Relaxation: nuclear spin-lattice

Ishol L. M., Scott T. A., Goldblatt M. Nuclear spin-lattice relaxation in solid and liquid 15N2 and 14N2, J. Magn. Res. 23, 313-20 (1976). 

A more general theory for outer-sphere paramagnetic relaxation enhancement, valid for an arbitrary relation between the Zeeman coupling and the axial static ZFS, has been developed by Kruk and co-workers (96 in the same paper which dealt with the inner-sphere case. The static ZFS was included, along with the Zeeman interaction in the unperturbed Hamiltonian. The general expression for the nuclear spin-lattice relaxation rate of the outer-sphere nuclei was written in terms of electron spin spectral densities, as ... 

The second role of the chemical exchange phenomena can be seen in Eq. (2) the exchange lifetime competes with the in-complex nuclear spin-lattice relaxation time and can become a limiting factor in the attainable PRE. This aspect of the problem is highly relevant in practical consideration in the case of Gd(III) complexes as a potential contrast agent, because the water exchange in these systems is not too fast. This issue is considered to be outside of the scope of this article and we refer to recent literature on the subject 5,160) and to other contributions in this volume. 

Fig. 7. H water proton relaxivity i.e., the nuclear spin-lattice relaxation rate per mM of metal, plotted as a function of the magnetic field strength expressed as the proton Larmor frequency for aqueous solutions of manganese(H) and iron(HI) ions at 298 K. (A) 0.10 mM manganese(II) chloride in 2.80 M perchloric acid (B) 0.1 mM aqueous manganese(H) chloride at pH 6.6 (C) 0.5 mM iron(HI) perchlorate in 2.80 M perchloric acid (D) 0.5 mM iron(IH) perchlorate in water at pH 3.1 (F) 2.0 mM Fe(HI) in 2.0 M ammonium fluoride at pH 7, which causes a distribution of species dominated by [FeFe]"-.

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

T, Tlo nuclear spin lattice relaxation time in the rotating frame. 

Other evidence for the existence in water of solid-like structures comes from NMR studies. Twari and Verma (146) studied the diffusive motion in water by a nuclear spin lattice relaxation technique. They conclude that solid-like vibrations exist in water at low temperature but that these decrease rapidly as the temperature increases from 0° to 40°C., at which temperature these solid-like motions appear to level off and... 

In practice nuclear spin-lattice relaxation is always within the Redfield limit, i.e. the interaction energy with the lattice is always much smaller than rc-1. This is true even with paramagnetic systems, where the nuclear spin-lattice interaction eneigy is often much larger than usual. On the other hand, it is not obvious that electrons are always in the Redfield limit. When electrons are outside the Redfield limit, although nuclear relaxation is in the Redfield limit, it is not easy... 

In this mechanistic scheme, the CIDNP intensities of reactant and product are determined by the competition of key steps at each stage of the reaction. For the system discussed here, the qualitative features of the observed polarization suggest that nuclear spin lattice relaxation during the lifetime of the olefin triplet state is negligible, that singlet and triplet pairs recombine with similar efficiencies, and that the triplet state decays to each of the isomers with equal efficiency. 

Fatkullin NF, Kimmich R, Kroutieva M (2000) The twice-renormalised Rouse formalism of polymer dynamics Segment diffusion, terminal relaxation, and nuclear spin-lattice relaxation. J Exp Theor Phys 91(1) 150-166 Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, London Ferry JD (1990) Some reflections on the early development of polymer dynamics Viscoelasticity, dielectric dispersion, and self-diffusion. Macromolecules 24 5237-5245 Ferry JD, Landel RF, Williams ML (1955) Extensions of the Rouse theory of viscoelastic properties to undilute linear polymers. J Appl Phys 26 359-362 Fikhman VD, Radushkevich BV, Vinogradov GV (1970) Reological properties of polymers under extension at constant deformation rate and at constant extension rate. In Vinogradov GV (ed) Uspekhi reologii polimerov (Advances in polymer rheology, in Russian). Khimija, Moscow, pp 9-23... 

Abstract Spatially-resolved NMR is used to probe antiferromagnetism in the vortex state of nearly optimally doped high-rc cuprate H2Ba2CuC>6+a (Tc = 85 K). The broadened 205Tl-spectra below 20 K and the temperature dependence of the enhanced nuclear spin-lattice relaxation rate 205 Tfl at the vortex core region indicate clear evidences of the antiferromagnetic order inside the vortex core ofTl2Ba2Cu06+J. 

Here Tq g and Tq q are the nuclear spin lattice relaxation times of the scavenged and in-cage products, respectively is the nuclear relaxation time in the escaped radical and ks is the rate constant of the formation of the scavenged products. Thus, unless ks is greater than or comparable to [T ] l, CIDNP of the scavenged products would not be observed. 

Fig, 10 Temperature dependence of the nuclear spin lattice relaxation times of benzoic acid [16] crystals. Upper set, QH5COOH lower set, QDsCOOH. The solid lines are obtained from the theoretical calculation taking into account phonon-assisted... 

The first ist the strong dependence of observed CIDNP intensities on the nuclear spin lattice relaxation times Ti of the products. As is seen from Eqs. 

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... 

Fatkullin, N., and Kimmich, R. (1994). Nuclear spin-lattice relaxation dispersion and segmental diffusion in entagled polymers. Renormalized Rouse formalism. J. Chem. Phys. 101, 822-832. 

In metals, the orbital interaction also gives rise to nuclear spin lattice relaxation. Because of energy conservation, only electron energy levels... 

Figure 13 Field dependence of the Se nuclear spin-lattice relaxation rate in...

Nuclear spin-lattice relaxation conducting regime. As for the spin sector in the conducting regime, an approach to the 1-D exponent can be attempted looking at the spin-lattice relaxation rate for which the 2k° contribution should become predominant at low temperature where 0deviation from linearity below 150 K or so (Fig. 11), signaling the onset of 2k fluctuations. These AF fluctuations become even more visible when T, is plotted... 

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