R.f.-driven spin diffusion

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. 4.5. Ratio of cross-peak to CH diagonal-peak intensity for r.f.-driven spin diffusion beween the CH and CH2 resonances of adamantane (powder sample) as a function of the offset of the r.f.-carrier frequency from the center of the two resonance lines. The circles represent experimental values obtained with a 30 ms cw spin-lock. The squares represent experimental values obtained with a 30 ms WALTZ-17 spin lock using a spin-lock pulse of...

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... 

In proton-driven spin diffusion, the diffusion constant depends much more on the S-spin density than in r.f.-driven spin diffusion. 

R.f.-driven spin diffusion in low-y spin systems shows exactly the same characteristic as spin diffusion in high-y spin systems. It is seldom, however, applied for spin diffusion over longer distances, because r.f. irradiation has to be applied during the entire spin-diffusion period which may be technically difficult. 

Fig. 4.12. (a) 2D quasi-equilibrium proton-driven spin-diffusion spectrum at 295 K of amorphous, atactic polystyrene C-enriched at the aromatic carbon Ci. The mixing time was set to 10 s. Within this time frame, a completely disordered environment is sampled (see Fig. 4.8(c)). (b) Rate-constants for r.f.-driven spin-diffusion obtained from mixing times smaller than 4 ms from the same compound, (c) Structure of a microstructure, constructed by Rapold et al. [71] to describe amorphous atactic polystyrene. The rate constants in (b) can be well explained by a set of such microstructures. From the microstructures, in turn, the weighted distributions p( 8)/sin /3 can be extracted. The result is given in (d). (Figure adapted from Refs. [30, 70]). 

Fig. 4.7. R.f.-driven ZAS experiment schematic diagram and application to a homogeneous and heterogeneous mixture of adamantane (a) and hexamethyethane (h) [76]. The appearance of cross-peaks, due to intermolecular spin diffusion between the two components, is seen clearly in the homogeneously mixed sample, while it is absent in the heterogeneous mixture, (Figure adapted from Ref. [33]).

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