Signals relaxation rates

The B-coefficients obtained from viscosity and NMR signal relaxation rates pertain to dilute solutions (they are the limiting slopes towards infinite dilution). However, an equation of the form of Eq. (3.6) for NMR spin-lattice relaxation rates holds up to fairly large concentrations. Chizhik (1997) reported values of relative water molecule reorientation times Tri/Trw at 22 °C, being <1 for Br , I, NH4+, NOs, and Ns , 1.0 for K+, and >1 for Li+, Na+, Mg +, Ca +, Sr +, Ba +, F , CH, H3O+, S04 , and COs, in more or less agreement with the signs of the Bnmr in dilute solutions. Table 3.1. 

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

The relaxation rates of the individual nuclei can be either measured or estimated by comparison with other related molecules. If a molecule has a very slow-relaxing proton, then it may be convenient not to adjust the delay time with reference to that proton and to tolerate the resulting inaccuracy in its intensity but adjust it according to the average relaxation rates of the other protons. In 2D spectra, where 90 pulses are often used, the delay between pulses is typically adjusted to 3T] or 4Ti (where T] is the spin-lattice relaxation time) to ensure no residual transverse magnetization from the previous pulse that could yield artifact signals. In ID proton NMR spectra, on the other hand, the tip angle 0 is usually kept at 30°-40°. 

Locahzed motion can also lead to local variations in correlation times. Folded peptides with unfolded C- or N-terminal residues, for example, will have varying correlation times for the rigid and flexible parts of the molecule, resulting in different cross-relaxation rates. Such effects can usually be distinguished by the Unewidths and intensities of the corresponding diagonal signals, since the autorelaxation rates also depend on the correlation time. 

Fig. 9.32 (a) Time evolution of the SRPAC signal (in log scale) for several temperatures obtained from the molecular glass former DBP doped with Fe-enriched ferrocene, (b) The relaxation rate X (in log scale) as a function of inverse temperature 1,000 obtained from analyzing the SRPAC... 

The signals from different components or sample environments are separated based on differences in relaxation rates. 

Because of the NOE and differences in relaxation rates, the intensity differences for carbon signals in a broad-band decoupled spectrum are extremely large, so that quantitative information is not available. 

Quantitative solid state 13C CP/MAS NMR has been used to determine the relative amounts of carbamazepine anhydrate and carbamazepine dihydrate in mixtures [59]. The 13C NMR spectra for the two forms did not appear different, although sufficient S/N for the spectrum of the anhydrous form required long accumulation times. This was determined to be due to the slow proton relaxation rate for this form. Utilizing the fact that different proton spin-lattice relaxation times exist for the two different pseudopolymorphic forms, a quantitative method was developed. The dihydrate form displayed a relatively short relaxation time, permitting interpulse delay times of only 10 seconds to obtain full-intensity spectra of the dihydrate form while displaying no signal due to the anhydrous... 

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