Other Factors Affecting Relaxation

In this chapter we have provided only a simple introduction to a complex subject. From our discussion of the several relaxation mechanisms, it might be supposed that the relaxation rates simply add to give the total relaxation rate for the 

The effects of cross correlation can be exploited as a rich source of information on molecular dynamics by measuring relaxation behavior as a single line of a spin multiplet is perturbed. In addition, experiments can be designed to take advantage of the partial cancellation of relaxation effects and thus to obtain narrower lines than might otherwise occur. For example, in two-dimensional NMR it has been possible to utilize the quadratic dependence of CSA on B0 to 

FIGURE 8.7 31P NMR spectra of Na2HP03 (202 MHz, 11.7 T) at the temperatures indicated. At 225 K, where 0Tt 1, the low frequency line is so broad that it is unobservable. From Farrar and Stringfellow,94 Encyclopedia of Nuclear Magnetic Resonance, D. M. Grant and R. K. Harris, Eds. Copyright 1996 John Wiley Sons Limited. Reproduced with permission. 

FIGURE 8.8 ( 2) Partially relaxed 13C NMR spectra from an inversion-recovery pulse sequence. (b) Values of Tj (seconds) for 13C nuclei in n-decanol. (c) Values of Tr for 13C nuclei in phenol. 

In some polymers such segmental motions can be important, whereas in others (e.g., proteins) the overall skeleton is rigid, but there are rapid internal motions of moieties relative to the skeleton. In this case, relaxation and NOE data are often analyzed by the Lipari-Szabo formalism,96 which yields values for an overall correlation time rM, a correlation time for fast motions re, and a generalized order parameter S (see Eq. 7.16), which describes the amplitudes of the internal motions. 

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Regarding quantitation in the CP/MAS experiment, for peak areas to accurately represent the number of nuclei resonating, one of the conditions that must be met is that the time constant for cross polarization must be significantly less than the time constant for proton spin lattice relaxation in the rotating fi ame, Tch or Tnh TipH. Other factors affecting quantitation in CP/MAS have been discussed in several reviews (28-33). Since no analyses of the spin dynamics were performed in this study, the solid state spectra presented in this manuscript will be interpreted only semiquantitatively. 

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

Two factors contribute to r K. One is the ratio of the magnetogryric ratios of the two different spins, and the other depends on relaxation mechanisms. Provided that the relaxation mechanism is purely dipole-dipole, other relaxation mechanisms affect spin I, then 4> may approach zero. Assuming that the dipolar mechanism is operational (no quadrupolar nuclei with I > 1/2 are present), r has the value ys/ 2y and is regarded as rimax. In the homonuclear case we have r max = 1/ 2. Usually one chooses nuclei where ys > y/ to ensure that the NOE is significant. For observation of 13C for instance, if the protons in the molecule are double irradiated, the ratio is 1.99 and 1 + r max equals approximately 3. To repeat a statement made above, proton broad-band irradiation enhances the intensity of the 13C nucleus, which otherwise has very low receptivity. 

Finally, one other factor that may affect the approach to equilibrium for simulated systems should be mentioned. There are indications from a recent study of the LJ system that supercooled samples approach constant energy much more rapidly when the sample size is small. Since macroscopic systems have a fixed (average) relaxation time for a given temperature and pressure, such a result is a matter of some concern. Extensive studies will be necessary to verify such effects, however, because statistical fluctuations obscure the relaxation of configurational properties close to equilibrium. 

The oscillations observed with but-l-ene at 150°C are made up of two different portions. One is of sinusoidal type and the other consists of relaxation jumps between low and high conversion states. The parameters, k and A 4, adsorption and desorption rate constants of but-l-ene on the platinum surface, ks the surface reaction rate constant between O2 and but-l-ene, Zq the capacity factor, change the characteristics of these oscillations. Operating conditions like reactor temperature, flow rate, volume, mass of catalyst and concentration of but-l-ene in the feed also affect these oscillations both experimentally and in computer simulations. 

This is a highly simplified picture of the effects of chemical bonding on photoelectron spectra. There are a variety of other factors that affect the binding energy of the electron and the kinetic energy of the ejected photoelectron for example, relaxation effects, stereochemistry, crystal structure, and lattice energy, to name a few. The electron senses the total of all these effects their proportionate contributions are very difficult to assign. 

Many parameters have been shown to effect the value of T,. Halpem conducted an extensive study of the factors that can effect the value of Tj in transition metal hydride complexes. He noted, among other conclusions, that relaxation can be affected by metals having a high gyromagnetic ratio, such as cobalt, rhenium, and manganese. Despite these issues, and later studies that express reservations about Halpem s conclusions, the Tj criterion is commonly used and can be powerful if used for metals other than Co, Re, and Mn (or with corrections for the relaxation provided by these metals) and with an imderstanding of potential pitfalls. 

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