Paramagnetic spin relaxation

In solutions of metal salts in non-aqueous solvents (particularly in systems with low permittivities), it is frequently necessary to take into account the formation of polynuclear species. Differentiation of the monomeric and homopolynuclear formations in solution is a difficult task in most cases. This is well reflected by investigations of various non-aqueous solutions of iron(III) chloride, for instance, which led to contradictory results in the above respect (c/., e.g., [We 62, Fa 68, Ca 62, Gu 70, Ar 65]). Study of the paramagnetic spin relaxation by Mossbauer spectroscopy is an excellent means for the differentiation of monomeric and polynuclear high-spin iron(III) species [Ve 78]. 

Phonon mode changes, determination of Debye temperature, determination of effective mass, determination of anisotropy of lattice vibration, electron hopping in spinels, diffusion, determination of jump frequency and diffusion coefficient, paramagnetic spin relaxation, spin-spin relaxation, spin-lattice relaxation, superparamagnetism, determination of grain size... 

Fig. 8.18 TR MFE curves obtained using 4 pairs of S+ / e , with cations distributed inside a sphere of radius of 50 A. [D] = 0.02 M. Blue triangle, circular symbol and solid line represents the TR MFE curves calculated in this work, by Borovkov and experiment respectively. Second curve with a lower magnetic field effect corresponds to pi] = 1 mM. a Spin relaxation treated phenomenologically at high field without allowance for reactions (15), (16) tmd (17). b No paramagnetic spin relaxation was assumed at high field but included reactions (15), (16) and (17)...

S spin remains in tliennal equilibrium on die time scale of the /-spin relaxation. This situation occurs in paramagnetic systems, where S is an electron spin. The spin-lattice relaxation rate for the / spin is then given by ... 

Here Ti is the spin-lattice relaxation time due to the paramagnetic ion d is the ion-nucleus distance Z) is a constant related to the magnetic moments, i is the Larmor frequency of the observed nucleus and sis the Larmor frequency of the paramagnetic elechon and s its spin relaxation time. Paramagnetic relaxation techniques have been employed in investigations of the hydrocarbon chain... 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

In paramagnetic materials, the relaxation frequency is in general determined by contributions from both spin-lattice relaxation and spin-spin relaxation. Spin-lattice relaxation processes can conveniently be studied in samples with low concentrations of paramagnetic ions because this results in slow spin-spin relaxation. Spin-spin relaxation processes can be investigated at low temperatures where the spin-lattice relaxation is negligible. Paramagnetic relaxation processes have... 

Spin-spin relaxation is primarily induced by magnetic dipole interactions between paramagnetic ions. Usually, the most important spin-spin relaxation process is the so-called cross-relaxation process in which a transition of an ion / from the state K) to toe state is accompanied by a transition of another ion j from the... 

Low temperatures are required to slow down paramagnetic relaxation in order to get sharp EPR spectra. However, when a paramagnet can relax back to the ground state only slowly, then it is easy to saturate the system with microwaves, and this will lead to deformed spectra. In this chapter we consider the two key experimental parameters power (intensity of the microwaves) and temperature (of the sample) in combination with the key system parameter the spin. For a given system of spin S at a temperature T there is a single optimal value of P, which must be determined experimentally. The combined set of P, T, and S determines the complexity and the costs of EPR spectroscopy. 

Specific Molecular Interactions (Jardetzky) Nuclear Paramagnetic (Spin-Spin) Relaxation in Solids 7 499... 

The MSB-equations were first presented by Connick and Mat (23) and by Reuben et al. (24). A formal derivation of these equations can be found, in a somewhat sketchy form, in the article by Gueron (25) and in a more stringent version in an article by Benetis et al. (26). Since oos 658m/ if / is a proton, and even more if it represents another nuclear spin, the first and third term of the DD part of Eq. (12) can safely be combined into a seven term , dispersing at msXc2 = 1 while the three term disperses at m/Td = 1. Similar equations can also be derived for the nuclear spin-spin relaxation rate in a paramagnetic complex ... 

The symbol xso denotes the electron spin relaxation time at zero magnetic field, where Ti = and is another correlation time, associated with distortions of the paramagnetic complex caused by molecular collisions. 

Fig. 3. Variation of the completely reduced dipole-dipole spectral density (see text) for the model of a low-symmetry complex for S = 3/2. Reprinted from J. Magn. Reson., vol. 59,Westlund, RO. Wennerstrom, H. Nordenskiold, L. Kowalewski, J. Benetis, N., Nuclear Spin-Lattice and Spin-Spin Relaxation in Paramagnetic Systems in the Slow-Motion Regime for Electron Spin. III. Dipole-Dipole and Scalar Spin-Spin Interaction for S = 3/2 and 5/2 , pp. 91-109, Copyright 1984, with permission from Elsevier.

Fig. 7. NMRD profiles calculated for slightly asymmetric, weakly deformable complexes with different electron spin quantum numbers (a) cylindrically-symmetric ZFS, E = 0 (b) maximum rhombicity E = DjS. Reprinted from J. Magn. Reson. vol. 146, Nilsson, T. Kowalewski, J., Slow-motion theory of nuclear spin relaxation in paramagnetic low-symmetry complexes A generalization to high electron spin , pp. 345-358, Copyright 2000, with permission from Elsevier.

Fig. 12. Experimental and calculated NMRD profiles for GdEDTA in aqueous solution in the presence (upper curve) and absence (lower curve) of bovine serum albumin. Reprinted from J. Magn. Reson. vol. 162, Kruk, D. Kowalewski, J., Nuclear Spin Relaxation in Paramagnetic Systems (S > 1) under Fast Rotation Conditions , pp. 229-240, Copyright 2003, with permission from Elsevier.

Theoretical models for outer-sphere nuclear spin relaxation in paramagnetic systems, including an improved description of the electron spin relaxation, have been developed intensively for the last couple of years. They can be treated as counterparts of the models of inner-sphere PRE, described in the Section V.B and V.C. 

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