Relaxation field decay constant

Early studies involving NMR include the work by Hanus and Gill is [6] in which spin-lattice relaxation decay constants were studied as a function of available surface area of colloidal silica suspended in water. Senturia and Robinson [7] and Loren and Robinson [8] used NMR to qualitatively correlate mean pore sizes and observed spin-lattice relaxation times. Schmidt, et. al. [9] have qualitatively measured pore size distributions in sandstones by assuming the value of the surface relaxation time. Brown, et. al. [10] obtained pore size distributions for silica, alumina, and sandstone samples by shifting the T, distribution until the best match was obtained between distributions obtained from porosimetry and NMR. More recently, low field (20 MHz) NMR spin-lattice relaxation measurements were successfully demonstrated by Gallegos and coworkers [11] as a method for quantitatively determining pore size distributions using porous media for which the "actual" pore size distribution is known apriori. Davis and co-workers have modified this approach to rapidly determine specific surface areas [12] of powders and porous solids. 

An example of a quantitatively-analysed experimental result for these constants is shown in Fig. 7.29 in mixed crystals of naphthalene-dg 0.1% quinoxaline, the ESR transition T. To for the field direction Bo Xquinoxaiine and at a temperature T = 1.8 K is an absorption signal in the stationary state (Fig. 7.29a), while the transition I To) T-) in the stationary state exhibits stimulated emission of microwaves (Fig. 7.29b). After the end of the UV excitation at t = 0, the absorption line temporarily becomes an emission tine and vice versa. The interpretation of these results is simple (Fig. 7.29d) due to the negligible spin-lattice relaxation at T= 1.8 K, the three Zeeman components decay after the end of the U V excitation independently of one another, each with its own lifetime tj = into the So ground state. Since the difference of the populations of the three states is directly proportional to the intensity of the ESR signals, their time dependence can be used to determine the individual lifetimes of the Zeeman components involved. In the case of the particular orientation Boll, the state is To) = IT ), and one obtains directly from the measurements, e.g. the decay constant feo = kx and thus the lifetime of the zero-field constant Tx) of quinoxaline. 

As we have described earher, the ODMR method can be used to determine the radiative pattern of the triplet sublevels as well as the individual sublevel decay constants, the relative intersystem crossing rates, and spin-lattice relaxation rates. To the extent that these kinetic parameters (as well as the zero-field sphltings) are sensitive to the environment of the triplet chromophore, ODMR appears to be considerably... 

So far we have neglected the fact that the levels a) and b) are not only coupled by transitions induced by the external field but may also decay by spontaneous emission or by other relaxation processes such as collision-induced transitions. We can include these decay phenomena in our formulas by adding phenomenological decay terms to (2.68), which can be expressed by the decay constant ya and yt (Fig. 2.17). A rigorous treatment requires quantum electrodynamics [2.23]. 

The component p (l) is dne to the electrostiictive effect (the movement of molecules under intense electric field) it is proportional to y and is characterized by the Brillouin relaxation constant and frequency Q. From Equations (9.9) and (9.19) one can see that this component gives rise to a propagating wave. On the other hand, the component p (f) is due to the thermoelastic contribution (proportional to p ) and is characterized by the thermal decay constant it is nonprop-agative. 

The decay of M to Mo is called longitudinal relaxation (because it is parallel with the field Ho), it is identical with the spin-lattice relaxation described earlier. The rate constant for this process is therefore l/T,. The decay of M, and My is... 

The transverse magnetization and the applied radiofrequency field will therefore periodically come in phase with one another, and then go out of phase. This causes a continuous variation of the magnetic field, which induces an alternating current in the receiver. Furthermore, the intensity of the signals does not remain constant but diminishes due to T and T2 relaxation effects. The detector therefore records both the exponential decay of the signal with time and the interference effects as the magnetization vectors and the applied radiofrequency alternately dephase and re-... 

Hence, a series of measurements with several Tcp values will provide a data set with variable decays due to both diffusion and relaxation. Numerical inversion can be applied to such data set to obtain the diffusion-relaxation correlation spectrum [44— 46]. However, this type of experiment is different from the 2D experiments, such as T,-T2. For example, the diffusion and relaxation effects are mixed and not separated as in the PFG-CPMG experiment Eq. (2.7.6). Furthermore, as the diffusion decay of CPMG is not a single exponential in a constant field gradient [41, 42], the above kernel is only an approximation. It is possible that the diffusion resolution may be compromised. 

A single exponential curve (cf. "Equation U") has been fitted to the birefringence decay curve after removal of the electric field the agreement is good for Cq = 0.5 at 25°C (Fig.l) and moderately good for Cq = 1.6 at 60°C (Fig.2b).The fits lead to the relaxation times Tj = 1/6 Dj reported in Table I. As to the other cases, the agreement is very poor (Fig.2a) a two exponential curve is then necessary to describe the decay curves behaviour.The two-time constants are reported in Table I. 

The excellent resolution of the 0-tensor components at W band has been used to measure the relaxation properties of QA in the Zn-substituted bRC of R. sphaeroides.m The experiment showed, in contrast to the respective ubiquinone radical in organic solution, an anisotropic relaxation behavior in the pulse high field ESE experiments. From the analysis of the T2 experiments a motional anisotropy of Q% in the protein pocket was deduced with a preferred libration about the C-O symmetry axis. Recently, similar experiments were also performed on Qb- in ZnbRCs. Compared to QA different echo decay time constants were found. A model was proposed in which the relaxation is related to reorientational fluctuations around the quinones specific H-bonds to the protein.142... 

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