Zeeman spin-lattice relaxation time

To study dipole-dipole relaxation, one must distinguish between homonuclear and heteronuclear (unlike) spin-1 pairs. The latter gives rise to the so-called 3/2 effect.29 For an isolated pair of like spin-i nuclei (/= 1) separated by an intemuclear distance r, the treatment of spin relaxation is identical to that for a spin-1 quadrupole system. The Zeeman spin-lattice relaxation time T1Z and spin-spin relaxation time T2 are given, respectively, by... 

Figure 8.2(c) is an inversion-recovery quadrupole echo pulse sequence, which is used to measure the Zeeman spin-lattice relaxation time,, with quadrupole echo detection [8,9,115]. Pre-saturation (Figure 8.2(d)) or progressive saturation (variation of the delay between transients) are also used to measure T. Notably, pre-saturation with spectral subtraction can separate the spectra of domains with different and is used to obtain the individual spectra of the amorphous and crystalline regions of semicrystalline polymers [8]. Also, Void and co-workers have recently presented methods involving selective inversion for the measurement of slow molecular reorientation, which provide an alternative to spin alignment or multidimensional methods [116]. 

Treatment of spin-lattice relaxation of an isolated spin- pair by intramolec-ular dipole-dipole interaction is identical to that for a one spin-1 system. Two like spin- nuclei separated by an internuclear distance r are considered. The Zeeman spin-lattice relaxation time Tiz is given by Eq. (5.40), but with a different multiplicative constant Kd which reflects the dipolar interaction strength. To find the off-diagonal Redfield s element jRi2 may be calculated for the case of dipole-dipole interaction ... 

Low-spin Fe(iii) porphyrins have been the subject of a number of studies. (638-650) The favourably short electronic spin-lattice relaxation time and appreciable anisotropic magnetic properties of low-spin Fe(iii) make it highly suited for NMR studies. Horrocks and Greenberg (638) have shown that both contact and dipolar shifts vary linearly with inverse temperature and have assessed the importance of second-order Zeeman (SOZ) effects and thermal population of excited states when evaluating the dipolar shifts in such systems. Estimation of dipolar shifts directly from g-tensor anisotropy without allowing for SOZ effects can lead to errors of up to 30% in either direction. Appreciable population of the excited orbital state(s) produces temperature dependent hyperfine splitting parameters. Such an explanation has been used to explain deviations between the measured and calculated shifts in bis-(l-methylimidazole) (641) and pyridine complexes (642) of ferriporphyrins. In the former complexes the contact shifts are considered to involve directly delocalized 7r-spin density... 

One such analysis in the review period involves the characterization of the rotation of the methyl groups in pyridoxine (vitamin B6).49 The temperature dependencies of the 1H spin-lattice relaxation time T, and Tld (the relaxation time constant characterizing the relaxation of dipolar order, a population distribution over the Zeeman spin levels, which corresponds to a density operator component T20, he. I z - Ii. I2, to equilibrium) at three different applied field strengths and for a variety of temperatures were determined, yielding the curves in Fig. 30. The only motion that could affect... 

The recovery of the Zeeman polarization to its equilibrium value is characterized by the longitudinal, or spin-lattice relaxation time constant Tiz. Spin-lattice relaxation occurs through dissipation of the excess energy of the spins to the surrounding lattice, brought about by fluctuating fields of the appropriate frequencies, i.e., close to the Larmor frequency cdq and to 2(Oq. 

In Section 3 the Zeeman polarization-enhanced method is discussed. The method demonstrates its efficiency when spin-lattice relaxation time of the NQR spin-system is long enough to ensure the feasibility of the adiabatic demagnetization process. 

Another particularly interesting type of experiment gives information about the Co parent atom. At temperatures of < IK the Zeeman levels of Co I — 1) atoms in iron metal are not equally occupied as their separation is kT. Assuming that the spin-lattice relaxation times are longer than the total nuclear decay time, the preferential orientation of the nucleus... 

Motions shorten spin-lattice relaxation times. Analysis can provide insight into molecular motions. Dynamics of a radicals can be studied by analysis of contributions due to rotational modulation of hyperfine and Zeeman anisotropies. 

When relaxation occurs among r.f. pulses, the t dependence in the above sequence provides a means to study spin-lattice relaxation. It is known [2.20] that the Zeeman Tiz) and quadrupole (Tig) spin-lattice relaxation times can be measured for deuterons in liquid crystals from the sum and difference of the doublet signal strengths after the third pulse, respectively. This can be shown using the formalism of rotation operators. The rotation operator R(0, ) provides a general method to describe the effect of a r.f. pulse with rotation angle 0 and phase angle when there are no cyclic commutation relations, such that the simple relation in Eq. (2.60) exists. Now... 

Cross-relaxation at the nematic-polymer interface. The liquid crystal protons and the polymer protons constitute a two phase proton system. The cross-relaxation at the boundary leads to an exchange of Zeeman energy between the two phases and couples their spin-lattice relaxation rates [202]. Cross-relaxation affects all molecules in the droplet if the exchange of molecules at the surface is so fast that within the spin-lattice relaxation time each molecule in the droplet takes part in this process. For this to take place, both the time required for a molecule to diffuse from the inside of the droplet to the surface Tog, and the time Tg for which the molecules remain anchored at the surface must be short compared to the spin-lattice relaxation time Ty. In the limit of very rapid cross-relaxation (k > (Tf(Tf )p) both phases relax with the same relaxation rate which is an weighted average... 

Overall molecular reorientations and internal motions take place in the 10 10 s time window and information about them can be accessed using relaxation rate measurements. By far the best approach is to use NMR experiments where deuterium Zeeman and quadrupolar spin-lattice relaxation times are measured on selectively deuteriated mesogens or on deuteriated probes dissolved in the mesophase. Frequency, orientation and temperature dependence of the spectral densities obtained in these relaxation studies give indications about the various motional modes and are extremely useful for testing orientational diffusion and chain dynamics models. Different deuterium relaxation experiments can be employed to extend the observable dynamic range the quadrupolar echo sequence gives spin-spin relaxation times sensitive to motions in the range s, while extremely slow motions... 

In principal, resolution of Individual carbon resonances in bulk polymers, allows relaxation experiments to be performed which can be Interpreted in terms of main chain and side chain motions in the solid. In addition to the spin-lattice relaxation time in the Zeeman field, the spin-spin relaxation time and nuclear Overhauser enhancement, other parameters providing data on polymer dynamics include the proton and carbon spin-lattice relaxation times in the rotating-frame, T p, the cross-relaxation time Tqr, and proton relaxation in the dipolar field. Schaefer and Stejskal have carried out pioneering work in exploring polymer dynamics using solid-state NMR techniques. Measurement of T values in glassy PMMA at ambient temperature reveals that the a-CH3 carbon relaxes in <0.1s, the ester methyJL and methylene carbons in ca. Is and the two non-protonated (carbonyl and quaternary) carbons in ca. 10s. These results are consistent with the onset of internal reorientation of a-CH3 at this temperature relatively... 

Boltzmann statistics, the difference in population of the Zeeman levels is therefore extremely small. The absorption of photons of energy h would rapidly equalize these populations (bringing the spin temperature to infinity) if no other process than Einstein s spontaneous emission would contribute to restore the equilibrium Boltzmann distribution. Indeed, the natural life time at these frequencies is of the order of 10 s, while in practice the equalization of the spin temperature with the lattice temperature requires time of the order of the second in liquids. The relaxation mechanisms which act in these circumstances are linked to the fluctuation of the magnetic field (or quadrupolar coupling) inside of the sample, more precisely to the Fourier component of this fluctuation at the NMR frequency. The relaxation so far described correspond to the recovery of the z component of the magnetisation which measures the actual difference of population of the Zeeman levels. Therefore it is called longitudinal or spin lattice relaxation time T. ... 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

For heteronuclear dipolar relaxation, the dipole-dipole coupling between two unlike spin- nuclei / and S (e.g., 13C-H pair) separated by an internuclear distance rIS is considered. The Zeeman spin-lattice (7jz) and spin-spin (T2) relaxation times for the / spin are given, respectively, by... 

One of the classical NMR methods used to determine molecular correlation times is provided by spin-lattice relaxation experiments. The spin-lattice relaxation rate 1 /T is determined by transitions among the Zeeman levels. For a liquid, the expression for the spin-lattice relaxation rate [81] is... 

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