Motional spin-diffusion

In the field of solid polymers, reviews by Schaefer and Stejskal and Lyerla of recently developed techniques for obtaining high-resolution spectra of solids are particularly welcome. High-resolution techniques are included in a wide-ranging article that also covers the use of more traditional broadline n.m.r. in studying molecular motion, spin-diffusion, self-diffusion, and phase structure in both synthetic and biological polymers. Useful specialized reviews have been published on phase structure in polyethylene, elastomers, interfacial effects, and radiation effects. ... 

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

In addition to giving conformational information, solid state NMR relaxation experiments can be used to probe the thermal motion of polymers in the hydrated cell wall (5). The motion of the polymers can give us clues as to the environment of the polymer. When there are both rigid and mobile polymers within a composite material, NMR spin-diffusion experiments can be used to find out how far apart they are. 

In all the approaches mentioned below, it is assumed that the correlation function can be factorized into a product of correlation functions for the three degrees of freedom rotational motion, translational diffusion and electron spin dynamics. 

Therefore, for a complete characterization of the cross-relaxation network, it is best to do all three experiments and to extract from each of them information that can be interpreted unambiguously. If the number of possible experiments is limited, then in the extreme-narrowing and the spin-diffusion regime it is best to record NOESY and in the intermediate motional regime ROESY or T-ROESY spectra. 

In the spin diffusion motional regime (small molecules at low temperatures or macromolecules at all temperatures) the cross-relaxation is so efficient that it can hardly be limited to a single-step magnetization transfer. The multistep magnetization transfer is known as spin diffusion. It manifests differently in NOESY and ROESY spectra, as can be illustrated by writing eq. (29b) explicitly for the process of cross relaxation ... 

Aside from the question of the precise model by which relaxation times are interpreted there is the more practical problem of isolating that part of the relaxation specifically caused by diffusion. The contributions of exchange processes (see below), spin-rotation interaction (9), and spin diffusion (9) can be identified by temperature dependences different from that which is solely the result of the motionally modulated nuclear dipolar interaction as sketched above, and corrections can be made. The molecular rotation contributions to dipolar relaxation can be removed or corrected for by (a) isotopic substitution methods (19), (b) the fact that rotation is in some cases much faster than diffusion, and its relaxation effects are shifted to much lower temperatures (7, 20), and (c) doping with paramagnetic impurities as outlined above. The last method has been used in almost all cases reported thus far, more by default than by design, because commercial zeolites are thus doped by their method of preparation this... 

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). 

In aqueous food materials Tj and T2 relaxation behavior of water are related to different aspects of the interaction and motion of the water molecules. The relationship is not so simple, especially in heterogeneous food materials [63-65]. There are at least four types of protons to be considered, namely free (or bulk) water, bound (or hydrated) water, exchangeable macro-moleculc protons such as those found in hydroxyl and amino groups, and unexchangeable macromolecule protons. Under such circumstances measurement of Ti is more reliable than T2 measurement, but can be complicated by the spin diffusion, while T2 relaxation can be complicated by slow translational diffusion and proton exchanges. 

It is this spin diffusion phenomenon that is used to provide an estimate of spatial dimensions in motionally inhomogeneous systems. The idea simply being that observation of the time required for equilibration of two regions in a spin system gives a measure of the dimension involved in the transport process, when the diffusion coefficient is known. 

Poly(Propylene). In principle, resolution of individual carbon resonances in bulk polymers allows relaxation experiments to be performed which can be interpreted in terms of mainchain and side chain motions in the solid. This is a distinct advantage over the more common proton NMR relaxation experiments where efficient spin-diffusion usually results in the averaging of the relaxation behavior over the ensemble of protons. Thus, a direct... 

Fig. 25. Schematic pulse sequence for the reduced four-dimensional experiment to probe the spatial heterogeneity of molecular motions.54" 5 As for the experiment in Fig. 24, part A of the sequence selects out only signal from any slow components in the system. This experiment differs from that in Fig. 24 only in that the central mixing time, rmb, provided to allow the motional timescale to change if it can, now allows H- H spin diffusion instead, so that the size of the region with slow molecular motions may be estimated. The two other mixing times rma and rmc are equal.

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... 

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... 

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. 

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