Longitudinal relaxation

Longitudinal relaxation is further divided into two categories relaxation with and without change in the quantum state of the electron spins under observation (A spins). The longitudinal relaxation accompanying the change in the quantum state of the A spins is induced by either of the following two interactions. 

1) Electron spin-lattice interaction. The transition between a and p spin states takes place by the interaction between the A spins and the lattice vibration of surrounding molecules. The excess energy of the A spin system is transferred to the surrounding molecules to induce lattice vibration. This relaxation takes place even for an isolated electron spin having no interaction with other electron spins at all. 

The above-mentioned types of relaxation and the mechanisms involved are summarized in Table 1. Dependence of the relaxation rate on the radical concentration is also given. 

Type of Relaxation and Interaction Mechanism Concentration Dependence 

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Canet D 1989 Construction, evolution and detection of magnetization modes designed for treating longitudinal relaxation of weakly coupled spin 1/2 systems with magnetic equivalence Prog. NMR Spectrosc. 21 237-91... 

In Debye solvents, x is tire longitudinal relaxation time. The prediction tliat solvent polarization dynamics would limit intramolecular electron transfer rates was stated tlieoretically [40] and observed experimentally [41]. 

H longitudinal relaxation time, measured by the inversion-recovery technique, at 293 K. 

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... 

In polymers one will often particularly be interested in very slow dynamic processes. The solid echo technique just described is still limited by the transverse relaxation time T being of the order of a few ps at most. The ultimate limitation in every NMR experiment however, is not T but the longitudinal relaxation time T, which for 2H in solid polymers typically is much longer, being in the range 10 ms to 10 s. The spin alignment technique (20) circumvents transverse relaxation and is limited by Tx only, thus ultraslow motions become accessible of experiment. 

Perrin model and the Johansson and Elvingston model fall above the experimental data. Also shown in this figure is the prediction from the Stokes-Einstein-Smoluchowski expression, whereby the Stokes-Einstein expression is modified with the inclusion of the Ein-stein-Smoluchowski expression for the effect of solute on viscosity. Penke et al. [290] found that the Mackie-Meares equation fit the water diffusion data however, upon consideration of water interactions with the polymer gel, through measurements of longitudinal relaxation, adsorption interactions incorporated within the volume averaging theory also well described the experimental results. The volume averaging theory had the advantage that it could describe the effect of Bis on the relaxation within the same framework as the description of the diffusion coefficient. 

Fig. 6.2 Theoretical Fe Mossbauer relaxation spectra for longitudinal relaxation with the indicated relaxation times and with a hyperline field that can assume the values 55 T. The symmetry direction of the axially symmetric EFG is assumed parallel to the magnetic hyperfine field. (Reprinted with permission from [9] copyright 1966 by the American Physical Society)...

Fig. 6.6 Mossbauer spectra of NH4( Teo.o2Alo.98)(S04)2-12H20 obtained at the indicated temperatures in a transverse magnetic field of 1.23 T. The full lines are fits to a model for longitudinal relaxation. (Reprinted with permission from [32] copyright 1979 by the Institute of Physics)...

As described in Section II.B, NMR is a powerful method for providing dynamic information. When signals of interest can be measured with a sufficient signal-to-noise ratio at different frequencies, the two relaxation times, the longitudinal relaxation time. 

One further point needs to be mentioned when probing the feasibility of a particular experiment. Apart from its dependence on temperature and concentration (for instance of ions, solutes, impurities, isotopes), relaxation times - in particular the longitudinal relaxation time Tj - depend on the field strength. This can be understood from the concept that energy exchange is most efficient if the timescale of molecular motion is equal to the Larmor frequency. Often, molecular motion takes place over a wide range of frequencies, so that the func-... 

W. E. Kenyon, P. I. Day, C. Straley, J. F. Willemsen 1988, (A three-part study of NMR longitudinal relaxation properties of water-saturated sandstones), SPEFE September, 622-636. 

The porosity cj)(z) for the voxel at z, is determined as described in Section 4.1.4.1. Note that the observed spin-displacement density function, q(z, vn), is not actually associated with the intrinsic value of spin density, q(z), due to the transverse and longitudinal relaxation. However, this does not affect the calculated average velocity given in Eq. (4.1.23) because the spin density terms in the denominator and nominator cancel each other. 

Longitudinal relaxation (T ) Recovery of magnetisation along the z axis. The energy lost manifests itself as an infinitesimal rise in temperature of the solution. This used to be called spin-lattice relaxation, a term which originated from solid-state NMR. 

Relaxation The process of nuclei losing absorbed energy after excitation. See longitudinal relaxation... 

Transverse relaxation (T2) Relaxation by transfer of energy from one spin to another (as opposed to loss to the external environment as in longitudinal relaxation). This used to be referred to as spin-spin... 

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