Diffusometry

In order to verify the conditions of this averaging process, one has to relate the displacements during the encoding time - the interval A between two gradient pulses, set to typically 250 ms in these experiments - with the characteristic sizes of the system. Even in the bulk state with a diffusion coefficient D0, the root mean square (rms) displacement Z2 of n-heptane or, indeed, any liquid does not exceed several 10 5 m (given that Z2 = 2D0 A). This is much smaller than the smallest pellet diameter of 1.5 mm, so that intraparticle diffusion determines the measured diffusion coefficient (see Chapter 3.1). This intrapartide diffusion is hindered by the obstades of the pore structure and is thus reduced relative to D0 the ratio between the measured and the bulk diffusion coeffident is called the tortuosity x. More predsely, the tortuosity r is defined as the ratio of the mean-squared displacements in the bulk and inside the pore space over identical times  

The intraporous self-diffusion coefficient D is then also time-independent and one can write x = D0/D  

It should be mentioned here that a different definition of the diffusion coefficient is often used in chemical engineering problems, which is more appropriate for the description of reactant or tracer transport. It takes into account the fact that the total fluid contained in a porous substance of porosity e is reduced by this factor relative to the bulk, so that an effective diffusion coefficient D of the reactants is defined such that 

The tortuosity for pore-filling liquids is ideally a purely geometric factor but can, in principle, depend on the fluid-surface interaction and the molecular size if very small pores are present such as in zeolites (see Chapter 3.1). To obtain a measure for a realistic situation, we have used n-heptane as a typical liquid and have computed x 

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Kimmioh R 1997 NMR—Tomography, Diffusometry, Re/axomefry (Berlin Springer)... 

However, mean pore sizes are often much larger than micrometers so that no restriction effect will show up in field gradient diffusometry experiments [16]. 

Under such circumstances, spin density diffusometry turned out to be more favorable. We are not discussing solvent intrusion experiments with solid-like materials, as they are typically carried out with the aid of stray field imaging [24]. 

Figure 2.9.3 shows typical maps [31] recorded with proton spin density diffusometry in a model object fabricated based on a computer generated percolation cluster (for descriptions of the so-called percolation theory see Refs. [6, 32, 33]).The pore space model is a two-dimensional site percolation cluster sites on a square lattice were occupied with a probability p (also called porosity ). Neighboring occupied sites are thought to be connected by a pore. With increasing p, clusters of neighboring occupied sites, that is pore networks, begin to form. At a critical probability pc, the so-called percolation threshold, an infinite cluster appears. On a finite system, the infinite cluster connects opposite sides of the lattice, so that transport across the pore network becomes possible. For two-dimensional site percolation clusters on a square lattice, pc was numerically found to be 0.592746 [6]. 

Fig. 2.9.3 Proton spin density diffusometry in a two-dimensional percolation model object [31]. The object was initially filled with heavy water and then brought into contact with an H2O gel reservoir, (a) Schematic drawing ofthe experimental set-up. The pore space is represented in white, (b) Maps ofthe proton spin density that were recorded after diffusion times t varying from 1.5 to 116 h. Projections of the...

R. Kimmich 1997, NMR Tomography, Diffusometry, Rdaxometry, Springer, Berlin. 

S-10 1 m velocity measurements and propagators are extensions of diffusometry and imaging, and are able to quantify displacements from micrometers up to the size of the reactor itself. 

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. 

Another approach that is worth mentioning, although it has not yet been used for enhanced diffusometry, has been dubbed NMR wool tube. Here, an alternative method of putting in contact silica and a solution for NMR analysis has been proposed, in which a functionalized glass-wool was inserted in the NMR tube.37... 

In this section, we provide an outline of the theoretical and practical aspects of diffusometry NMR experiments that are the core of chrom-NMR. This issue has been reviewed at large38,39 and thus only the key and most relevant aspects will be mentioned below. The displacement of a given molecular tracer is followed by a classical Stejskal-Tanner experiment. In this, pulses of magnetic field gradients are used to label the initial position of the tracer, and to follow its displacement along the direction of the gradient, Az. Indeed, in a spin-echo experiment, any displacement corresponds to a reduction of the efficiency of the echo formation. 

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. 

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