Carbon-proton dipolar Interaction

In an organic solid representative broadenings are 150 ppm for aromatic carbon chemical shift anisotropy and 25 kHz (full width at half-height) for a rather strong carbon-proton dipolar interaction. At a carbon Larmor frequency of 15 MHz, the shift anisotropy corresponds to 2.25 kHz. In high magnetic fields the forms of the respective Hamiltonians are... 

The carbon-proton dipolar interaction and the chemical shift anisotropies broaden the lines in solid state 13C NMR spectra. The major effect arises from the dipolar coupling of the carbon nuclei with neighboring protons homonuclear dipolar couplings between two adjacent 13C nuclei are neglegible because of their low natural abundance. The large magnitude of dipolar 13C— H coupling (up to 40 kHz) results in broad and structureless proton-coupled 13C NMR absorptions. 

For the common situation of carbon-13 observation in the presence of proton saturation (broadband decoupling), 7h/7c 4 and NOE enhancements can be as much as 200%, equating to a three-fold intensity increase. Since the relaxation of carbon nuclei is largely dominated by proton dipolar interactions, this maximum is almost met in practice. This is clearly a valuable route to sensitivity enhancement and, at least for the case of C, compares favourably for routine acquisitions with the factor of four attainable with the H to polarisation transfer sequences, given in Chapter 4. The maximum NOE enhancements for a variety of nuclei in the presence of proton saturation, denoted X H), are summarised in Table 8.2. 

NMR can, in principle, provide complementary information on motional processes in liquid crystals. The dipole-dipole interaction between a C-H pair and the quadrupolar interaction when the proton is replaced with a deuteron share the same principal interaction axis. In the case where the carbon is not directly bonded to a proton, there is still dipole-dipole relaxation by nearby protons, but it is also necessary to include an additional relaxation mechanism, the modulation of the chemical shift anisotropy. Proton spin decoupling is necessary to give well-resolved chemically shifted lines in the mesophase of liquid crystals. Furthermore, it is not practical to determine individual spectral density parameters from measured relaxation rates. Proton-proton dipolar interactions may not be ignored even when observation is exclusively confined to the resonant spin [5.31]. This is because proton relaxation causes population flow among the proton spin levels through dipolar (or scalar) coupling. As a consequence, cross-... 

Carbon NMR in solution is the method of choice for many types of material characterisation. While the sensitivity is much lower than for protons (Table 3.1), synthetic polymers are often soluble at concentrations as high as 5-20 wt%, so C-NMR spectra with a high signal-to-noise ratio can be acquired in a few hours. One major advantage of carbon NMR is that the chemical shifts are dispersed over 200 ppm rather than the 10 ppm typically observed for protons [1]. In addition, C-NMR is frequently used to study polymer molecular dynamics because the relaxation is predominantly due to carbon-hydrogen dipolar interactions with directly bonded protons. The C-H distances are fixed by the bond lengths, so the relaxation times can be used to measure the rotational correlation times directly (eqn (3.4)). 

One well-known and often used technique employed in conjunction with MAS is proton decoupling, where the influence of protons surrounding the measured species, usually carbon or lithium, is inactivated or saturated by a 90° pulse train at the proton frequency, a so-called broad band decoupling. The resulting spectral line is then free from proton dipolar interactions and is considerably narrowed. Another advantage of this technique is that the heteronucleus directly bonded to a proton will be affected much more than other sites that are not, therefore facilitating spectral assignments. 

This is the beauty of this quantity which provides specifically a direct geometrical information (1 /r% ) provided that the dynamical part of Equation (16) can be inferred from appropriate experimental determinations. This cross-relaxation rate, first discovered by Overhau-ser in 1953 about proton-electron dipolar interactions,8 led to the so-called NOE in the case of nucleus-nucleus dipolar interactions, and has found tremendous applications in NMR.2 As a matter of fact, this review is purposely limited to the determination of proton-carbon-13 cross-relaxation rates in small or medium-size molecules and to their interpretation. 

It can be noticed that the maximum NOE factor (2 when A is a carbon-13 and B a proton) is reached under extreme narrowing (see Section 6) conditions and if RA arises exclusively from the A-B dipolar interaction. On the other hand, the cross-relaxation rate gab is easily deduced from the NOE factor and from the A specific relaxation rate... 

Finally, it can be noted that there also exist dipolar-dipolar crosscorrelation rates which involve two different dipolar interactions. These quantities may play a role, for instance, in the carbon-13 longitudinal relaxation of a CH2 grouping.11,12 Due to the complexity of the relevant theory and to their marginal effect under proton decoupling conditions, they will be disregarded in the following. 

In the case of pharmaceutical solids that are dominated by carbon and proton nuclei, the dipole-dipole interactions may be simplified. The carbon and proton nuclei may be perceived as dilute and abundant based upon then-isotopic natural abundance, respectively (Table 1). Homonuclear 13C—13C dipolar interactions essentially do not exist because of the low concentration of 13C nuclei (natural abundance of 1.1%). On the other hand, H—13C dipolar interactions contribute significantly to the broad resonances, but this heteronuclear interaction may be removed through simple high-power proton decoupling fields, similar to solution-phase techniques. 

Only one complication to the determination of carbon Ffp has been identified but it illustrates the role of the strongly interacting proton dipolar system, a role which must be examined in even more detail for the non-spinning case (39). 

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