Time-Averaged Chemical Shift

The chemical shift in the high-field approximation is given by Eq. (2.38) when fi Ho, 

Note that iSn, 1S22, and 533 are not principal components of the order matrix. A similar equation for the component of chemical shift tensor in the direction of the external magnetic field can be written using the principal axis (x y,z) frame of the order matrix. In a liquid crystalline phase where this frame has been defined, the following expression is obtained  

For the aromatic carbons, axx yy is of the order of 100 ppm. In liquid crystals, fast conformational changes, such as 7r-flip of benzene rings around the paroraxis, which is to a first approximation along the principal 2 axis, effectively average out this difference so that axx — ( yy The above equation simplifies to [2.11] 

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The shift reagent is added in incremental portions and the spectrum scanned after each addition. Coordination of the metal to basic sites is a reversible process and time-averaged chemical shifts are... 

Aqueous solutions with normal water cannot be used for H NMR measurements but heavy water, D2O, must be used instead. NMR data, however, can be used with normal water and H NMR spectra can be used with non-aqueous media. The quantities measured with NMR are time-averaged chemical shifts, as proton exchange is fast on the NMR time-scale. Other chemical shifts, such as those of can be measured. 

Experiments were performed at 5°C in order to arrest the cis-trans isomerization of the protonated Schiff base. Spectra with one equivalent of acid and different mixing times showed one NOE cross-peak between H15 of the retinal molecule and the proton on the counterion, as shown for a mixing time of 0.4 s in Figure 10. The strong chemical shift dependence of the H15 resonance on the concentration of the acid dictated the use of less than one equivalent of the protonating formic acid, and therefore an incomplete protonation (>80%) of the retinal, in order to avoid an overlap between the formate and the H15 peaks in the spectrum. This should not affect the observed result since an average chemical shift, between those of HI 5 of the retinal in its nonprotonated and protonated... 

In the solution state, there is a free rotation around the C(l)—N (fast on the NMR time scale) and, thus, average chemical shifts are observed for C2 and C6 and likewise for C3 and C5 in azobenzene as well as in 4,4 -disubstituted trans-azobenzenes. In the solid state, locked planar trans configurations are detected, resulting in nonequivalence of C2/C6 and C3/C5 signal pairs. Chippendale et al.86 reported in 1981 the I3C solid-state NMR spectra of azobenzene and symmetrically 4,4 -disubstituted rranj-azobenzenes (26). 13C chemical shifts are given in Table 12. 

As will be shown below, jthe average chemical shift is always positive. It is convenient to calculate A using Migdal s (1941) theory of sudden perturbations. According to this theory, the electron wave function does not manage to change within the /1-decay time, and so the average chemical shift... 

For details on the use of dynamic nmr to obtain kinetic parameters, the reader is referred to standard texts and other reviews. 2-5) For the present purpose, it is useful to remember that the nmr spectrum of conformations which interconvert rapidly on the so-called nmr time scale will show averaged chemical shifts and coupling constants. When the interconversion... 

The location of the lead cations in a series of lead-containing A, X and Y-zeolites and their mobility on exposure to water have been studied by a combination of ° Pb NMR and Al- ° Pb double resonance (SEDOR) experiments (Niessen et al. 2001). Systematic changes in the ° Pb relaxation time and the average chemical shift with water content suggest that the chemical environment of the lead cations is strongly affected by the sorption of water and supports a 2-site exchange model for the formation of Pb OH entities (Niessen et al. 2001). 

If each rotational isomer is a separate species, the time-weighted average chemical shift is given by (Pople, 1958a)... 

Here, 00 is the spin-lock rf frequency and Wq is population-averaged chemical shift. In the presence of an exchange between the two sites A and B, R2 =R 2 +l ex> in which R°2 is the relaxation constant due to relaxation mechanism other than exchange. For two-site exchange that is fast on the chemical shift time scale [20,90,91],... 

The observed upfield shifts indicate changes in the molecular packing and the bond conformation as the sample is converted from a highly ordered crystal to the isotropic melt. In the melt, the Si resonance gives the fast exchange-averaged chemical shift for a dynamic equilibrium between different rotational isomeric states of the Si—O and Si—C bonds. The fact that the Si chemical shift is identical for the melt and the /x-phase demonstrates a dynamically disordered conformational state also below the isotropic transition. This is confirmed by Si spin-lattice relaxation experiments. The T1 time was 23 s for the melt at 330 K and 25 s for the /x-phase at 300 K. Thus, the motional state and the conformational equilibrium of the molecular segments remain very much the... 

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