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Relaxation Effects in Nuclear Magnetic Resonance Absorption

Relaxation Effects in Nuclear Magnetic Resonance Absorption,10.1103/PhysRev.73.679,Physical Review,Nicolaas Bloembergen,E. M. Purcell,R. V. Pound

Relaxation Effects in Nuclear Magnetic Resonance Absorption   (Citations: 504)
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The exchange of energy between a system of nuclear spins immersed in a strong magnetic field, and the heat reservoir consisting of the other degrees of freedom (the "lattice") of the substance containing the magnetic nuclei, serves to bring the spin system into equilibrium at a finite temperature. In this condition the system can absorb energy from an applied radiofrequency field. With the absorption of energy, however, the spin temperature tends to rise and the rate of absorption to decrease. Through this "saturation" effect, and in some cases by a more direct method, the spin-lattice relaxation time T1 can be measured. The interaction among the magnetic nuclei, with which a characteristic time T2' is associated, contributes to the width of the absorption line. Both interactions have been studied in a variety of substances, but with the emphasis on liquids containing hydrogen. Magnetic resonance absorption is observed by means of a radiofrequency bridge; the magnetic field at the sample is modulated at a low frequency. A detailed analysis of the method by which T1 is derived from saturation experiments is given. Relaxation times observed range from 10-4 to 102 seconds. In liquids T1 ordinarily decreases with increasing viscosity, in some cases reaching a minimum value after which it increases with further increase in viscosity. The line width meanwhile increases monotonically from an extremely small value toward a value determined by the spin-spin interaction in the rigid lattice. The effect of paramagnetic ions in solution upon the proton relaxation time and line width has been investigated. The relaxation time and line width in ice have been measured at various temperatures. The results can be explained by a theory which takes into account the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction. The local magnetic field produced at one nucleus by neighboring magnetic nuclei, or even by electronic magnetic moments of paramagnetic ions, is spread out into a spectrum extending to frequencies of the order of 1tauc, where tauc is a correlation time associated with the local Brownian motion and closely related to the characteristic time which occurs in Debye's theory of polar liquids. If the nuclear Larmor frequency omega is much less than 1tauc, the perturbations caused by the local field nearly average out, T1 is inversely proportional to tauc, and the width of the resonance line, in frequency, is about 1T1. A similar situation is found in hydrogen gas where tauc is the time between collisions. In very viscous liquids and in some solids where omegatauc>1, a quite different behavior is predicted, and observed. Values of tauc for ice, inferred from nuclear relaxation measurements, correlate well with dielectric dispersion data. Formulas useful in estimating the detectability of magnetic resonance absorption in various cases are derived in the appendix.
Journal: Physical Review - PHYS REV X , vol. 73, no. 7, pp. 679-712, 1948
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    • ...The relaxation rate contribution due to these reorientations is given by the well-known BPP expression 21, which depends on a correlation time τ R and a pre-factor A R...

    M. Rajeswariet al. Slow molecular processes in a nematic liquid crystal confined to rando...

    • ...Data are in qualitative agreement with literature (when available) taking into account that they are B0 dependent [7,8]...

    A. Galanteet al. Mobile NMR for surface analysis

    • ...According to the BPP (Bloembergen, Purcell, and Pound) theory, the relationship between T1 and τc is described as where γC is the magnetogyric ratio of 13C, γH is the magnetogyric ratio of 1H, ωC is the resonance frequency of 13C, ωH is the resonance frequency of 1H, r is the 1H-13C bond distance, τc is the correlation time of motion, and h is the Planck constant [15, 29, 30]...

    Ken-Ichiro Komiyaet al. Molecular Dynamics in Smectic and Crystalline Phases Studied by C-NMR ...

    • ...With allowance for Eq. (2), within the framework of the standard Bloembergen–Pursell–Pound (BPP) model [28], the graph of the dependence of on T –1 must be linear in the limits of both slow and fast motion, and its slope must be equal to –E a /k B and +Ea/kB , respectively...
    • ...where R1d(Ea) is the value of the dipole contribution obtained from the standard BPP formulas [28] and Eq. (2) at a fixed value of E a . For the parametrization of experimental data, we assume that both peaks in (3) are Gaussian functions...

    A. V. Solonininet al. Effect of mechanical milling on the mobility of hydrogen in the ZrTi 2...

    • ...The need to determine experimentally the relaxation times stems from the fact that no theory can satisfactorily predict, from a quantitative point of view, the values of tissues’ water proton relaxation times, despite the fact that, in pure liquids, successful relaxation theories were developed decades ago[8,9]...

    Yuhua Penget al. Noninvasive Temperature Measurement Using MRI Based on T2 Relaxation T...

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