Self-diffusion coefficients application

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

The measurement of transport numbers by the above electrochemical methods entails a significant amount of experimental effort to generate high-quality data. In addition, the methods do not appear applicable to many of the newer non-haloalu-minate ionic liquid systems. An interesting alternative to the above method utilizes the NMR-generated self-diffusion coefficient data discussed above. If both the cation (Dr+) and anion (Dx ) self-diffusion coefficients are measured, then both the cation (tR+) and anion (tx ) transport numbers can be determined by using the following Equations (3.6-6) and (3.6-7) [41, 44] ... 

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

For soils without appreciable clay aggregation, the experimental results and theoretical analysis described here indicate that when diffusion is rate-limiting, the ratio of the hydrodynamic dispersion coefficient to the estimated soil self-diffusion coefficient may be a useful indicator of the applicability of the local equilibrium assumption. For reacting solutes in laboratory columns such as those used in this study, systems with ratios near unity can be modeled using equilibrium chemistry. 

Examples of Ihe deterniinalioii of self-diffusion coefficients in solids are Ihe diffusion of hydrogen ions and water molecules (labelled with T and O, respectively) in alums, of Cl (labelled with Cl) in AgCl, and of 1 (labelled with l) in Agl. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radio-tracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. 

The number of NMR groups specializing in PGSE NMR methods has, until recently, been relatively small. This situation is partly because of a perception that the method is solely applicable to the measurement of self-diffusion coefficients, but also because of the difficulty in developing a reliable apparatus. Since the advent of gradient pulse switching capabilities... 

It has been demonstrated that the combined application of various NMR techniques for observing molecular rotations and migrations on different time scales can contribute to a deeper understanding of the elementary steps of molecular diffusion in zeolite catalysts. The NMR results (self-diffusion coefficients, anisotropic diffiisivities, jump lengths, and residence times) can be correlated with corresponding neutron scattering data and sorption kinetics as well as molecular dynamics calculations, thus giving a comprehensive picture of molecular motions in porous solids. 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

Most of the current applications of perfluorosulfonate membranes involve electrochemical cells in which concentrated electrolyte solutions are employed, often at elevated temperatures. Relatively little diffusion data are available under these conditions, although a larger amount of membrane resistance and other operating data have been published. Sodium ion self-diffusion coefficients have been measured in various Nafion membranes in concentrated NaOH solutions at elevated temperatures (23). This... 

Diffusion measurements make possible the determination of association constants for complexes with small chemical shift changes induced by the association. A representative example of such application is the evaluation of association constants for the complexes of y-CyD with 12-crown-4 and its tetraaza and tetrathia analogues [27]. A titration experiment with self-diffusion coefficient detection was also used for determination of the association constants of the 1-adamantanecarboxylic acid- -CyD complex at two temperatures [28]. 

Application of continuous wave techniques and line shape analysis to wide-line n.m.r. spectra Cf D-xylose, D-mannose, D-glucose, D-fructose, and D-sorbose suggests that the lattice is effectively rigid in all except possibly D-fructose. Previously published C n.m.r. data for arabinosides and ribosides have been tabulated with correlation diagrams constructed in such a way that the data on new compounds can be used to assign the anomerlc configurations and ring size. Measurements of self-diffusion coefficients of carbo-... 

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