Relaxation rate mechanisms

From SCRP spectra one can always identify the sign of the exchange or dipolar interaction by direct exammation of the phase of the polarization. Often it is possible to quantify the absolute magnitude of D or J by computer simulation. The shape of SCRP spectra are very sensitive to dynamics, so temperature and viscosity dependencies are infonnative when knowledge of relaxation rates of competition between RPM and SCRP mechanisms is desired. Much use of SCRP theory has been made in the field of photosynthesis, where stnicture/fiinction relationships in reaction centres have been connected to their spin physics in considerable detail [, Mj. 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Dawson, M.J., Gadian, D.G., Wilkie, D.R. (1980). Mechanical relaxation rate and metabolism studied in fatiguing muscle by phosphorus nuclear magnetic resonance. J. Physiol. 299,465-484. 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

Fig. 35. Spin-state relaxation rate constant k versus temperature T for PSS-doped [Fe(6-Mepy)2(py)tren](CIOj2- Experimental data are indicated by filled circles. The solid line represents the fit to the tuimeling model of Hopfield, the dashed line the fit to the quantum mechanical theory of Buhks et al. According to Ref [138]...

For polyatomic gases in porous media, however, the relaxation rate commonly decreases as the pore size decreases [18-19]. Given that the relaxation mechanism is entirely different, this result is not surprising. If collision frequency determines the Ti, then in pores whose dimensions are in the order of the typical mean free path of a gas, the additional gas-wall collisions should drastically alter the T,. For typical laboratory conditions, an increase in pressure (or collision frequency) causes a proportional lengthening of T1 so the change in T, from additional wall collisions should be a good measure of pore size. 

The relaxation of gaseous methane, ethane and propane is by the spin-rotation mechanism and each pure component can be correlated with density and temperature [15]. However, the relaxation rate is also a function of the collision cross section of each component and this must be taken into account for mixtures [16]. This is in contrast to the liquid hydrocarbons and their mixtures that relax by dipole-dipole interactions and thus correlate with the viscosity/temperature ratio. 

In the case of dynamic mechanical relaxation the Zimm model leads to a specific frequency ( ) dependence of the storage [G ( )] and loss [G"(cd)] part of the intrinsic shear modulus [G ( )] [1]. The smallest relaxation rate l/xz [see Eq. (80)], which determines the position of the log G (oi) and log G"(o>) curves on the logarithmic -scale relates to 2Z(Q), if R3/xz is compared with Q(Q)/Q3. The experimental results from dilute PDMS and PS solutions under -conditions [113,114] fit perfectly to the theoretically predicted line shape of the components of the modulus. In addition l/xz is in complete agreement with the theoretical prediction based on the pre-averaged Oseen tensor. 

As we shall see, all relaxation rates are expressed as linear combinations of spectral densities. We shall retain the two relaxation mechanisms which are involved in the present study the dipolar interaction and the so-called chemical shift anisotropy (csa) which can be important for carbon-13 relaxation. We shall disregard all other mechanisms because it is very likely that they will not affect carbon-13 relaxation. Let us denote by 1 the inverse of Tt. Rt governs the recovery of the longitudinal component of polarization, Iz, and, of course, the usual nuclear magnetization which is simply the nuclear polarization times the gyromagnetic constant A. The relevant evolution equation is one of the famous Bloch equations,1 valid, in principle, for a single spin but which, in many cases, can be used as a first approximation. 

The second argument offered in [359] was based on the observation of 71Ga / j 1 rates at different temperatures that were faster than those calculated assuming Korringa relaxation as the only mechanism. However, this observation cannot be used to exclude the presence of Korringa relaxation, since additional mechanisms can always contribute additively to relaxation rates. Indeed, exactly such behavior has been observed for 71Ga MAS-NMR of h-GaN co-doped with Ge and Mn, where... 

By now, water exchange has been studied on more than one hundred Gdm complexes with the help of 170 NMR, and the large body of data available has been reviewed recently (48). Variable temperature 170 transverse relaxation rate measurements provide the rate of the water exchange, whereas the mechanism can be assessed by determining the activation volume, AVt, from variable pressure 170 T2 measurements (49,50). The technique of 170 NMR has been described in detail (51). 

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