Cross-polarization time constant

NMR relaxation measurements such as cross-polarization time constants (7ch) can also yield useful information regarding alkyl-chain mobility. Sindorf and Maciel [159] have characterized the relative mobility of low-density Cg and Cig stationary phases ( 2.6 and 1.7 p,mol/m, respectively) as a function of carbon position from the... 

Figure 4. The influence of magic angle spinning on the SL cross polarization time constant. In the PlP-cured epoxy the time constant for the nonprotonated carbons increases by about 50% for = 1-3 kHz while those of the protonated carbons are virtually unchanged over this range.

Figure 5. The rf pulse sequences for determining SL cross polarization time constant Ten, C-13 T,p and C-13 Tj under proton decoupling. Each experiment starts with a SL cross polarization.

Io is the maximum intensity, TCp is the cross polarization time constant and Tiph and TlpC are the relaxation times for ll and 13C in the rotating frame. The cross polarization rate (l/TCp) depends on the square of the dipolar interaction while the relaxation time in the rotating frame provides... 

Octacalciumphosphate - for the chemical formula see Table 2 Cross-polarization time constant for the I-S model Proton diffusion time constant... 

Time period of forward CP in DCP - see text and Fig. 14 Depolarisation time period in DCP - see text and Fig. 14 P spin-lattice relaxation time in the laboratory frame Cross-polarization time constant for the I-P-S model H spin-lattice relaxation time in the rotation frame H spin-spin relaxation time in the laboratory frame Recycle delay... 

Cross-polarization time constants, Tch, are short enough to allow the C nuclei to equilibrate with the protons during cross-polarization (if there is extensive motion, the CP process can become very inefficient in the mobile region compared to the more rigid portions) [78]. 

Thus, for a given nitrogen the full polarization transfer can be reached only to the extent that the cross polarization time t is given the appropriate value. Moreover the HARTMANN-HAHN condition [Eq. (3.1)] is less easily fullfilled in the liquid state than for solids since the tolerable mismatch is now of the order of the scalar coupling constants which are at least two orders of magnitude smaller than the dipolar ones. The homogeneity of the rf fields is also a critical condition and in practice probe coils doubly tuned for and protons have been especially constructed. (See also (C 28)). 

The transfer of polarization between I- and S-spin systems is controlled by a cross-relaxation time constant, Tcr. The rate (Tq ) at which I- and S-spins reach thermal equilibrium in the double-rotating frame depends, in... 

Fig. 13. Magic angle spinning alters the cross-polarization rates. Here TCH is the time constant for spin lock cross-polarization under the Hart-mann-Hahn condition at r.f. fields of 38 kHz62 ...

Clearly, in order to correctly apply CP pulse sequences for quantitative analysis (or even qualitative analysis), many relaxation processes (Tic, T pH, Till. TCp) must be considered and spectral acquisition parameters appropriately set. While a CP spectrum may be obtained when Tic > 7) 11 3TlpH Tqp, a quantitative CP spectrum requires that the recycle delay is sufficient (on the order of Tm) for the protons to be uniformly relaxed at the beginning of the contact time,25 all proton magnetization spin locked in the rotating frame decays at the same rate (T ph), and the contact time is sufficient to allow complete cross polarization (at least 5 times the longest TCp)26 Except when relative peak intensities are constant and appear to be correct, single contact time measurements should be avoided. Instead, 13C spectra and relaxation times should be measured and complete magnetization curves analyzed. 

If the coupling constants are known in advance, the total mixing time can be reduced in multiple-step selective coherence-transfer experiments by using the selective homonuclear analog of the optimized heteronuclear two-step Hartmann-Hahn transfer technique proposed by Majumdar and Zuiderweg (1995). In this technique [concatenated cross-polarization (CCP)] a doubly selective transfer step (DCP) is concatenated with a triple selective mking step (TCP). For the case of a linear three-spin system with effective planar coupling tensors, a CCP experiment yields complete polarization transfer between the first and the third spin and the total transfer... 

Homonuclear and heteronuclear coupling constants can be determined from the mixing-time dependence of Hartmann-Hahn transfer (see Sections II and VI). For example, for two heteronuclear spins 1 /2, the ideal polarization-transfer frequency under planar Hartmann-Hahn mbdng is 7,5/2 (see Section VI). Heteronuclear H- Si coupling constants have been determined in IS, I2S, and I S spin systems by Fourier analysis of the cross-polarization intensity as a function of the mbdng time (Bertrand et al., 1978a) and by an iterative fitting procedure (Murphy et al., 1979). 

Regarding quantitation in the CP/MAS experiment, for peak areas to accurately represent the number of nuclei resonating, one of the conditions that must be met is that the time constant for cross polarization must be significantly less than the time constant for proton spin lattice relaxation in the rotating fi ame, Tch or Tnh TipH. Other factors affecting quantitation in CP/MAS have been discussed in several reviews (28-33). Since no analyses of the spin dynamics were performed in this study, the solid state spectra presented in this manuscript will be interpreted only semiquantitatively. 

---