Signal intensity spin-lattice relaxation time

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°. 

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... 

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. 

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. 

Relaxation parameters provide valuable information about molecular motions. The spin-lattice relaxation time T is usually determined by the so-called inversion recovery pulse sequence (65). The experiment comprises a set of spectra with different interpulse delays, and Tx is determined by fitting the signal intensities for a given nucleus to Eq. 2, where A and B are constants, x is the respective interpulse delay, and /,is the intensity measured at that delay ... 

This is proportional to the reciprocal of the spin-lattice relaxation time Tf. Therefore, while the spin-spin relaxation time T2 is estimated directly from the half-width of the signal before "saturation," Ti is obtained from a saturation experiment For example, when increasing Hi leads, for instance, to a halving of the signal intensity, then at this half intensity the condition yzH1zT1T2 = 1 is satisfied, and the spin-lattice relaxation time T, is estimated from the known Hi and T2. 

Selected spin-lattice relaxation times are shown in Fig. 1. Carbon nuclei bonded to protons in typical complexes of the type reviewed here frequently have short spin-lattice relaxation times (7 ) and hence relatively large tilt angles can be used in routine FT measurements. Tx is considerably longer for carbon nuclei not directly bonded to protons, e.g., a value of 56 sec has been measured for the meso-allyl carbon atom in 6, which accounts, in part, for the low intensity of the signals of such nuclei under standard measurement conditions. 

Eigure 12.5 presents TR ESR and ET ESR spectra obtained under photolysis of DAR (Scheme 12.1). One can observe a broadened signal of benzoyl radical in the ET ESR (or a signal of much lower apparent intensity). The intensity of the signals in CW TR ESR is determined by polarization, longitudinal (spin lattice) relaxation time Ti and by the rate of chemical disappearance of r. The intensity of signals in ET ESR is determined by polarization, and phase memory time Tm, which includes Ti, transverse (spin-spin) relaxation time T2, and a rate of chemical disappearance of r. Broad ESR components have short Tm, and they are difficult to observe. Broadening of components in spin adducts is ascribed to a hindered rotation around a Cp bond or cis-trans isomerization (Scheme 12.4). ... 

With a chromatographic technique capable of routinely yielding preparative fractions, quantitative and C FT NMR was the major spectroscopic tool used for chemical characterization. The established utility of and C NMR for characterization of coal products is documented well. Unfortunately, high-resolution C FT NMR is not quantitative normally under operating conditions used typically. (It should be noted that quantitative FT NMR measurements also are not obtained routinely. The problem of variable spin lattice relaxation times (Ti s) is present also in FT NMR. In addition, the greater signal intensity of NMR in comparison with C FT NMR poses an additional potential problem of detector linearity in the FT NMR receiver.) For C FT NMR, variable spin lattice relaxation times (Ti s) and nuclear Over-hauser effects (a result of pseudo random noise decoupling) usually... 

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