Spin lattice signal intensity

The spin-lattice relaxation time, T/, is the time constant for spin-lattice relaxation which is specific for every nuclear spin. In FT NMR spectroscopy the spin-lattice relaxation must keep pace with the exciting pulses. If the sequence of pulses is too rapid, e.g. faster than BT/max of the slowest C atom of a moleeule in carbon-13 resonance, a decrease in signal intensity is observed for the slow C atom due to the spin-lattice relaxation getting out of step. For this reason, quaternary C atoms can be recognised in carbon-13 NMR spectra by their weak signals. 

Thus, in the series of Ti measurements of 2-octanol (42, Fig. 2.27) for the methyl group at the hydrophobic end of the molecule, the signal intensity passes through zero at Tq = 3.8 s. From this, using equation 10, a spin-lattice relaxation time of Ti = 5.5 s can be calculated. A complete relaxation of this methyl C atom requires about five times longer (more than 30 s) than is shown in the last experiment of the series (Fig. 2.27) Tj itself is the time constant for an exponential increase, in other words, after T/ the difference between the observed signal intensity and its final value is still 1/e of the final amplitude. 

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°. 

NMR signals are highly sensitive to the unusual behavior of pore fluids because of the characteristic effect of pore confinement on surface adsorption and molecular motion. Increased surface adsorption leads to modifications of the spin-lattice (T,) and spin-spin (T2) relaxation times, enhances NMR signal intensities and produces distinct chemical shifts for gaseous versus adsorbed phases [17-22]. Changes in molecular motions due to molecular collision frequencies and altered adsorbate residence times again modify the relaxation times [26], and also result in a time-dependence of the NMR measured molecular diffusion coefficient [26-27]. 

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... 

As is the case for NMR of liquids, another important consideration for SSNMR spectroscopy is relaxation. There are different types of relaxation present during a SSNMR experiment. The spin-lattice relaxation, Ti, dictates how fast one can repeat scans. This time between experiments must be set greater than five times T1 in order for complete relaxation to occur. Otherwise, the full signal intensity will not be... 

This technique involves transfer of polarization from one NMR active nucleus to another [166-168]. Traditionally cross polarization (CP) was employed to transfer polarization from a more abundant nucleus (1) to a less abundant nucleus (S) for two reasons to enhance the signal intensity and to reduce the time needed to acquire spectrum of the less abundant nuclei [168]. Thus CP relies on the magnetization of I nuclei which is large compared to S nuclei. The short spin-lattice relaxation time of the most abundant nuclei (usually proton) compared to the long spin-lattice relaxation time of the less abundant nuclei, allows faster signal averaging (e.g., Si or C). CP is not quantitative as the intensity of S nuclei closer to 1 nuclei are selectively enhanced. Nowadays CP has been extended to other pairs of... 

One can imagine two protons, and He, being part of the same molecule and undergoing chemical exchange, at a rate knu- When is irradiated, it remembers the new condition and transfers this information to Hj as a result of the chemical exchange. The newly arrived He proton does not contribute to the normal amount of signal intensity in the final NMR spectrum. If the initial intensity of Hj is 4, and the final intensity for Hg as a result of irradiation of is If, then the rate of exchange knu is defined by Eq. (7), where Tj refers to the spin-lattice relaxation time. 

Isotopes in low abundance have long spin-lattice relaxation times which give rise to poor signal-to-noise ratios. Sensitivity can be improved by using a technique known as cross polarization where a complex pulse sequence transfers polarization from an abundant nucleus to the dilute spin thereby enhancing the intensity of its signal. 

Nuclear Overhauser enhancements and spin-lattice relaxation times are individual for each carbon. As a result, signal intensities cannot be evaluated from PFT 13C NMR spectra obtained with continuous proton broadband decoupling. 

The pronounced relaxation acceleration observed for slowly relaxing nuclei in the presence of paramagnetic compounds is exploited in Fourier transform, 3C NMR spectroscopy. On use of the fast pulse sequences that are frequently necessary, the spin-lattice relaxation of slow 13C nuclei can no longer follow excitation, and the corresponding 13C signals have low intensities. In such cases, addition of small amounts of relaxation accelerators, such as radicals or transition metal salts, to the sample amplifies these signals [153]. 

It is very important that there be sufficient time between pulses in FT-NMR experiments so that the nuclei can return to the original equilibrium state. If the equilibrium state has not been reached before the next H pulse, the still-excited nuclei will not participate in the transition and thus will produce a decreased signal intensity relative to the previous signal. As the experiment proceeds and more pulses are applied, more nuclei will remain in the exited state until eventually none of the nuclei will be in the lower energy state when pulsed. At this point the sample is saturated and will not produce a signal. The length of time required for the nuclei to relax is called the spin-lattice or T relaxation time. 

Because of the 100% isotopoic abundance of 27A1 and its very short spin-lattice relaxation time, even traces of aluminum are often detectable by MAS NMR. For example, Thomas et al. (156) were able to show that aluminum present as an impurity in soda glass is four-coordinated. However, quantitative determination of Al concentration in the sample is only possible when the quadrupolar effects are not so large as to affect significantly the apparent intensity of the 27A1 signal. 

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