Spatial spin diffusion

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. 

Fig. 4.5.5 Pulsed field gradient sequences to obtain velocity and diffusion data (a) spin-echo (PGSE) and (b) stimulated-echo (PGSTE). The application of imaging gradients C Gy and Gz allows the measurement of velcocity maps and spatially-resolved diffusion coefficients and size distribution in emulsions.

To continue the investigation, carbon detected proton T relaxation data were also collected and were used to calculate proton T relaxation times. Similarly, 19F T measurements were also made. The calculated relaxation values are shown above each peak of interest in Fig. 10.25. A substantial difference is evident in the proton T relaxation times across the API peaks in both carbon spectra. Due to spin diffusion, the protons can exchange their signals with each other even when separated by as much as tens of nanometers. Since a potential API-excipient interaction would act on the molecular scale, spin diffusion occurs between the API and excipient molecules, and the protons therefore show a single, uniform relaxation time regardless of whether they are on the API or the excipients. On the other hand, in the case of a physical mixture, the molecules of API and excipients are well separated spatially, and so no bulk spin diffusion can occur. Two unique proton relaxation rates are then expected, one for the API and another for the excipients. This is evident in the carbon spectrum of the physical mixture shown on the bottom of Fig. 10.25. Comparing this reference to the relaxation data for the formulation, it is readily apparent that the formulation exhibits essentially one proton T1 relaxation time across the carbon spectrum. This therefore demonstrates that there is indeed an interaction between the drug substance and the excipients in the formulation. 

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. 

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.

A 2D CPMAS exchange experiment in which through-space (site) correlation is established via proton spin diffusion was proposed by Wilhelm et al.292 for probing the isotropic chemical shift correlations. This technique has a number of advantages, including site selectivity, multiple correlations and broad spatial correlation range (1-200 nm). It was shown that this technique... 

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.

The term spin diffusion has been coined by Bloembergen [1] to characterize the polarization-exchange process in a strongly dipolar-coupled many-spin system. As pointed out by Bloembergen, this process leads to a spatial spread of polarization originating on a given spin that mimics, under certain conditions, a diffusion process. In a true diffusion process, the entropy increases monotonically. In the exact quantum description of the spin-diffusion process, however, the entropy is conserved and the process is, in principle, fully reversible. 

The application of proton-driven CSA correlation spectroscopy to amino-acid specifically carboxylic-labeled spider silk [63] is shown in Fig. 4.11. Spider silk is known to consist of alanine- and glycine-rich domains [64, 65] and is known to be semicrystalline. The assignment of alanine to the (crystalline) /3-sheet domains [66] is clearly supported by the chemical-shift correlation spectrum of Fig. 4.11. Because the tensors in a j8-sheet structure are almost parallel, or antiparallel, with the tensors in spatial proximity, a diagonal spin-diffusion spectrum is expected for that structure and is indeed found. In contrast, the glycine spectrum shows considerable off-diagonal intensity. Simulations have shown that the spectrum is compatible with a local 3i-helical structure [63]. 

Fig. 5.16. Imaging polymer morphology by spin-diffusion contrast on a sample of electrically aged polyethylene, (a) Sample for electrical aging in needle-plate geometry and region cut out for spin diffusion imaging with one-dimensional spatial resolution, (b) Spatially resolved distribution of the domain sizes derived from fitting theoretical diffusion curves of a sandwich layer model to the experimental data. Pronounced changes in the thickness for crystalline, interfacial and amorphous layers are obtained [58].

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-... 

In this section 10.2, we review the various solid-state NMR methods used to investigate interpolymer interactions, molecular motion and the spatial structure of a polymer blend. An interaction between component polymers affects the chemical shifts and lineshapes (see Section 10.2.2.1) and the molecular motions of the component polymers (see Section 10.2.2.2). In Section 10.2.3.1, microheterogeneity from 2 to 50 nm is studied by measuring spin diffusion indirectly from its effects on H spin-lattice relaxation. The spin-diffusion processes can also be monitored by several methods based on the Goldman-Shen experiment [8] (see Section 10.2.3.2). Homonuclear and heteronuclear two-dimensional correlation experiments reveal how and to what extent component polymers interact with each other (see Section... 

Information on the short distance spatial proximity of different segments of molecules can be obtained using the proton spin-diffusion NMR. This is a particularly valuable method for the... 

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