Domain sizes spin diffusion

Spin diffusion Domain sizing e.g. polymers, connectivity Caravatti et al. (1983), (1982)... 

The mean value of the i Vs for each sample was calculated. The calculated mean values of T/ s and the standard deviations are presented in Table 2. It is seen, from Table 2, that the standard deviation in both blends and complex is negligibly small. This indicates that the spin-dilfusion among all protons in the blends and the complex can average out the whole relaxation process and hence the domain size of these samples is smaller than the spin-diffusion path length within the time frame of Ti . From the obtained value of Ti and using the Eq. (1) with 10 m s it is believed that the PAA/PVP blends are intimately mixed on the Ti measurement scale of 32-39 nm. 

As reviewed in the previous section, measurements of Ti and Tip can provide an estimation of the length scale of miscibility of polymer blends. Compared with such kinds of experiments, the results of the spin-diffusion experiments are more quantitative and straightforward. The accuracy of the results of spin-diffusion experiments relies, to a large extent, on the values of spin-diffusion coefficients (7)) employed in calculation of the constituent phase components. Despite efforts that have been made, there still lacks a suitably applicable method of directly measuring the spin-diffusion coefficients, at least for polymers. For rigid polymer below Tg, 0.8 nm /ms has been turned out to be a reliable value of spin-diffusion coefficient. The difficulty left then concerns how to determine the coefficient of the mobile phase, which is very sample dependent. Recently, through studies on diblock copolymers and blend samples with known domain sizes, Mellinger et al established empirical relations between the T2 and D as follows ... 

In spin-diffusion studies it is possible to detect not only two but three domain sizes. The third domain can be considered the interface (i) between the other two domains, which can be different chemical species in a polymer blend or rigid crystalline (r) and mobile amorphous (m) material in a semicrystalline polymer. To illustrate this point, a mobility timescale is depicted in Fig. 7.2.25(a) and the simplified ID domain structure of PE underneath in (b). Rigid crystalline and mobile amorphous materials exhibit motion of chain segments with different correlation times Tc. The chains at the interface between both domains exhibit intermediate mobility. The exact ranges of correlation times in the individual domains depend on the particular choice of filters. Therefore, the values of domain sizes derived through spin-diffusion NMR also depend on the type of filters used. In particular, the interface is defined solely by the NMR experiment and can only be detected if the filters are properly chosen. 

Fig. 4.8, Schematic representation of the spin-diffusion process by a wave-front in (a) a compound consisting of different domains, e.g., a polymer blend (b) a regular structure with long-range order (e.g., a crystal) and (c) a microscopically disordered compound. The resonance frequency is encoded into the density of the filling pattern and simultaneously into the direction of the long elliptical axis, symbolizing that it can be determined either by the isotropic shift or the orientation of the shift tensor. Quasi-equilibrium is reached in (a), if the wave has extended over a typical domain size in (b) after the spin-diffusion wave has reached the next neighbors and in (c) after the wave has sampled all possible orientations, leading to the typical pattern for amorphous compounds discussed below.

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].

X 10 cm s The sizes of domains over which spin diffusion may be investigated by this technique is then limited by D and Ti. A typical value of Ti for polymers is roughly 1 s. If in time, t, the diffusion distance is roughly then for polymers with densities of protons similar to alkanes, the maximum distance sampled by spin diffusion would be about 29 nm, and minimum distances sampled of order of a few tenths of a nm. 

As a final example of the use of proton NMR invoking spin diffusion to study miscibility of polymer blends, the use of CRAMPS to remove proton dipolar coupling in a blend of an aromatic poly(ether-imid) (PEI), and a poly(aryl-ether-ketone) (PEEK), with detection of the magnetization of the C in the blend under high resolution conditions is cited [51]. Here, detailed information on the chemical composition of the phases present, as inferred from high resolution NMR of C, is linked to typical sizes of domains as reflected in spin diffusion of proton magnetization. 

Since miscibility (degree of mixing) influences macroscopic properties of a blend significantly, it is important to know the size and morphological information of domains in a blend. In Section 10.2.3.1, the effects of spin diffusion on Ti and Tip are discussed, which can be used to deduce the domain size on a scale of 2-50 nm. Sections 10.2.3.2, 10.2.3.3 and 10.2.3.4 discuss several experiments to monitor spin diffusion. To monitor spin diffusion, the following three periods, which are formally analogous to cross-relaxation and chemical exchange NMR experiments in liquids, may be required ... 

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