# A Wide-Ranging NMR Probe for Multiscale Structures
## 5 Applications
### Polymers
The PIB/PEB-23 blend instead showed two distinct peaks, indicating that xenon diffused in two different surroundings, characterized by higher length scales of mixing, or domain sizes, compared to the PIB/PEB-66 blend. Xenon diffusion coefficients were used to obtain quantitative data: for the PIB/PEB-66 blend, a length scale of less than 70 nm was calculated, while, for the other blend, it was assumed to be greater than 70 nm (Figure 4). The study of the free volume of polymers can give important information regarding the effects of crosslinking on their morphology, and the high sensitivity of xenon has been exploited for this purpose. For example, in one of the first works on polymers, the presence of four distinct peaks in the range 198.5-201.0 ppm in the spectrum of crude EPDM (ethylene propylene diene monomer) was interpreted as the presence of four physically distinct domains in the amorphous region of the polymer [14]. The chemical shift of these peaks was associated to the relative sizes of these environments: the peak at 198.5 ppm was attributed to the largest free volume, the one at 201.0 ppm indicated the smallest void space, and the intermediate peaks were indicative of phases of in-between sizes. This interpretation was supported by the analysis of the same polymer after sulfur curing: the spectrum was completely different and the peak at 198.5 ppm was no longer observable, consistently with the disappearance of large void spaces due to crosslinking. In another study, a method to determine the crosslink density via xenon NMR data was proposed. A calibration curve of the \({}^{129}\)Xe chemical shift versus \(N_{\mathrm{m}}\) (average number of monomer units between crosslinks) was constructed for PB (polybutadiene) using swelling data [84]. This curve was then used to determine the degree of crosslinking of the reinforcing PB phase in high-impact polystyrene (HIPS), which was obtained by mixing PB with styrene and starting the polymerization. Indeed, the bonding between polystyrene and the rubbery phase in HIPS made it impossible to determine the crosslink density of PB via direct swelling measurements, while, in \({}^{129}\)Xe NMR spectra, signals characteristics of both phases were observed, allowing them to be studied independently. In a very recent work, the \({}^{129}\)Xe NMR analysis of a series of polymeric membranes for CO\({}_{2}\) separation has been reported [85]. Membranes were prepared by photopolymerization  
Figure 4: Schematic representation of the mixing length scales of (**a**) the PIB/PEB-23 blend and (**b**) or (**c**) the PIB/PEB-66 blend. For the latter, both representations are possible since the length scale is less than 70 nm in both cases. Reprinted with permission from reference [83]. Copyright 2004 American Chemical Society. of 2-hydroxyethyl methacrylate, ethylene glycol dimethacrylate, and polymerizable ionic liquids, constituted by a tetraalkylphosphonium cation, containing a vinylbenzene moiety, and variable counter anions. Xenon NMR was performed on the membranes covered in water to keep them wet and to simulate the conditions of typical systems containing CO\({}_{2}\). In the spectra obtained at 30 \({}^{\circ}\)C, two downfield signals could be observed for all the samples, as shown in Figure 5 ([P\({}_{\rm nnn}\)VB] indicates the phosphonium cation containing the vinylbenzene moiety and three linear alkyl chains with n carbon atoms each). The signal at 188 ppm was attributed to xenon in water, while the other one to xenon in the membrane. As can be seen from the (a), (b), and (c) spectra, the chemical shift for poly[P\({}_{\rm nnn}\)VB][BF4]+acrylates increased when going from ethyl to butyl chains, but then decreased again with further increase of the chain length. This was due to the strong influence of both the relative amount of aliphatic fraction and the terminal -CH\({}_{3}\) groups of the phosphonium cation on the chemical shift.