Spectral spin diffusion

The temperature dependence of the spectral spin diffusion and crossrelaxation was examined by Mueller et a/.287,288 with spin- and spin-1 systems. They showed that the diffusion rate can be strongly temperature dependent if it is motionally driven. It is therefore, unreliable to discriminate spin diffusion and chemical exchange by variable-temperature measurement of 2D exchange spectra. Mueller et al. suggested that the dependence of the polarization transfer rate on the spectral difference of the relevant resonances should be measured in a single crystal to safely distinguish the two different polarization transfer processes (see also ref. 289). They also explained satisfactorily why the relaxation of the quadrupolar order is much faster than the Zeeman order. This... 

Spectral spin diffusion in the solid state involves simultaneous flipflop transitions of dipolar-coupled spins with different resonance frequencies 11,39,63-76], whereas spatial spin diffusion transports spin polarization between spatially separated equivalent spins. In this review we deal only with the first case. The interaction of spins undergoing spin diffusion with the proton reservoir provides compensation for the energy imbalance (extraneous spins mechanism) [68,70,73,74]. Spin diffusion results in an exchange of magnetization between the nuclei responsible for resolved NMR signals, which can be conveniently detected by observing the relevant cross-peaks in the 2D spin-diffusion spectrum [63-65]. This technique, formally analogous to the NOESY experiment in liquids, is already well established for solids and can also be applied to the study of catalysts. 

Suter D, Ernst RR (1982) Spectral spin diffusion in the presence of an extraneous dipolar reservoir. Phys Rev B 25 6038-6041... 

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. 

The 2D spin diffusion NMR experiment allows us to examine further the spectral assigments obtained from the ID and the 2D J-resolved experiments [51]. It also provides new details concerning distribution of hydrocarbons in zeolite ZSM-5. Spectral spin diffusion in the solid state involves simultaneous flip-flop transitions of dipolar-... 

The temperature dependence of the spectral spin diffusion and cross-relaxation was examined by Mueller et with spin- and spin-1 systems. 

For the dilute aH spins surrounded by a large number of the 2H spins, the heteronuclear aH-H dipolar interaction is dominant, lifting the spectral overlap between the 1H packets. H spin diffusion is driven by the flip-flop term of the 1H-1H dipolar interaction, which becomes secular in the presence of spectral overlap. Thus, spin diffusion would be accelerated if it had not been for the 1H-2H dipolar interaction. In order to confirm this prediction, they used another RF channel of the OPENCORE... 

In addition to measuring TCH for the polymorphic system in question, the proton T value must be determined since the repetition rate of a CP experiment is dependent upon the recovery of the proton magnetization. Common convention states that a delay time between successive pulses of 1-5 X T, must be used. Figure 10B outlines the pulse sequence for measuring the proton Tx through the carbon intensity. One advantage to solids NMR work is that a common proton Tx value will be measured, since protons communicate through a spin-diffusion process. An example of spectral results obtained from this pulse sequence is displayed in Fig. 12. 

For quantitative interpretation of cross-relaxation spectra in the spin-diffusion regimes it is necessary to take spin diffusion into account. From the mathematical point of view, this means that the Taylor series in eq. (36) must be used without truncation. In other words, the basic formula, eq. (8), must be used and the full spectral matrix must be analyzed. 

In practice, the full matrix analysis is rarely applicable because of spectral overlap and because of the global error propagation. In full matrix analysis all the elements are interconnected and the error in one volume element propagates into all cross-relaxation rates. This property is not favorable in practical situations in which a part of the spectrum may be ill-defined although a good portion of the spectrum is of a satisfactory quality. Then, the more favorable analysis is localized, i.e., errors are confined within respective cross-relaxation rates. However, such analysis is possible only on data in which spin diffusion is not dominant. 

Further possibilities are offered by various two-dimensional NMR methods. For example, heteronuclear solid-state correlation spectroscopy (27) is capable of correlating the spectra of abundant and dilute spins in solids, simplifying spectral assignment and permitting determination of shielding tensors. Futhermore, spin diffusion among abundant spins can be directly observed by this method. 

Saturation transfer difference. The origins of the STD experiment1721 can be traced to the spin-saturation transfer experiment or Forsen-Hoffman experiment from the 1960s.1911 In the STD experiment, a subset of the protein II resonances are saturated by means of a train of frequency-selective radiofrequency pulses applied to a narrow spectral region devoid of ligand resonances. The saturation is transferred by spin diffusion ( H- H crossrelaxation pathways) to the rest of the protein, a process that becomes more efficient with... 

It has been known for a long time that the kind of simplistic distance calibration suggested by Eq. [8] may be subject to systematic errors. First, the intensity of an NOE depends on the spectral density function for the reorientation of the vector between relaxing nuclei. This means that Eq. [8] is valid only if the reference distance and unknown distance are undergoing the same motions. As this is not likely to be the case, distance calibrations have attempted to allow for the possibility of systematic errors.23 Equation [8] also assumes that the dipolar relaxation can be considered in terms of isolated spins relaxing each other. In the presence of spin diffusion, this will lead to a systematic underestimation of distances.41 57 58... 

Fig. 10.3.7 Pulse sequence for spin-diffusion imaging with ID spatial resolution [Wei8] and effect of mobility filters, (a) The magnetization source is selected by the dipolar filter which suppresses the magnetization in the sink. During the spin-diffiision time the magnetization dif ses from the source to the sink, (b) The dipolar filter selects magnetization from chain segments which are highly mobile and intermediately mobile. By use of a lineshape filter the signal loss is analysed only for the mobile components. IP(Tc) is the probability for a particular correlation time to arise in the sample. It is essentially the spectral density of motion.

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).

For such an experiment to work, we have to be able to distinguish the different domains during the evolution and the detection period of the two-dimensional experiment. Since proton spectral resolution in typical solids is very poor, we have to use homonuclear dipolar-decoupling methods to narrow the lines sufficiently to obtain spectral resolution. The 2D spin-diffusion CRAMPS spectrum was first recorded by Caravatti et al. [68] for blends of polystyrene (PS) and polyvinyl methyl-ether (PVME). There are other methods to generate an initial nonequilibrium polarization based on differences in linewidth or relaxation times. The reader is referred to the excellent book of Schmidt-Rohr and Spiess [67] for an overview. 

Fig. 6.4.10, [44]). Additional dimensions including chemical shift and spin diffusion have also been demonstrated. This latter use of spin diffusion will lead to site specific assignments while the improved resolution will lead to the essential spectral resolution for resolving the signals from uniformly labeled samples. 

The latter can be of either spectral or spatial type, the former relying on overlap of the relevant bands in the spectrum. In this context, it becomes important to ensure the highest resolution situation in the F spectrum during the time allowed for spin diffusion. This, in turn, suggests that proton decoupling should be employed during that time. The WISE (two-dimen-... 

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