parts designed to cushion the backward motion of a cannon by springs, or by the slow passage of air or fluid thru holes in the piston when the gun is... 

Undulation or wavelike motion of viewed surfaces Euphoria, general stimulation, ruminative state Slowed passage of time Transient sexual feelings and synesthesias A few auditory hallucinations... 

Slow Passage or Equilibrium or Steady-State Solution. We seek the "slow-passage" or "equilibrium" or "steady-state" solution, where all three time derivatives in Eq. (11.21.11) are set equal to zero the answers are... 

The Bloch equations can be solved analytically under the condition of slow passage, for which the time derivatives of Eq. 2.48 are assumed to be zero to create a steady state. The nuclear induction can be shown to consist of two components, absorption, which is 90° out of phase with B, and has a Lorentzian line shape, and dispersion, which is in phase with B,. The shapes of these signals are shown in Fig. 2.10. By appropriate electronic means (see Section 3.3), we can select either of these two signals, usually the absorption mode. 

The Fourier transform revolution changed the face of NMR. Slow passage cw methods are now largely relegated to lower field, lower cost instruments and to samples for which signal/noise ratio and speed of data acquisition do not present serious problems. The advantage of the pulse FT approach is that a sufficiently powerful rf pulse excites the entire spectrum simultaneously, as we showed in Section 2.9, and Fourier transformation permits us to disentangle the many frequencies that are present in the free induction decay that is the time response to the pulse. 

For NMR spectra, it is known that if s(t) is the free induction decay following a pulse, S((o) represents the slow passage spectrum. We shall also use the FT relationship in other ways—for example, for data processing (in Section 3.4) and for analyzing random molecular motions (in Chapter 8). We return to the use of pulse Fourier transform methods in Section 3.6. 

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