Spin-diffusion rate

From numerical calculations using these equations, it can be shown that when the spin-diffusion rate is at least 10 times faster than the values, the apparent relaxation decays for both MA and MB become practically identical and can be expressed by a single exponential with a common relaxation rate. In this fast spin-diffusion case, the apparent relaxation rate... 

When the spin-diffusion rate is comparable to the values, the relaxation decay curves become non-single exponential, and when the spin-diffusion rate is less than 10% of the values, the relaxation decay curve can be described by a single exponential with an intrinsic relaxation rate. 

Using the pulse sequences shown in Figure 4, the spin diffusion rate between two inorganic phases such as HAp/HDAp can be estimated. The results show that the 3 P spin diffusion rates of HAp/HDAP and ACP/ HDAp are approximately the same, whereas the rate of HAp / ACP is considerably smaller. In other words, ACP and HDAp are in close proximity,... 

Let us finally also mention here the results of proton nuclear relaxation time 7 measurements on TEA(TCNQ)2 [53,54], From the frequency dependence of 7, it is deduced that the spin motion is a nearly one-dimensional diffusion. Moreover, the temperature dependence of the on-chain spin diffusion rate shows a quite remarkable feature while it is thermally activated below 220 K, it suddenly becomes temperature independent above 220 K. 

With increasing zero-quantum line width the spin-diffusion rate constant increases and reaches a maximum when the width of the zero-quantum line is equal to the chemical-shift difference of the two S-spins. If the line width is increased even further, the spin-diffusion rate constant decreases slowly but continuously due to the decreased intensity of the zero-quantum line at frequency zero (see Fig. 4.3). 

Hz) about the magic angle and the mixing time is synchronized with the sample rotation. The rotation speed has to be slower than the fluctuations of the local fields but faster than the spin-diffusion rate constant. Under this condition one can rewrite Equation (4.11) and define an average rate constant... 

The most efficient way to speed up spin diffusion is the so-called r.f.-driven spin-diffusion experiment [15, 19] where the chemical-shift differences are removed by r.f. irradiation. For small chemical-shift differences, r.f.-driven spin diffusion can be implemented by applying a continuous-wave r.f. field to the S-spins which can theoretically be described by a transformation into a tilted rotating frame (see Appendix B). To zeroth-order average Hamiltonian theory the chemical-shift differences are removed (fl, — fty = 0 for all spins i and j) and the dipolar-coupling frequencies are scaled by a factor s = -1/2. The scaled-down (or ideally vanishing) chemical-shift difference allows one to keep the zero-quantum line narrow by decoupling the protons. This results in fast spin-diffusion rates. Furthermore, the rate constants are now determined by the S-spin coupling network, and the proton spins need not be considered for the data analysis. 

Fig. 4.4. Spectral factor/ fj(0) in the spin-diffusion rate constant calculated from the experimental separated-local-field spectrum of amorphous polystyrene [21, 30] for (a) a static sample, and (b) for a spectrum obtained under slow-MAS conditions. (Adapted from Ref. [21], with permission).

Proton and r.f.-driven spin diffusion are nonselective and ideally influence all carbon spin pairs in the same way. Rotor-driven spin diffusion, however, is highly selective and enhances the spin-diffusion rate constant only if the spinning speed is matched to the isotropic chemical-shift difference (Equation... 

This shows that the quasi-equilibrium spectra only provide information about the relative orientation of the sites of interest (i.e., the Euler angles (a, jS, yj)) and not about their distance (r,y) which is encoded in the spin-diffusion rate constant W,y. 

Note added in proof Very recently, the first direct determination of the spin-diffusion rate constant (Equation (4.2)) was performed (W. Zhang and D.G. Cory, Phys. Rev. Lett. 80 (1998) 1324). In a Cap2 single crystal values of D = 0.71 0.05 nm /ms and 0.53 0.03 nm /ms were found for two different orientations of the crystal. 

The spin-diffusion rate kc can be used to calculate the domain size by adopting a proper morphology [86, 97, 98]. For example, the domain size of PPO//-PS is calculated to be 5 nm by putting kc = 135 s and D = 5 x 10 m s into Equation (10.6). From the relaxation experiments, the value of kc can be obtained only when the characteristic nonsingle exponential decay curves are observed, that is, only when kc is comparable to the ATa and Kq values. Unfortunately, in most miscible blends, kc is so fast that the decay curves are identical or too slow to average the decays. 

The lai er fraction of the deuterium ( 21 at. %) exhibits a broad doublet line shapie (Section lb), and the values of T, for this line are considerably larger as shown at the top of Fig. 15. Leopold et al. (1982) speculate that the long r, occurs because the quadrupolar spUtting greatly reduces the deuterium spin diffusion rate, thus efifectively eliminating the paradeuterium molecules as relaxation centers. 

Other important examples of dynamic processes are polarization transfer rates such as cross-relaxation rate and spin diffusion rate which are discussed in the previous two subsections. 

The spectral spin diffusion rate caused by nuclear spin flip processes in the bulk nuclear spin system in the sample pentacene-h2di2 in p-terphenyl-dn is slower than in the case of a normal, protonated mixed crystal [251. Nevertheless all three possible configurations of the proton nuclei appear in the spectrum implying that the effective spin diffusion time is still much shorter than the time of 10 minutes needed to record the spectrum. 

Fig. 5.14 Room temperature spin-diffusion rates, as obtained from NMR (O, ) and from ESR ( ), and conductivity in polyaniline as a function of the protonation level. (From Ref. 12.) ad is the measured conductivity, and al has been calculated from Dl, using crl = ne DllkT, with rt. the carrier concentration, proportional to y.

Conductivities along (2 ), and perpendicular to (Jx) the stretching direction spin diffusion rate along (Z>n) and perpendicular to (Dx) the chains /c is the cutoff frequency of the spectrum motion. Source Ref. 103. 

Table 5.4 Spin Diffusion Rates and Microscopic Conductivities, cTj and for Four Polythiophene Family Compounds...

Because the spin diffusion rate strongly depends on the distance between nuclei, spin diffusion is confined to neighboring molecules. So if spin diffusion occurs between two species, they must be mixed intimately on the molecular level. Useful semiquantitative information about domain size can be obtained from the equation ... 

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