Nuclear spins relaxation

Various relaxation mechanisms (DD, dipole-dipole SC, scalar SR, spin-rotation CSA, chemical shift anisotropy) contribute to Si nuclear spin relaxation, described by the time constants Ti for spin-lattice (longitudinal) and T2 for spin-spin (transversal) relaxation times (Eq. (1)). In the absence of scalar contributions it hold for liquids that T k, T2. 

In most organosilicon compounds, when studied at field strengths Ryg ll.TT, DD and SR interactions dominate the relaxation (Fig. 5). The CSA mechanism is 

As already mentioned, DD interactions influence the appearance of NMR spectra because of the negative NOE (see also Fig. 5 ), and in some cases, this may cancel the Si NMR signal (Eqs. (2) and (3)). Considering the opposite temperature dependence of DD and SR interactions, experimental conditions can be selected accordingly. 

Scalar relaxation due to chemical exchange has the usual influence (broadening) on the appearance of Si NMR spectra. A consequence of such exchange processes, depending on the rate of exchange, is that PT techniques may not work very well or sometimes not at all. Scalar relaxation of the second kind affects the line widths by j. sc(29si) jf silicon atom is bonded to one or more quadrupolar nuclei as in 

There are also examples of spin-1/2 nuclei with short-lived spin states, in particular in the cases of heavy nuclei such as. Pt or Hg, for which chemical-shift-anisotropy relaxation can become efficient at high field strengths Bq (Fig. 7). 

Spectra, recorded at high field strength Bo, indicates anisotropic surroundings of the tin nuclei. Such properties are, of course, readily verified by solid-state Sn NMR spectra confirming the information on the chemical shift anisotropy.  

In tin compounds, irrespective of the formal oxidation sate -1-2 or -f-4 of tin, the increase in the coordination number is accompanied by a marked increase in Sn nuclear shielding. Nowadays, a large number of examples have proven to be consistent with this observation. This also includes rather weak intra- or 

The values for stannocenes are found within a narrow range, apparently independent of the 

The negative A Sn values are typical, although their magnitude varies with the system under investigation. Very often intra-molecular association, adduct formation or inter-molecular aggregation (e.g. in 

The influence of various substituents on 5 Sn for series of tetra-coordinate tin(I V) compounds SnX4 n Yn (n = 0 ) can be graphically depicted as U-shaped curves. These substituent effects are not linear, but approximately pair-wise additive. Some representative Sn NMR data are given in Table 2.1.3 (tin hydrides). Table 2.1.4 (tetraorgano. tin). Table 2.1.5 (tin halides). Table 2.1.6 (tin chalcogenides), and Table 2.1.7 (compounds with Sn—N, Sn—P, Sn—As, Sn—Sb, and Sn—Bi bonds). 

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Nuclear spin relaxation is caused by fluctuating interactions involving nuclear spins. We write the corresponding Hamiltonians (which act as perturbations to the static or time-averaged Hamiltonian, detemiming the energy level structure) in tenns of a scalar contraction of spherical tensors ... 

Table Bl.13.2 Interactions giving rise to nuclear spin relaxation.

Woessner D E 1962 Nuclear spin relaxation in ellipsoids undergoing rotational Brownian motion J. Chem. Rhys. 37 647-54... 

Maler L, Widmalm G and Kowalewski J 1996 Dynamical behavior of carbohydrates as studied by carbon-13 and proton nuclear spin relaxation J. Phys. Chem. 100 17 103-10... 

Dayie K T, Wagner G and Lefeevre J F 1996 Theory and practice of nuclear spin relaxation in proteins Anna. Rev. Phys. Chem. 47 243-82... 

Kowalewski J 1990 Nuclear spin relaxation in diamagnetic fluids Part 1 Annu. Rep. NMR Spectrosc. 22 308-414 1991 Part 2 Annu. Rep. NMR Spectrosc. 23 289-374... 

Bloom M., Bridges F., Hardy W. N. Nuclear spin relaxation in gaseous methane and its deuterated modifications, Can. J. Phys. 45, 3533-54 (1967). 

Purcell E. M. Nuclear spin relaxation and nuclear electric dipole molecules. Phys. Rev. 117, 828-31, (1960). 

Gordon R. G. Kinetic theory of nuclear spin relaxation in gases, J. Chem. Phys. 44, 228-34 (1966). 

Courtney J. A., Armstrong R. L. A nuclear spin relaxation study of the spin-rotation interaction in spherical top molecules. Can. J. Phys. 50, 1252-61 (1972). 

Beckmann P. A., Burnell E. E. Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas, Can. J. Phys. 55, 1354-5 (1977). 

On the other hand, NMR spectra appear in general as the average of the spectra of the two spin states [36, 153]. This observation determines an upper limit for the spin-state lifetime shorter than the nuclear spin relaxation time Tl = l/ktH < lO s. In general, therefore, either the superposition or the average of the particular spectroscopic properties of the two spin states is observed, subject to the relative magnitude of lifetime of the excited spectroscopic state and the rate of spin-state conversion. The rate /clh is thus estimated... 

R. Y. Dong, M. Bloom 1970, (Determination of spin-rotation constants in flu-orinated methane molecules by means of nuclear spin relaxation measurements), Can. J. Phys. 48, 793. 

J. Kowalewski and L. Maler, Nuclear Spin Relaxation in Liquids Theory, Experiments and Applications. Taylor Francis, New York, 2006. 

The widths of the lines in Fig. 3.1 vary because the anisotropies of g and A (to be discussed in Chapter 4) are not completely averaged out when the molecule or ion tumbles in solution. This issue was implicit in the classic work of Bloembergen, Purcell and Pound2a on nuclear spin relaxation and was formulated in a useful way for EPR by Daniel Kivelson and co-workers.2b d As described in Chapter 2, they showed that the widths, in units of Hz, can often be written as a power series in mr with terms up to second-order (a third-order term is sometimes significant) ... 

Spiess HW (1978) Rotations of molecular and nuclear spin relaxation. Springer, Berlin... 

Wolf D (1979) Spin-temperature and nuclear-spin relaxation in matter basic principles and applications. Clarendon Press, Oxford... 

The use of magnetic resonance imaging (MRI) to study flow patterns in reactors as well as to perform spatially resolved spectroscopy is reviewed by Lynn Gladden, Michael Mantle, and Andrew Sederman (University of Cambridge). This method allows even unsteady-state processes to be studied because of the rapid data acquisition pulse sequence methods that can now be used. In addition, MRI can be used to study systems with short nuclear spin relaxation times—e.g., to study coke distribution in catalytic reactors. 

Further, neglecting the effect of nuclear spin relaxation, the acquired signal dS in an element of volume dr at position r with spin density p(r) is given by... 

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