**3.1. Diffusion in zeolites, nanoparticles and liquid crystals**

As noted for other material studies, heterogeneities in the magnetic susceptibility or restricted molecular motions within zeolite crystallites lead to broadening of the NMR signal, such that resolution of individual species in mixtures becomes difficult. HR-MAS NMR resolves this issue, and has led to the utilization of PFG NMR diffusion experiments on organic mixtures in zeolites. This technique has been used to study the diffusion of *n*butane in silicalite-1,[88] ethane, water and benzene mixtures adsorbed to the zeolite NaX,[89] acetone-*n*-alkane (C6 to C9) mixtures in nanoporous silica,[90] or mixtures of *n*butane and *iso*-butane adsorbed in MFI zeolite. The increased resolution afforded by these PFG HR-MAS studies on mixtures reveal the obstructive influence of the isopropyl molecules or bulky benzene on the diffusion of other molecular species, [89, 91] and that the creation of acetone-alkane complexes greatly impacts the observed diffusion properties.[90]

PFG HR-MAS NMR has also been used to obtain 2D DOSY (**D**iffusion **O**rdered **S**pectroscop**Y**) spectra of surface modified iron oxide NPs. These results were able to distinguish between NP-bound and free ligands in these materials.[58] These types of PFG HR-MAS NMR experiments should prove useful in understanding the surface-ligand dynamics present in modified NPs.

Diffusion experiments using HR-MAS NMR has also been found useful in the analysis of transport properties in lipid membranes.[92-94] Due to the anisotropic molecular reorientation of these liquid crystalline (LC) systems, significant dipolar coupling remains, leading to broad lines and short relaxation times. However dipolar coupling can be reduced through the use of MAS. Surprisingly, the use of PFG HR-MAS NMR for non-biological LCs is more limited, with the single investigation of local molecular dynamics of the thermotropic LC 4'-pentyl-4-cyanobiphenyl (5CB) confined in Bioran glasses with pore diameters of 30 nm and 200 nm being reported. By utilizing PFG techniques it was possible to measure the diffusion constants as a function of temperature through the isotropization temperature of the liquid crystal, thus demonstrating that for this case there is only a minor reduction in the diffusion rates with molecular confinement.[51]

## **3.2. Diffusion in polymers**

296 Advanced Aspects of Spectroscopy

**Figure 9.** Diffusion pulse sequences. Pulse Field Gradient (PFG) A) Spin-Echo, B) PFG Stimulated Echo with dipolar gradients and spoil gradient based on Cotts *el al.* 13-interval sequence[85], and C) PFG Stimulated Echo with dipolar gradients and spoil gradient with an additional eddy current delay. GMAS

As noted for other material studies, heterogeneities in the magnetic susceptibility or restricted molecular motions within zeolite crystallites lead to broadening of the NMR signal, such that resolution of individual species in mixtures becomes difficult. HR-MAS NMR resolves this issue, and has led to the utilization of PFG NMR diffusion experiments on organic mixtures in zeolites. This technique has been used to study the diffusion of *n*butane in silicalite-1,[88] ethane, water and benzene mixtures adsorbed to the zeolite NaX,[89] acetone-*n*-alkane (C6 to C9) mixtures in nanoporous silica,[90] or mixtures of *n*butane and *iso*-butane adsorbed in MFI zeolite. The increased resolution afforded by these PFG HR-MAS studies on mixtures reveal the obstructive influence of the isopropyl molecules or bulky benzene on the diffusion of other molecular species, [89, 91] and that the creation of acetone-alkane complexes greatly impacts the observed diffusion properties.[90] PFG HR-MAS NMR has also been used to obtain 2D DOSY (**D**iffusion **O**rdered **S**pectroscop**Y**) spectra of surface modified iron oxide NPs. These results were able to distinguish between NP-bound and free ligands in these materials.[58] These types of PFG

indicates that the gradient is applied along the magic angle.

**3.1. Diffusion in zeolites, nanoparticles and liquid crystals** 

There is extensive literature on the use of PFG NMR to measure diffusion of polymer solutions and melts, along with PFG diffusion measurements of different species adsorbed into polymers, including gases, water, organic solvents and electrolytes. There have been a limited number of examples where the improved resolution afforded by HR-MAS NMR was coupled with PFG. This work includes the development of diffusion filtered HR-MAS NMR techniques to study the gelation process of super-molecular gels,[95] along with a combination diffusion-filtering and a spin-echo enhanced (*T2* –filtered) experiment on DMFswollen resins.[96] These techniques allowed the identification of free and surface bound molecules, while eliminating the signal from the immobile bulk resin matrix. In complex mixtures there may be future avenues for HR-MAS to resolve subtle differences in the local chemical environments as demonstrated in the following example.

#### *3.2.1. Example of HR-MAS diffusion in anion exchange membranes*

As discussed in Section 2.1.1, four distinct resonances were observed in the 1D 1H HR-MAS NMR spectra of AEM polymers swollen in a 1N methanol solution. In Figure 10A, NMR spectra for three AEM polymers with different ion exchange capacities (IEC) are shown. Two resonances were observed for both water and methanol, and were assigned to free (F) and membrane-associated (A) environments. From this HR-MAS data it is easy to see that there is a correlation between chemical shift of the associated species and the IEC of the membrane, with both the associated water and methanol resonance shifting to lower ppm with decreasing IEC. This decrease in chemical shift is most likely due to a change in hydrogen bonding between the solvent components and the membrane, reflecting how strongly the solvent molecules are associated with the membrane. Recall that the resolution of these individual environments was not observable in the static NMR spectra (Figure 2A). Using 1H HR-MAS PFG diffusion experiments, the self-diffusion constants were obtained for each of these four different environments, which were not accessible from the static data. Because the 1H signal for the AEM membrane is not readily observable under HR-MAS conditions, the diffusion rates obtained for the resolved solvent resonances were not biased by the polymer membrane. Figure 10B shows the signal decay for the associate methanol environment as a function of gradient strength for the three different IEC levels. The magic angle gradients were used to perform diffusion measurements utilizing a PFG Stimulated Echo with dipolar gradients and spoil gradient with a Δ=100ms (Figure 9B). The signal decay shows that there is a correlation between diffusion rate and IEC, exhibiting a faster diffusion rate with increasing IEC values. A more detailed analysis of this work is forth coming, but this example demonstrates the power of combining HR-MAS and PFG diffusion experiments.

**Figure 10.** A) 1H HR-MAS NMR spectra with the assigned free [F] and associated [A] water and methanol environments. B) The diffusion rates for the associated methanol in three different anion exchange membranes with varying ion exchange capacity (IEC) values. The colored peaks in the 1H HR-MAS NMR spectra correlate to the colored symbols in the diffusion plot of the associated methanol peak of IEC = 2.2 (█), 1.9 (●), and 1.7 mequiv/g (▲).

#### **4. Conclusions**

The application of HR-MAS NMR to the characterization of materials or material interfaces that exist in the semi-solid range has been demonstrated. A wide variety of different material systems have been explored, showing that this technique can provide resolution and dynamic information where standard solution or solid state NMR techniques were unsuccessful. HR-MAS NMR is a powerful tool for the detailed characterization of modified surfaces and surface adsorbed species. This technique also provides a direct probe of differences in local mobility as reflected by line width variations. Through the combination of the enhanced resolution afforded by HR-MAS with pulse field gradient (PFG) capabilities, selective filtering and diffusion measurements of complex heterogeneous materials can also be realized. The ability to resolve and obtain diffusion rates for multiple environments in materials will prove beneficial for understanding the diffusion process in mixed chemical systems. While HR-MAS NMR is considered a mature, relatively routine technique, the application to the materials field is expected to continue being an active area of development. It is hoped that this review will encourage researchers to explore the application of HR-MAS NMR techniques to their different material systems.
