Fast exchange model

Localized NMR spectroscopy, which is often called as MRS in comparison with MRI, is not so familiar technique in food science, because a specific pulse sequence such as ISIS and a facility which can precisely follow the pulse sequence without any contamination from other position is needed for localization of position. The localized NMR is usually used together with NMR imaging. The study of solid/liquid ratios, fat structure and polymorphism and the kinetics of fat crystallization was reviewed [24], The potential of applications in food process development and control was offered. The localized spectra of sausages in areas of 0.3 mm X 0.05 mm (thickness of sample =1.5 mm) were obtained by the spin echo 2DFT method [113], in which the difference in the tissue structure was discussed with relation to the process and original materials. McCarthy et al. determined mobility of water in foams by using a localized spectroscopy [114]. T2 relaxation time varies in the foam as function of diameter and its variation was analyzed by the classic 2-state fast exchange model. 

Halle et al. (1981) measured NMR relaxation for solutions of several proteins as a function of frequency and protein concentration. They estimated hydration by use of a two-state fast-exchange model with local anisotropy and with assumed values of the order parameter and several other variables. The hydration values ranged from 0.43 to 0.98 h for five proteins, corresponding approximately to a double layer of water about a protein. The correlation time for water reorientation was, averaged over the set of proteins, 20 psec, about eight times slower than that for bulk water. A slow correlation time of about 10 nsec was attributed to an ordering of water by protein at very high concentration. 

Once Scu has been found, the same fast-exchange model can be used to derive the average surface composition Rui- CUy from the measured variation of the shift with overall composition Rui cCUj . It is then found... 

The value of the NMR spin-lattice relaxation time in each of the pixels of an image may be converted to a pore size by the adoption of a relaxation model. For a liquid imbibed in a pore space the relaxation rate is enhanced. This is believed to be due to interactions between a thin layer of liquid and the solid matrix at the solid/liquid interface increasing the relaxation rate. There is then also difllisional exchange between this surface-affected layer and the rest (bulk) of the liquid in the rest of the pore. In the case here where the pore sizes are several orders of magnitude smaller than the rms displacement of the probe water molecules employed, the "two-fraction fast-exchange" model of Brownstein and Tarr [7] will be used, where the overall measured value of T, is given by ... 

From the two-fraction fast-exchange model, the measured Tj can be related to the pore hydraulic radius by... 

A number of systems besides porous rocks have been investigated. For instance, the two-site fast-exchange model has been apphed successfully to measure the pore space of cement pastes during hydration." Results show that two distinct pore volume components are present. " ... 

Porous silicas are usually mesoporous materials and they can be made with a variety of pore dimensions. In particular, silica glasses can be made with well-defined pore diameters, typically in the range 30-250 A, using sol-gel methods. Such a system provides a good model for testing the models of relaxation behaviour of fluids in porous solids. It is normally found that the two-site fast-exchange model for relaxation described above for macroporous systems is still valid. For instance, H and relaxation times have been measured during both adsorption and desorption of water in a porous silica. Despite hysteresis in the observed adsorption isotherms, it was found that the relaxation times depended solely on water content.For deuterated water in some porous silicas, multicomponent relaxation behaviour for T2 and Tip has been observed, and this has been attributed to the fractal nature of the pore structure. 

Paramagnetic impurities in the cement (e.g. Fe ) provide FI relaxation centres at pore surfaces. These particles have strong dipole moments due to unpaired electrons, which causes very fast spin relaxation. Barberon et al. (2003), Godefroy et al. (2001), Korb et al. (1997) and McDonald et al. (2005) showed how the surface relaxivity of water on pore surfaces may be calculated given the surface density of paramagnetic Fe impurities. A measure of the pore volume then develops from the fast-exchange model of relaxation of Brownstein and Tarr (1979) and Zimmerman and Brittin (1957). 

Researchers have studied the relationship between relaxation rates obtained by H-NMR relaxometry and pore size. The fast-exchange model (also called the fast-diffusion model) developed by Brownstein and Tarr (1979), and Cohen and Mendelson (1982) relates and T2 relaxation... 

Figure 7.6 Illustration of surface water molecules and bulk water molecules with two different relaxation rates. This hypothesis is the basis of the fast-exchange model of relaxation in pores (Brownstein and Tarr 1979 Cohen and Mendelson 1982). Only a few molecules of each population are shown.

Figure 7.24 CPMG Tj results for a vyhite cement paste mixed at w/c = 0.40 and cured sealed throughout the hydration at 20°C measured with a 7.5 MHz spectrometer. Data are presented from 28 minutes after mixing up to 62 days of sealed hydration. Distinct water populations are rapidly observed being, from short to long relaxation times, C-S-H interlayer water, C-S-H gel water, interhydrate water and water in large capillary pores. Tj times can be translated into pore size using the fast-exchange model described in Section 7.2.4. For this, the surface relaxivity parameter is required. (Adapted from Muller 2014.)...

The associated relaxation times are shown in Eigure 7.28 for C-S-H interlayer water, C-S-H gel water and capillary water. The fast-exchange model of water relaxation in pores leads to average pore sizes of 0.85 nm (C-S-H interlayer spacing), 2.5 nm (gel pores) and 8.0 nm (interhydrate pores beyond 2 days of hydration) (Muller et al. 2013b). It needs to be specified... 

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