Relaxation times and linewidths

Relaxation times and linewidths can also provide a variety of information on local dynamics below the glass-transition temperature. The main relaxation times that are of interest in high-resolution solid-state NMR for the carbon-13 nucleus are the spin-lattice relaxation time Ti( C), the spin-lattice relaxation time in the rotating frame and the spin-spin 

As already mentioned in the Introduction, magnetic relaxation in the solid state may be governed not only by dynamic phenomena but there may also exist a contribution from static phenomena such as spin diffusion, which consists of mutual exchanges of spin state, or flip-flops , between strongly coupled nuclei that have the same precession frequency but antiparallel spins. This mechanism is explained in more detail in chapter 7. It does not involve any variation in the energy of the system. When it occurs, magnetic relaxation times cannot be interpreted in terms of local dynamics only, but the two contributions have to be separated. 

The situation is quite different in the rotating frame. As for TiC C), is usually not determined by spin diffusion. However, as 

In rigid materials such as crystalline polymers where there is almost no motion, 

In contrast, when the spectral density at is important, the relaxation time essentially reflects the local dynamics. 

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Adriamycin and daunomycin (fig. 3) are two antibiotics currently highly investigated because of their effectiveness against malignant cells. The interaction of daunomycin with lanthanide chlorides (Eu, Gd, Tb, Yb) yields complexes that have been analyzed by Mariam and Wells (1984) and Mariam et al. (1984) by spectrophotometry and NMR spectroscopy. Molar ratio and continuous-variation methods indicate the presence of predominantly a ML2 species at metal-to-ligand ratios less than one MjL and ML species are also present. Proton spin-lattice relaxation time and linewidth measurements utilizing the relaxation probe Gd(III) indicate that the primary coordination site is in the 11,12-positions. 

Table 4. Examples of N Relaxation Times and Linewidths at Ambient Temperatures...

These nuclei (and they form by far the majority of the NMR-active nuclei ) are subject to relaxation mechanisms which involve interactions with the quadrupole moment. The relaxation times Tj and T2 (T2 is a second relaxation variable called the spin-spin relaxation time) of such nuclei are very short, so that very broad NMR lines are normally observed. The relaxation times, and the linewidths, depend on the symmetry of the electronic environment. If the charge distribution is spherically symmetrical the lines are sharp, but if it is ellipsoidal they are broad. 

The results that have been obtained indicate that the major influence of the crystalline regions on segmental motions, and hence to the structure of the non-crystalline regions, is in the linewidth and T2. The different morphologies are reflected in different values of T2- The segmental motions in long chain molecules which exert major influence on the spin-lattice relaxation times and the nuclear Overhauser enhancements are not in general the same motions which determine the resonant linewidth. 

The Cl carbon resonances for the aryl groups, unlike the C resonances of the alky groups are too broad for detection. The proton relaxation times and as well as the linewidths in three different magnetic fields, corresponding to proton frequencies of 250, 400, and 600 MHz, show an increase with the field strength. 

J. L. Evelhoch, C. S. Ewy, B. A. Siegfried, J. J. H. Ackerman, D. W. Rice and R. W. Briggs, P spin-lattice relaxation times and resonance linewidths of rat tissue in vivo dependence upon the static magnetic field strength. Magn. Reson. Med., 1985, 2,410-417. 

On adding dioxygen to the fully reduced laccase of the lacquer tree Rhus vemicifera, the type-1 Cu and the type-3 Cu-pair were oxidized in the ms range and an optical intermediate was observed at 360 nm At liquid helium temperatures an EPR signal was observed, which was tentatively interpreted as due to O ", as a result of its very short relaxation time and of the increase of its linewidth when the reduced laccase of the fungus Polyporus versicolor was treated with 0 A similar paramagnetic oxygen intermediate was also observed with the laccase of another lacquer tree Rhus succedanea and with ceruloplasmin. The decay of the intermediate at 25 °C (tj = 1 s at pH 5.5 with R. succedanea laccase) was accompanied by the reoxidation of the type-2 Cu >. One would expect, however, such an intermediate to be extremely reactive (See Sect. 3.3), while it was stable in tree laccase depleted of type-2 Cu(II)... 

Fig. 5.10. Predominance of dipolar, contact or Curie relaxation in signal linewidths at 800 MHz for different rotational and electron relaxation times, and for different constants for the contact interaction. Calculations have been performed for protons at 5 A from a S = 5h ion.

Nuclei with a spin number 7 of one or higher have a nonspherical charge distribution. This asymmetry is described by an electrical quadrupole moment, which, as we shall see later, affects the relaxation time and, consequently, the linewidth of the signal and coupling with neighboring nuclei. In quantum mechanical terms, the spin number 7 determines the number of orientations a nucleus may assume in an external uniform magnetic field in accordance with the formula 27+1. We are concerned with the proton whose spin number 7 is 1/2. 

At fast flow rates, the saturation of signals is avoided because spins leave the NMR active region, thus leading to an increase in S/N. The NMR linewidth is related to transverse relaxation time and, in a flow system, the linewidth is further influenced by the residence time. As a result, short residence times at fast flow rates yield broader NMR signals with low S/N. Ideally, detection of each analyte should be optimized using suitable acquisition parameters to obtain NMR spectra with comparable S/N. In addition, the overall temperature change in buffer by Joule heating may also contribute to linewidth increase [44],... 

Tie and Tae are the electron spin relaxation times and % is the rate constant for proton exchange. Thus, if this mechanism is dominant the observed linewidths, Aui[ = (71X2) ], must reflect the r dependence on the electron-nuclear distance. Hyperfine exchange relaxation, however, is given by the expressions ... 

Nuclei with spin 7 1 display another problem arising from the electric quadrupole moment which interacts with the electric field gradient created by the surrounding electrons. This property leads to a decrease of the relaxation times and, accordingly, an increase of the linewidths. This situation theoretically limits the use of NMR to nuclei with highly symmetric environments. The cluster effect , as suggested by Rehder [8], sometimes leads to important exceptions to this rule, as shown below. 

The metabolic pathways of 5-FU and its prodrugs have been well characterized in the liver as well as in liver tumors and metastases by in vivo 19F MR spectroscopy. The liver and extrahepatic spaces catabolize 5-FU, which is subsequently excreted in the urine [3-5, 7-10, 46, 59], Active metabolites (fluoronucleotides) are created by anabolism in tumors. Even though clinical studies showed significant individual subject variations [3, 5, 7-10, 26,46,47], spectral characteristics such as resonance frequency, linewidth, relaxation time, and amplitude were not related to the therapeutic response. However, dynamic processes, specifically the accumulation and retention of 5-FU in the tumor, were indicative of response. Patients showing tumor half-lives of free 5-FU of 20 minutes or longer observed in patients were characterized by Wolff el al. [47, 53] as trappers. While over 50% of the evaluated population were nontrappers, approximately 60% of the patients who responded to therapy were trappers [3-5, 7-10],... 

Recent advances in Ge NMR spectroscopy are reviewed. Following the introduction (Section 1), Section 2 describes recently determined chemical shifts and linewidths for a variety of organogermanium compounds which range from normal (tetravalent) to hypercoordinated (up to heptavalent) species. The role of linewidth as evidence for hypercoordination is discussed. In Section 3, coupling constants, relaxation times and relaxation mechanisms are discussed in detail, showing that in some cases a mechanism other than quadrupolar is involved. In the last section, high-resolution solid-state Ge NMR spectroscopy is covered which has not been treated in previous reviews. 

The temperature-dependent shift of the resonance line is strongly connected with the nuclear magnetic relaxation times and the linewidth. The fluctuating magnetic field at the nucleus usually has components perpendicular to the external magnetic field. The Fourier spectrum of these field components contains terms with resonance frequencies, which induce transitions between nuclear energy levels. One may foresee the temperature... 

The main experimental information that usually can be deduced from ESR experiments in metals are the g-shift and the linewidth broadening. Both quantities can be measured as a function of an external parameter, like temperature or pressure. The g-shift corresponds to the Knight-shift in NMR experiments and yields information about the static susceptibility. This review nicely documents how the experimental results on the g-shifts in metals provide direct and detailed information on the band structure. The ESR linewidth in metals is determined by the spin-lattice relaxation time and has to be compared to l/T) as deduced from NMR results. The linewidth is determined by the density of states, but in addition yields detailed information on the low-frequency spectrum of spin fluctuations. This is of high relevance in the field of high-Tc superconductors and heavy-fermion compounds. 

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