Paramagnetic relaxation processes

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 

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The presence of low-lying excited levels can greatly increase the efficiency of the relaxation processes, especially in the case of paramagnetic centers with half-integer spins. 

For a reUable extraction of distances, it is important that dipolar relaxation is strongly dominating other relaxation processes. Hence, it is important to avoid paramagnetic ions or molecules such as transition metals or (paramagnetic) oxygen. Especially solution of small molecules therefore have to be carefully degased. 

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... 

Although relaxation measurements have been widely used in nuclear magnetic resonance studies of solid catalysts and adsorbed molecules, they have not found such favor in similar ESR work. Relaxation phenomena, however, do play a very important role in any magnetic resonance experiment, whether or not this aspect of the problem is studied. In fact, the temperature at which most ESR experiments are conducted is dictated by the relaxation process. Furthermore, even qualitative data on relaxation times can be used as supporting evidence in the identification of a paramagnetic species. 

In this article, we study some aspects of irreversible processes in spins systems. We essentially treat nuclear paramagnetic relaxation the case of ferromagnetism is not discussed. 

The most important relaxation processes in NMR involve interactions with other nuclear spins that are in the state of random thermal motion. This is called spin-lattice relaxation and results in a simple exponential recovery process after the spins are disturbed in an NMR experiment. The exponential recovery is characterised by a time constant Tj that can be measured for different types of nuclei. For organic liquids and samples in solution, Tj is typically of the order of several seconds. In the presence of paramagnetic impurities or in very viscous solvents, relaxation of the spins can be very efficient and NMR spectra obtained become broad. 

As the temperature is further lowered, the natural processes that maintain the Boltzmann distribution (relaxation processes) may be no longer able to keep up with the rate of transitions induced by the microwave radiation. Power saturation leads to a decrease in signal at low temperatures and high levels of microwave power. Because the rate and temperature dependence of relaxation processes is very different in different systems, different paramagnetic species saturate at different levels of power and are best observed at different temperatures. Organic radicals are best observed at relatively high temperature and low levels of power transition metals, especially in systems in which S > 7, are usually observed at cryogenic temperatures because of their rapid relaxation rates. 

Tfi is an important quantity used to describe the relaxation processes in broad line paramagnetic spectroscopy (BNMR). The fluctuation time is commonly referred to as correlation time in the NMR literature. 

R[m (Eq. (7.10)). This can be intuitively understood because cross relaxation in a non-selective experiment contributes less to signal recovery, especially at the beginning of the experiment, and the latter is dominated by paramagnetic effects (RjM). In any case, when pi in paramagnetic systems is very large (e.g. 100-1000 s ), it means that R[m dominates the relaxation processes and the results of selective and non-selective experiments are close to one another. 

In Eqs. (7-11), fi is the nuclear gyromagnetic ratio, g is the electron g factor, fiB is the Bohr magneton, rGdH is the electron spin - proton distance, co, and cos are the nuclear and electron Larmor frequencies, respectively (co=yB, where B is the magnetic field), and A/fl is the hyperfine or scalar coupling constant between the electron of the paramagnetic center and the proton of the coordinated water. The correlation times that are characteristic of the relaxation processes are depicted as ... 

The restoration process of the spin magnetization toward the thermal equilibrium is called paramagnetic relaxation. It can be divided into two categories longitudinal relaxation and transverse relaxation. The z-component of the total magnetization is restored by the former relaxation, while the coherence in precessing on the xy-plane is destroyed by the latter relaxation. 

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