Nuclear spin relaxation mechanisms

If intramolecular pathways dominate the nuclear spin relaxation mechanism, a separation between translational and rotational contributions is... 

The essential requirement for the effect to occur is a coupling of the nuclear spins with the electronic spins so that the predominant nuclear spin relaxation mechanism is via the electron spin system. In metals this coupling is via the hyperfine interaction. Another source of coupling is via the dipole-dipole interaction between nuclear and electronic spins. 

Chemical shift anisotropy (CSA)—the dependence of the chemical shift on the orientation of the nuclear spin with respect to the magnetic field a nuclear spin relaxation mechanism is important for C, N, and F. 

Experimental techniques for the measurement of Si nmr spectra (mainly for solutions) are briefly discussed, followed from considerations of the nuclear-spin relaxation mechanisms with emphasis on the Si nucleus. Chemical shifts 5 Si and indirect nuclear spin-spin coupling constants j( Si,x), the most prominent nmr parameters, are discussed in more detail The increasing reliability of quantum chemical methods for the calculation of these parameters is pointed out. The relationship between the electronic structure and the nmr parameters b Si and j( Si,x) is indicated... 

Fig. 5. 59.8 MHz Si NMR spectra of two hexasilane isomers. The broad hump is the signal for silicate in the glass and serves for correct phasing of the signals. There is competition between dipole-dipole and spin-rotation interactions as dominant nuclear spin relaxation mechanisms for Si nuclei. Si nuclei in SiHs groups at a more peripheric position of the molecule relax predominantly by spin-rotation interactions as a result of the high mobility of these groups. The SiH2 or SiH groups in the chains are less mobile and therefore, dipole-dipole interactions become competitive. Adapted from ref. 25.

In the solid state, Si nuclear spin relaxation mechanisms are much less efficient when compared with solutions. In inorganic solids, the presence of small amounts (traces) of paramagnetic impurities accelerates the relaxation rate, which otherwise... 

Nuclear spin relaxation is considered here using a semi-classical approach, i.e., the relaxing spin system is treated quantum mechanically, while the thermal bath or lattice is treated classically. Relaxation is a process by which a spin system is restored to its equilibrium state, and the return to equilibrium can be monitored by its relaxation rates, which determine how the NMR signals detected from the spin system evolve as a function of time. The Redfield relaxation theory36 based on a density matrix formalism can provide... 

The quantum alternative for the description of the vibrational degrees of freedom has been commented by Westlund et al. (85). The comments indicate that, to get a reasonable description of the field-dependent electron spin relaxation caused by the quantum vibrations, one needs to consider the first as well as the second order coupling between the spin and the vibrational modes in the ZFS interaction, and to take into account the lifetime of a vibrational state, Tw, as well as the time constant,T2V, associated with a width of vibrational transitions. A model of nuclear spin relaxation, including the electron spin subsystem coupled to a quantum vibrational bath, has been proposed (7d5). The contributions of the T2V and Tw vibrational relaxation (associated with the linear and the quadratic term in the Taylor expansion of the ZFS tensor, respectively) to the electron spin relaxation was considered. The description of the electron spin dynamics was included in the calculations of the PRE by the SBM approach, as well as in the framework of the general slow-motion theory, with appropriate modifications. The theoretical predictions were compared once again with the experimental PRE values for the Ni(H20)g complex in aqueous solution. This work can be treated as a quantum-mechanical counterpart of the classical approach presented in the paper by Kruk and Kowalewski (161). 

Structural information on hemoproteins can also be obtained from investigations of the enhancement of the nuclear spin relaxation in the bulk water. In this section a qualitative discussion is presented of relaxation mechanisms in solutions of diamagnetic and paramagnetic metallo-proteins, followed by a brief survey of experiments with hemoproteins. 

Figure 2 The four-level diagram for a system of two interacting spins, in this case an electron (S) and nucleus with a positive gyromagnetic ratio (/). The intrinsic electron and nuclear spin relaxation are given by p and w°, respectively, and the dipolar and/or scalar interactions between the electron and nuclear spin are represented by p, w0, w, and w2. The transition w0 is known as the zero-quantum transition, while w, is the singlequantum transition and w2 is the double-quantum transition. Nuclear and electronic relaxation through mechanisms other than scalar or dipolar coupling are denoted with w° — 1/Tio and p — 1/Tie, where Ti0 and T1e are the longitudinal relaxation times of the nucleus and electron in the absence of any coupling between them. Since much stronger relaxation mechanisms are available to the electron spin, the assumption p>p can be safely made. Adapted with permission from Ref. [24].

It is largely accepted that the dominant mechanism of nuclear spin relaxation in condensed polymers is due to dipolar interactions between the spins. The truncated homonuclear dipolar Hamiltonian has the form [15] ... 

A widespread view is that the feature comes from some crossover in the electronic density of states (DOS). The main result of the present paper is that after a proper re-arrangement of the experimental data no PG feature exists in the 63 Cu nuclear spin relaxation time behaviour. Instead, the data show two independent parallel relaxation mechanisms a temperature independent one that we attribute to stripes caused by the presence of external dopants and an "universal temperature dependent term which turns out to be exactly the same as in the stoichiometric compound YBCO 124. 

We have found that in a temperature interval above Tc and below some T 300 K the nuclear spin relaxation for a broad class of cuprates comes from two independent mechanisms relaxation on the stripe -like excitations that leads to a temperature independent contribution to 1 /63i and an universal temperature dependent term. For Lai.seSro.nCuC we obtained a correct quantitative estimate for the value of the first term. We concluded from eq.(l) and Fig.3 that "stripes always come about with external doping and may be pinned by structural defects. We argue that the whole pattern fits well the notion of the dynamical PS into coexisting metallic and IC magnetic phases. Experimentally, it seems that with the temperature decrease dynamical PS acquires the static character with the IC symmetry breaking for AF phase dictated by the competition between the lattice and the Coulomb forces. The form of coexistence of the IC magnetism with SC below Tc remains not understood as well as behaviour of stoichiometric cuprates. 

The studies of intermolecular quadnipolar relaxation with MD simulations (and Monte Carlo simulations) was initiated by Engstrom et al. [49] in the beginning of the eighties [50-54]. The problem then concerned the nuclear spin relaxation of ions in water. Very successful and well accepted theoretical models of the electrostatic mechanism had been developed, and with computer simulations it was possible to examine some of the assumptions of these models [37,38]. Furthermore, the performance of the electrostatic models could be compared to that of theoretical models of the collision induced mechanism [36,55]. 

Experimentally, the activation energy, Ea, of the nuclear spin relaxation has been studied systematically to evaluate different theoretical models [71]. Reproducing activation energies constitute a crucial test for MD simulations of the relaxation mechanism. It has been studied in MD simulations for both inert and ionic solutes [62,66]. For Ne, Kr, and Xe in acetonitrile [66], it was difficult to relate the Ea for the relaxation and those for individual molecular processes. This reflects the general problem of rationalizing Ea for collective processes. 

MD simulations of nuclear spin relaxation in liquids were initiated at a time when the development of theoretical models for many mechanisms was more or less stagnant. Since then simulations have been used in combination with both theory and experiment to develop new ideas, and MD simulations is becoming recognized as a vital tool for the understanding of the relaxation processes. 

The principal idea behind the MD simulations is to repeatedly calculate the Fq t) tensor, and its correlation function, as the simulation proceeds. The time scale of the source of the nuclear spin relaxation is suitable for MD simulations, but the different relaxation mechanisms are more or less easily implemented in the MD simulation techniques. The through-space dipole-dipole Fq t) tensor depends only on the positions of the nuclei, whereas other mechanisms require the calculation of electrostatic and electron information to derive the Fg t) tensor. Because of the complications in deriving the Fq t) tensor at each time step during the simulation, some of the studies are concerned only with the time-scale or only with the strength of the perturbing interaction. We also review those articles, since they have the same conceptual goal as those where the TCP of the Fq t) tensor actually is calculated. 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

Various relaxation mechanisms (DD = dipole-dipole SC = scalar SR = spin-rotation CSA = chemical shift anisotropy) have been shown to contribute to " Sn nuclear spin relaxation. In axially symmetrical organotin compounds, " Sn nuclear spin relaxation is governed mainly by the... 

Nuclear spin relaxation is not a spontaneous process, it requires stimulation by a suitable fluctuating field to Induce the necessary spin transitions and there are four principal mechanisms that ate able to do this, the dipole-dipole, chemical shift anisotropy, spin rotation and quadiupolat mechanisms. Which of these is the dominant process can directly influence the appearance of an NMR spectrum and it is these factors we consider here. The emphasis is not so much on the explicit details of the underiying mechanisms, which can be found in physical NMR texts [7], but on the manner m which the spectra are affected by these mechanisms and how, as a result, different experimental conditions influence the observed spectrum. 

Nuclei with spin I greater than 1/2 possess quadrupole moments (produced by asymmetries in the electronic environment) that interact with electric held gradients at the nucleus. Fluctuations in this interaction arising from translational or rotational diffusive motions in the liquid can provide an efficient mechanism of nuclear spin relaxation. Equation 1 governs this relaxation for 23Na (18,19). 

The most fascinating development in this field of CIDNP within the last years has been the observation, by Zysmilich and McDermott [146], of nuclear spin polarized (solid state) 15NNMR spectra from photosynthetic reaction centers in which the forward electron transfer from the primary charge-separated state to the accepting quinone was blocked. The all-emissive polarizations were proposed to be due to a radical pair mechanism, though many of the details are still not very clear. The reaction scheme is virtually identical to that of Chart VIII (Section V.A.2), the donor D being the special pair and the acceptor A the pheophytin. As in that example, the polarizations from the triplet exit channel are hidden in the triplet product 3D for the lifetime of the latter. This feature, in combination with the fact that nuclear spin relaxation in the molecular triplet localized on the special pair is relatively fast, serves to avoid the cancellation of CIDNP that would occur otherwise because the products from both exit channels are identical. 

A detailed study of I iSe and 3lp nuclear spin relaxation in tri(tertbutyI)phosphine selenide has been reported 6 and the kinetics and mechanism of formation of tetracoordinate P(V) sulphides from the reaction of tricoordinate phosphorus compounds with diaryl trisulphides have been investigated.1 ... 

Recalling the spin-sorting nature of the radical pair mechanism, we can anticipate that in the absence of nuclear spin relaxation, random recombination will eventually lead to exact cancellation of the + polarization when the + polarization in A is transferred to A (making the usual assumption that chemical reaction preserves nuclear spin orientation). In such a situation, polarization in A could only be observed in a time-resolved experiment before all the radicals had recombined. Relaxation of the nuclei A , however, allows some of the escape polarization to "leak away preventing complete cancellation (II). Thus, unless the radical lifetime is very much smaller than the nuclear... 

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