Relaxation field experimental limitations

In the field of ultrasonics the tern "Relaxation spectrum" very often refers to a plot of a limited number of a/f values (a being the sound absorption coefficient and f being the frequency of sound) vs f or log f where f covers 1-2 decades in the MHz region. If this plot shows a curvature almost S-shaped an ultrasonic relaxation is experimentally observed. If the plot shows a horizontal line no ultrasonic relaxation is observed. A given ultrasonic relaxation spectrum does not give direct information about the type of phenomenon that actually causes the observed effect. Since this information is necessary in order to extract... 

Assuming that (13.11) makes sense in the context of the system under investigation (i.e., that physical relaxation times are in the appropriate range for the condition of local equilibrium to be satisfactorily approximated), we seek the field-type differential equation that describes asymptotic (-evolution of fields Rfx, y, z, t) toward the known metric geometrical limit. Solutions of this equation are expected to describe a wide variety of thermal, acoustic, and diffusion phenomena in nonequilibrium conditions where local thermodynamic variables retain experimental meaning. 

The information content of nuclear longitudinal relaxation measurements in both paramagnetic and diamagnetic systems can be greatly increased by performing such measurements as a function of the magnetic field. For paramagnetic species, the reason is apparent from the functional form of the equations discussed in Chapter 3 and from the relevant experimental data, reported in Chapter 5. The field dependence of a relaxation rate is called relaxation dispersion, and is abbreviated as NMRD. In principle, NMRD would be helpful for any chemical system, but practical limitations, as will be shown, restrict its use, with a few exceptions, to water protons. 

The latter technique is particularly appreciated by coordination chemists because of its simple mathematical formulation and the limited amount of experimental data to be collected (longitudinal relaxation times at a single magnetic field obtained by the inversion-recovery method (Void et al., 1968)). However, the a priori choice of a reference distance (rref) requires a partial modeling of the complex and the extracted distances strongly depend on the accuracy of this original choice. 

Redfield limit, and the values for the CH2 protons of his- N,N-diethyldithiocarbamato)iron(iii) iodide, Fe(dtc)2l, a compound for which Te r- When z, rotational reorientation dominates the nuclear relaxation and the Redfield theory can account for the experimental results. When Te Ti values do not increase with Bq as current theory predicts, and non-Redfield relaxation theory (33) has to be employed. By assuming that the spacings of the electron-nuclear spin energy levels are not dominated by Bq but depend on the value of the zero-field splitting parameter, the frequency dependence of the Tj values can be explained. Doddrell et al. (35) have examined the variable temperature and variable field nuclear spin-lattice relaxation times for the protons in Cu(acac)2 and Ru(acac)3. These complexes were chosen since, in the former complex, rotational reorientation appears to be the dominant time-dependent process (36) whereas in the latter complex other time-dependent effects, possibly dynamic Jahn-Teller effects, may be operative. Again current theory will account for the observed Ty values when rotational reorientation dominates the electron and nuclear spin relaxation processes but is inadequate in other situations. More recent studies (37) on the temperature dependence of Ty values of protons of metal acetylacetonate complexes have led to somewhat different conclusions. If rotational reorientation dominates the nuclear and/or electron spin relaxation processes, then a plot of ln( Ty ) against T should be linear with slope Er/R, where r is the activation energy for rotational reorientation. This was found to be the case for Cu, Cr, and Fe complexes with Er 9-2kJ mol" However, for V, Mn, and... 

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