PFG NMR

For lithium salts in liquid battery electrolytes the most commonly used method is pfg-NMR. A large magnetic field is applied to the sample, changing in time and space, resulting in a spin echo signal of the nuclei with amplitude A. If there occurs any diffusion in a time interval, the amplitude A reduces to amphtude Ao and the ratio of the two amplitudes gives the so-called tracer diffusion coefficient [498]  

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Group 2 Radiotracer pulsed field gradient NMR measurements (PFG NMR) ... 

The wealth of information accessible by analyzing this type of PFG NMR data is reflected in Figure 3.1.1. This shows a representation of the (smoothed) propagators for ethane in zeolites NaCaA (a special type of nanoporous crystallite) at two different temperatures and for two different crystal sizes. Owing to their symmetry in space, it is sufficient to reproduce only one half of the propagators. In fact,... 

Fig. 3.1.2 Details of molecular transport in beds of nanoporous particles as accessed by PFG NMR. Three different situations inherent to different regimes of molecular motion are shown ...

In many cases, including transport phenomena which differ from normal diffusion, Eq. (3.1.4) turns out to be a good approximation, in particular if only small magnitudes of the gradient intensity ybg (sometimes referred to as the generalized scattering vector of PFG NMR) are considered. Under these circumstances, the genuine diffusivity D is replaced by an effective diffusivity, Deff... 

As a typical example, in the long time limit, t —> oo, of diffusion confined to spheres of radius R, the effective diffusivity of PFG NMR measurements is found to be [4, 8, 10]... 

Introduction of PFG NMR to zeolite science and technology has revolutionized our understanding of intracrystalline diffusion [19]. In many cases, molecular uptake by beds of zeolites turned out to be limited by external processes such as resistances, surface barriers or the finite rate of sorbate supply, rather than by intracrystalline diffusion, as previously assumed [10, 20-24]. Thus, the magnitude of intracrystalline diffusivities had to be corrected by up to five orders of magnitude to higher values [25, 26],... 

Fig. 3.1.4 Anisotropic self-diffusion of water in and filled symbols, respectively). The horizon-MCM-41 as studied by PFG NMR. (a) Depen- tal lines indicate the limiting values for the axial dence of the parallel (filled rectangles) and (full lines) and radial (dotted lines) compo-perpendicular (circles) components of the axi- nents of the mean square displacements for symmetrical self-diffusion tensor on the inverse restricted diffusion in cylindrical rods of length temperature at an observation time of 10 ms. / and diameter d. The oblique lines, which are The dotted lines can be used as a visual guide, plotted for short observation times only, repre-The full line represents the self-diffusion sent the calculated time dependences of the...

Fig. 3.1.5 Temperature dependence of the coefficient of long-range self-diffusion of ethane measured by PFG NMR in a bed of crystallites of zeolite NaX (points) and comparison with the theoretical estimate (line). The theoretical estimate is based on the sketched models of the prevailing Knudsen diffusion...

Fig. 3.1.6 Temperature dependence of the intraparticle diffusivity of n-octane in an FCC catalyst and the intracrystalline diffusivity of n-octane in large crystals of USY zeolite measured by PFG NMR. The concentration of n-octane in the samples was in all cases 0.62 mmol g 1. Lines show the results of the extrapolation of the intracrystalline diffusivity and of the intraparticle diffusivity of n-octane to higher temperatures, including in particular a temperature of 800 K, typical of FCC catalysis.

Figure 3.1.1, bottom left, illustrates a situation where PFG NMR may provide immediate evidence about the existence and intensity of additional transport resistances on the surface of the individual crystallites, the so-called surface barriers [60, 61]. This option is based on the sensitivity of PFG NMR towards molecular displacements. Molecules traveling over distances exceeding the typical crystallite sizes have to leave the individual crystallites (and are captured by some other crystallite(s) on their further trajectory). This fraction of molecules contributes to the broad part of the propagator. Plotting the relative intensity of the broad part of the propagator as a function of t we thus obtain the relative number y (t) of molecules, which have left their (starting) crystallites at time t. The function y(t) is... 

Comparison between xf a as determined on the basis of Eq. (3.1.15) from the microscopically determined crystallite radius and the intracrystalline diffusivity measured by PFG NMR for sufficiently short observation times t (top left of Figure 3.1.1), with the actual exchange time xintra resulting from the NMR tracer desorption technique, provides a simple means for quantifying possible surface barriers. In the case of coinciding values, any substantial influence of the surface barriers can be excluded. Any enhancement of xintra in comparison with x a, on the other side, may be considered as a quantitative measure of the surface barriers. 

It is worth noting that within a range of 20 %, five different methods of analyzing the crystallite size, viz., (a) microscopic inspection, (b) application of Eq. (3.1.7) for restricted diffusion in the limit of large observation times, (c) application of Eq. (3.1.15) to the results of the PFG NMR tracer desorption technique, and, finally, consideration of the limit of short observation times for (d) reflecting boundaries [Eq. (3.1.16)] and (e) absorbing boundaries [Eq. (3.1.17)], have led to results for the size of the crystallites under study that coincide. 

Owing to its ability to monitor the probability distribution of molecular displacements over microscopic scales from hundreds of nanometers up to several millimeters, PFG NMR is a most versatile technique for probing the internal structure of complex materials. As this probing is based on an analysis of the effect of the structural properties on molecular propagation, the properties of the material studied are those which are mainly of relevance for the transport processes inherent to their technical application. 

Studies of flow-induced coalescence are possible with the methods described here. Effects of flow conditions and emulsion properties, such as shear rate, initial droplet size, viscosity and type of surfactant can be investigated in detail. Recently developed, fast (3-10 s) [82, 83] PFG NMR methods of measuring droplet size distributions have provided nearly real-time droplet distribution curves during evolving flows such as emulsification [83], Studies of other destabilization mechanisms in emulsions such as creaming and flocculation can also be performed. 

K. G. Hollingsworth, M. L. Johns 2003, (Measurement of emulsion droplet sizes using PFG NMR and regularization methods),/. Colloid Interface Sci. 258, 383. 

S. Han, S. Stapf, B. Bliimich 2000, (Two-dimensional PFG-NMR for encoding correlations of position, velocity and acceleration in fluid transport), J. Magn. Reson. 146, 169. 

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients , or PFG-NMR, for selective ID and 2D experiments. The basic pulsed gradient spin-echo (PGSE) experiment [174] relies on the use of pulsed linear magnetic field gradients (of amplitude g, duration 8 and separation A) that are applied during a spin-echo experiment [184],... 

Pulsed field gradient NMR has become a standard method for measurement of diffusion rates. Stilbs [272] and others have exploited in particular the FT version for the study of mixtures. An added advantage of PFG-NMR is that it can be employed to simplify complex NMR spectra. This simplification is achieved by attenuation of resonances based on the differential diffusion properties of components present in the mixture. 

DOSY was developed to provide useful displays of PFG-NMR data sets that incorporate all reliable information about the system under study obtained from PFG-NMR data and prior knowledge. Various pulse sequences for DOSY have been developed [273,274]. 

DOSY is a technique that may prove successful in the determination of additives in mixtures [279]. Using different field gradients it is possible to distinguish components in a mixture on the basis of their diffusion coefficients. Morris and Johnson [271] have developed diffusion-ordered 2D NMR experiments for the analysis of mixtures. PFG-NMR can thus be used to identify those components in a mixture that have similar (or overlapping) chemical shifts but different diffusional properties. Multivariate curve resolution (MCR) analysis of DOSY data allows generation of pure spectra of the individual components for identification. The pure spin-echo diffusion decays that are obtained for the individual components may be used to determine the diffusion coefficient/distribution [281]. Mixtures of molecules of very similar sizes can readily be analysed by DOSY. Diffusion-ordered spectroscopy [273,282], which does not require prior separation, is a viable competitor for techniques such as HPLC-NMR that are based on chemical separation. 

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