Spin-lattice relaxation 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. 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

In the spectrum of fully reductively [ C] methylated glycophorin A, the resonance at 42.8 p.p.m. must correspond to the N, N -di[ C]methylated, N-terminal amino acid residue. The ratio of the integrated intensities of the N, N -di[ C]methylLeu resonance to the N, N -di[ C]methyllysine resonances is 5 1, as expected. The integration values determined were valid, because the recycle times of spectra in Figs. 3B, 3C, and 3D were twice the spin-lattice relaxation-times (Tj values) of those of the di[ C]methyl carbon atoms, and also because the n.O.e. values of the N, N -di[ C]methyl and N, N -di[ C]methyl carbon atoms were equivalent. ... 

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°. 

T3C n.m.r. spectra were recorded for the oils produced at 400°, 450°, 550° and 600°C. As the temperature increased the aromatic carbon bands became much more intense compared to the aliphatic carbon bands (see Figure 8). Quantitative estimation of the peak areas was not attempted due to the effect of variations in spin-lattice relaxation times and nuclear Overhauser enhancement with different carbon atoms. Superimposed on the aliphatic carbon bands were sharp lines at 14, 23, 32, 29, and 29.5 ppm, which are due to the a, 8, y, 6, and e-carbons of long aliphatic chains (15). As the temperature increases, these lines... 

The saturation behavior of a spectrum - the variation of integrated intensity with microwave power - is related to the spin-lattice relaxation time, a measure of the rate of energy transfer between the electron spin and its surroundings. Saturation often depends on the same structural and dynamic properties as line widths. 

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... 

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

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... 

The second difficulty is not encountered in proton spectroscopy, where proportionality between peak area and concentration of the respective sequence is virtually guaranteed, but is present in caibon spectroscopy where one works under heteronuclear broad-band decoupling conditions. Under such conditions, both the nuclear Oveihauser effect (NOE) and the differences in spin-lattice relaxation time T, can alter the intensity. In this connection, however, Schaefer showed that for the different C nuclei inside the polymer chain, because of the restricted molecular movement, there are no large differences in NOE (121). 

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. 

Fig. 1. Pulse sequences for determining spin-lattice relaxation time constants. Thin bars represent tt/2 pulses and thick bars represent tt pulses, (a) The inversion-recovery sequence, (b) the INEPT-enhanced inversion recovery, (c) a two-dimensional proton-detected INEPT-enhanced sequence and (d) the CREPE sequence. T is the waiting period between individual scans. In (b) and (c), A is set to (1 /4) Jm and A is set to (1 /4) Jm to maximize the intensity of IH heteronuclei and to (1/8) Jm to maximize the intensity of IH2 spins. The phase cycling in (c) is as follows 4>i = 8(j/),8(-j/) 3 = -y,y A = 2(x),2(-x) Acq = X, 2 —x), X, —X, 2(x), —x, —x, 2(x), —x, x, 2 —x),x. The one-dimensional version of the proton-detected experiment can be obtained by omitting the f delay. In sequence (d), the phase 4> is chosen as increments of 27r/16 in a series of 16 experiments.

Most relaxation measurements are conducted in such a way as to record the resulting magnetization after a variable delay, r, during which the initially created state is allowed to relax. In the spin-lattice relaxation experiment, the T relaxation time can be evaluated by non-linear three-parameter fitting of the following expression [31] to the intensities ... 

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