NMR diffusometry

The attenuation factor of the echo amplitude due to translational diffusion is given by 

Te is the echo time and tp is the (precession) phase a spin possesses at time t=Tg. The brackets represent an ensemble average over all spins in the sample. In the following, this expression will be analyzed for different pulse sequences. 

Any echo attenuation by relaxation occurs independently of diffusive attenuation and is of marginal interest in this context. It can readily be separated by either keeping all pulse intervals constant (and varying the gradient strength) or by compensating for relaxation losses in experimental protocols especially designed for this purpose. 

Hahn Spin Echo in the Short Gradient Pulse Limit (S A) 

We consider the coherence evolution of uncoupled spins 7=1/2 during the pulsed gradient Hahn spin echo sequence schematically shown in Fig. 2a. A suitable basis for the treatment is the spherical product operator formalism. Explanations, definitions, and rules of the spin operator formahsm needed in this context can be found in Ref [2]. Times just before and immediately after RF (radio frequency) and field gradient pulses will be indicated by minus and plus signs, respectively. 

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NMR diffusometry Decay of spin echoes in the presence of a magnetic field gradient (echo attenuation curve) Price (1996, 1997, 1998a)... 

Mariette, F., Topgaard, D., Jonsson, B., and Soderman, O. 2002. 1H NMR diffusometry study of water in casein dispersions and gels. J. Agric. Food Chem. 50, 4295-4302. 

Abstract The principle of chromatographic NMR, a version of NMR diffuso-metry devised for a facilitated study of mixtures using the addition of a selectively retarding agent, is illustrated. The technical requirements for acquiring exploitable H NMR diffusometry spectra for a heterogeneous solution/solid mix are described. Applications of the technique to test mixtures for several choices of solvents/ interacting phase are reviewed. Key Words Mixtures, Porous materials, Diffusion, HRMAS, DOSY. 

The study of the composition of a mixture is an extremely common problem in analytical and bioanalytical chemistry. While chromatography and solvent extraction are commonly employed to simplify the analysis prior to characterization of the constituents, NMR has provided a series of tools that help in unravelling the components of complex samples, when a previous separation of the pure compounds is not feasible or complete. Thus, TOCSY, NMR diffusometry (DOSY, among all) and heteronuclear correlation experiments are widely used to this purpose, for example, for the characterization of small molecules in biologically relevant samples, such as in metabolomics,1 plant extracts analysis,2 food quality control,3 4 to name a few cases. 

Figure 6 Polymer-induced pseudo-chromatographic effect in NMR diffusometry using polyvinylpyrrolidone (PVP) of an MW of 10,000 in deuterated chloroform. Regular DOSY (left) and chrom-NMR (right) on a mixture of benzylalcohol, p-methylphenol and p-xylene mixture. Adapted with permission from Ref. 24. Copyright 2009 American Chemical Society.

Diffusion can be divided into free and restricted diffusion. A combination of NMR diffusometry and microscopy has proved useful for the study of probe diffusion in gels and emulsions (Hagslatt et al. 2003 Loren et al. 2005 Hermansson et al. 2006 Walther et al. 2006) For such studies the probe should be much larger than water so that the obstruction can be clearly observed in NMR difiusometiy. Small molecules... 

Walther, B., Loren, N., Nyden, M., and Hermansson, A.M. (2006). Influenee of kappa-carrageenan gel structures on diffusion of probe molecules determined by transmission electron microscopy and NMR diffusometry. Langmuir, 22, 8221-8228. 

Mass Transport Studies Using a Combination of Microscopy and NMR Diffusometry... 

The fact that the microstructure is heterogeneous is very important, because it means that the diffusion behavior varies from one part of the microstructure to another. For instance, in dense parts, the diffusion is slower than in open parts. Diffusion simulations by finite element methods (FEMLAB ) and Monte Carlo methods make it possible to combine microscopy and NMR diffusometry in a qualitative and quantitative manner. 

The properties of food products such as margarine or low-fat spreads are extremely dependent on the droplet size distribution. Water and fat diffusion in cheese have been studied in this context (Callaghan et al., 1983) and the size distribution of water droplets in margarine products has been measured (Van den Enden et al., 1990). The Gaussian phase distribution (GPD) approximation has been used to determine the size distribution of water droplets in margarine and low-fat spreads (Balinov et al., 1994). NMR diffusometry studies have been compared in some cases with results from image analysis (Fourel et al., 1995). However, up to now, most studies assume that the emulsion droplets are more or less spherical. 

Figure 5.13 shows a comparison between the echo decay calculated directly from the microstructure as described in the previous section and the measured echo decay using NMR diffusometry at A = 100,200 and 500 msec. It was found that the calculated echo decay fitted reasonably well with the experimental echo decay, especially at intermediate and high ( -values. There is an inverse relation between the ( -values and the length scales in the microstructure, i.e., low ( -values correspond to long distances in the microstructure and vice versa. Another way to look at it is to say that low (j-values correspond to large details in the microstructure, and high ( -values correspond to fine details in the microstructure. Three CLSM micrographs showing different length scales in the structure are inserted in Figure 5.13. They are inserted in order to show which t)q5e of structure affects different...

Comparison between the calculated echo decay (full lines) and the measured echo decay using NMR diffusometry (discrete symbols), and the pertinent microstructure on different length scales, (a) 16 X. The bright fluorescent phase is fat. (b) 40 X. (c) 200 X. Triangles, dashed line = 100 msec Stars, dotted line = 200 msec Plus, full line = 500 msec. 

Informative probe diffusion alone cannot reveal structural and intermolecular interaction details because the echo decay from a probe in a heterogeneous matrix is not imique and a large number of different structures and/or interaction possibilities may give rise to the same echo decay. One way to attack this problem is to use a similar approach to the one mentioned previously, regarding water diffusion in emulsions. In order to succeed with this, however, we believe that a three-dimensional gel structure must be used for diffusion simulations. For this reason work is in progress to develop a new combination of methods, NMR diffusometry, microscopy, mathematical reconstruction, image analysis and diffusion calculations/simulations by Monte Carlo and finite element methods (to be published shortly). 

Karlson, L., C. Malmborg, K. Thuresson, and O. Soderman. 2003. Complex formed in the system hydrophobically modified polyethylene glycol/methylated a-cyclodextrin/water. An NMR diffusometry study. Colloids and Surfaces A Physicochemical and Engineering Aspects 228 (1-3) 171-179. 

M. Cifelli, A practical tutorial to set up NMR diffusometry equipment application to liquid crystals, Magn. Reson. Chem. 52 (10) (2014) 640-648. 

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