Dephasing angle

We have seen above that the dephasing angle (p between intensity and voltage can be modified by using various combinations of inductive and capacitive reactance. 

The so-called dephasing angle A depends linearly on the number n of rotation periods over which the tt pulses are applied and after rotation periods is given by... 

The quality factor of a low-pass filter is much greater than that of a bandpass filter, and so a low-pass filter can be used to eliminate the noise by recovering the desired information in the DC component. Since the value of the amplitude of signal Sr is known and dephase angle cp can be determined, the unknown value of amplitude Aj of the signal can be directly obtained. This principle is familiar during the operation of a cw-EPR spectrometer, in which the receiver is tuned to the field modulation frequency and one adjusts the phase of the receiver to maximize the receiver voltage. 

From the voltage-frequency transfer curve, one obtains the expression for the frequency as a function of the dephase angle ... 

It is important to note that a nonzero dephase angle between the VCO and reference remains eonstant when their frequeneies are the same. In faet, if one expresses the phase differenee as a fiinetion of tire frequeney of VCO... 

The rotational phase shift 5, which cannot exceed a mean angle of a molecular rotation during collisional time (anc), is certainly small in the case of non-adiabatic collisions. This condition is exactly that needed for anisotropic scattering (or IR absorption) spectrum narrowing, just as vibrational dephasing must be weak for an isotropic spectrum to narrow. 

Fig. 1.22 RARE sequence. Here the formation of the first spin echo is conventional. The CPMG form of spin echo is used to avoid the accumulation of flip angle errors over the echo train. However, before the second echo can be acquired, the phase-encoding has to be rewound to undo the dephasing of the spins. Therefore, a phase encoding step of equal...

To avoid the interference from intramolecular REDOR dephasing, peptides with 15NH, labels could be mixed with peptides with 13COy labels in a 1 1 ratio before fibrillization, where i and j denote the residues with isotopic enhancement at the amide and carbonyl sites, respectively. If an in-register parallel (3-sheet is considered as the hypothetical structure, the most adequate model for the analysis of the 13C 15N REDOR data measured for the case of i = j should be a 15N-13C-15N spin system, where the NCN angle is ca. 127° and the two 15N-13C distances are 5.3 and 5.5 A (Fig. 4a). For the case of i = j + 1, the NCN angle should be 154° and the two 15N-13C distances 4.2 and 5.6 A. Other combinations of i and j for an... 

Fig. 8 Schematic diagrams for the following pulse sequences (A) single pulse excitation/magic-angle spinning, (B) total suppression of sidebands, and (C) delayed decoupling, or dipolar dephasing.

As a main point of this subsection,186 it is shown that due to sufficiently strong lateral interactions of adsorbed molecules on a two-dimensional triangular lattice, the spectral line for collective vibrations manifests some characteristic peculiar relationships between its dephasing-induced broadening and the resonance width 77 for the low-frequency mode The line width changes as Tj n(l/rf) for surface-normal and as rjm for surface-parallel molecular orientations, and takes nonzero values (independent of 77) for inclined molecules with the inclination angle ranging from 47° to 90°. 

Since dipolar interaction is a distance-dependent interaction, the heteronuclear interaction between spins 1 and S can be exploited to get information about the distance between these nuclei. Heteronuclear dipolar interactions that are averaged by magic angle spiiming can be reintroduced by suitable dephasing pulses that are synchronized with the sample spinning. It is a difference spectroscopy... 

The trick introduced by Meiboom and Gill (14) is to dephase all n pulses in the Carr Purcell train by an angle of 90° with respect to the initial ti/2 pulse. It is easily shown that, without this phase change, imperfections of the 71 pulses are cumulative, whereas with the 90° phase change, a self-compensation occurs for all echoes of even number. The CPMG (Carr-Purcell-Meiboom-Gill) experiment can be handled in two ways ... 

NMR. NMR analyses were performed on selected samples using dipolar dephasing and off magic angle spinning methods developed at the University of Utah (18-22). This work was performed at the University of Utah under the direction of Professor Ronald Pugmire. The technique allows quantitative analysis of functional groups in the solid coals and chars. 

D. J. Tannor To understand the role of dissipation in quantum mechanics, it is useful to consider the density operator in the Wigner phase-space representation. Energy relaxation in a harmonic oscillator looks as shown in Fig. 1, whereas phase relaxation looks as shown in Fig. 2 that is, in pure dephasing the density spreads out over the energy shell (i.e., spreads in angle) while not changing its radial distribution... 

A new type of REDOR experiment (SEDOR) was proposed,104 in which the echo amplitude is measured as a function of the spin flip angle S instead of the dephasing time as in the original REDOR. This flip angle is stepped from 0° to 180°. It is found that this 6-REDOR (SEDOR) can be used to determine how many S spins couple the observed spin I, offering an alternative way of counting spins. 

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