Spin-diffusion lattice relaxation

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

Maryott A. A., Farrar T. C., Malmberg M. S. 35C1 and 19F NMR spin-lattice relaxation time measurements and rotational diffusion in liquid CIO3F. J. Chem. Phys. 54, 64-71 (1971). 

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

Zi(Air, x) and 7)(N2, x) are spin-lattice relaxation times of nitroxides in samples equilibrated with atmospheric air and nitrogen, respectively. Note that W(x) is normalized to the sample equilibrated with the atmospheric air. W(x) is proportional to the product of the local translational diffusion coefficient D(x) and the local concentration C(x) of oxygen at a depth x in the membrane, which is in equilibrium with the atmospheric air ... 

It is found that the relaxation parameter T p as a function of temperature does not follow an increase with chain length, as the square of the number of methylene carbons. Nor is it linear with N, the number of methylene carbons, which should be true if relaxation to the lattice were rate controlling. Rather, it shows a temperature-induced increase of the minimum value of Tjp with about the 1.6 of N. So, both spin diffusion and spin lattice coupling are reflected. For a spin diffusion coefficient D of approximately 2 x 10 12 cm.2/sec., the mean square distance for diffusion of spin energy in a time t is the ft1 = 200/T A, or about 15A on a Tjp time scale. 

Another limiting situation arises when the paramagnetic species interact only weakly with the molecules carrying the nuclear spins. In such a case, it is not meaningful to speak about exchange between discrete sites, but rather about free diffusion or diffusion in a potential. One then speaks about outer-sphere PRE, still referring to the enhancement of the spin-lattice relaxation rate. The outer-sphere PRE is also proportional to the concentration of... 

Fig. 3. Schematic representation of the topological space of hydration water in silica fine-particle cluster (45). The processes responsible for the water spin-lattice relaxation behavior are restricted rotational diffusion about an axis normal to the local surface (y process), reorientations mediated by translational displacements on the length scale of a monomer (P process), reorientations mediated by translational displacements in the length scale of the clusters (a process), and exchange with free water as a cutoff limit.

Fig. 8. The water-proton spin-lattice relaxation rates vs. magnetic field strength plotted as the Larmor frequency at 282 K for hexacyanochromate(II) ion ( ), trioxalatochromate(III) ion ( ), and trimalonatochromate(III) ion (A). The lines were computed using translational diffusion models developed by Freed with and without the inclusion of electron spin relaxation effects 54,121).

Reif 97) has observed the effects of point defects on nuclear resonance lines of Br , Br, Na , and Li in cubic crystals. The effect of temperature on the line widths and spin-lattice relaxation times was investigated for various impurity levels in AgBr and found to be quite pronounced due to vacancy association and diffusion. 

Spin-lattice relaxation of C nuclei is, in principle, very attractive for it is determined by local fluctuations at to c or cuof (rotating or lab frame respectively) spin diffusion among nuclei does not average relaxation rates among chemically distinct carbons. In solids one must append a cautionary note. 

Fig. 14. A scheme of the spin-lattice relaxation process together with spin diffusion. A and are two kind of spins in the component polymers A and B. Its assumed that 7) of A is much shorter than that of B.

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

Figure 2. Fluorine NMR relaxation times for a sample of Linde molecular sieve 13X containing about 6.6 molecules of SFg per cage O, spin lattice relaxation time , spin-spin relaxation time T2 characterized by exponential decay V and A, T2 characterizedby two relaxation times ticked O, decay as r2. Solid lines are theory to the left of 10Z/T = 6 based on molecular diffusion to the right of 10Z/T controlled by Tu. For dashed lines see text (20)...

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

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