Field Gradient Methods

For ionic solids, measurement of the ionic conductivity, 7 , has long provided a method for studying their atomic diffusion [25, 209, 225, 226] (see also Chapter 3). The measurements are usually made with an alternating current (AC) bridge operating at a fixed frequency, f (typically 1 kHz), to avoid polarization effects. The early studies were restricted to measurements on single crystals, and in this case (7i and the tracer diffusion coefficient were seen to be related by the Nernst-Einstein equation [25]  

For jumps involving single point defects, is accurately known for the different crystal structures. Ionic conductivity measurements, coupled with other diffusion measurements, have proved to represent a very powerful method for identifying diffusion mechanisms. However, the requirement for single-crystal samples proved to be very restrictive in terms of the materials that could be investigated, and the approach has been used successfully only for very simple systems. Examples include the combination of conductivity and diffusion in the study of alkali and silver halides [226], and the combination of conductivity and NMR in the study of barium fluoride [219]. 

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In this chapter we will focus on molecular ordering and confinement effects in pores. Diffusion experiments with the pulse-field gradient method ([162-165] and references therein) and characterization of the surface properties using NMR of noble gases such as 129Xe ([166-171] and references therein), or 83Kr [172], will be omitted due to excellent reviews that have appeared quite recently in these areas. 

Diffusional behavior of sorbed species is studied by NMR using one of three approaches the van Vleck method of moments, relaxation measurements, and the pulsed-field-gradient method. An example of the use of the method of moments is the work of Stevenson (194) on H resonances in zeolite H-Y (see Section III,K). Another is the study by Lechert and Wittem (284) of C6H6 and C6H3D3 adsorbed on zeolite Na-X. Analysis of second moments of H resonances allowed the intra- and intermolecular contributions to the spectra to be extracted. Similarly, second moments of H and 19F spectra of cyclohexane, benzene, fluorobenzene, and dioxane on Na-X provided information about orientation of molecules within zeolitic cavities (284-287). 

Since the pioneering work of Stejskal, the pulse field gradient method is currently used to characterize the diffusion process of small molecules or of macromolecules in dilute or semi-dilute solutions [18-20]. In this Chapter, the NMR approach is illustrated from the self-diffiision of ( dohexane molecules through polybutadiene. Variations of the Ds self-diffusion coefficient of cyclohexane in polybutadiene have been reported as a temperature function considering several concentrations [21]. 

The obtained parameter values are summarized in Table 3. The self-diffusion coefficient of the proton decreases with lowering temperature, suggesting that the translational motion of water molecules is restricted at the low temperatures. This is probably because of the water-water interaction will be enhanced with decreasing temperature. The self-diffusion coefficients obtained from QENS are less than those determined by the H-NMR pulsed-field gradient method. A probable reason for the difference in Z h is ascribed to different time scales observed by both methods ( 200 peV for LAM40). 

The next three sections deal with steady and pulsed field gradient methods for measuring translational diffusion in liquids and plastic solids. There are other methods for measuring slower diffusion which we will not really touch upon. See, for example, Ailion, referenced in IV.C.l., and Burnett and Harmon (1972). 

Pulsed field gradient methods may be used in combination with a spin-echo pulse sequence to measure average molecular displacements in a time In liquids, PFG methods can therefore be used to measure self-diffusion coefficients (i.e. the rate of diffusion due to Brownian motion in the absence of a concentration gradient). In porous media, there is the possibility of obtaining information about the pore geometry because the pore boundaries will influence molecular transport. PFG techniques can measure restricted diffusion and thus provide valuable information on pore sizes in the range 5-100 (im. 

The most recent, successful and widely applicable approach to suppressing zero-quantum contributions employs a pulsed field gradient method for the net dephasing of these coherences in a single scan with no requirement for experiment repetition [88]. Since PFGs alone cannot manipulate ZQCs, the gradients must be applied in a rather ingenious manner to be effective, tbe operation of wbicb may be understood as follows. 

Some of the most successful methods of nuclear magnetic resonance used in the study of disordered porous media have been reviewed and their applications to the measurement of pore size distribution, diffusion coefficients and permeability have been presented. This is the case of nuclear relaxation and pulsed field gradient method of a specific imbibed solvent in various fully or partially saturated organic or inorganic porous media. The cases of narrow and large distributions of pores have been... 

The pulsed field gradient method of self-diffusion measurement was originally developed by Stcjskal and Tanner " for the measurement of diffusion in liquids. The self-diffusivity is measured directly and no prior estimate of jump distance is needed so the results are, in principle, more reliable. The development and application of this technique to the study diffusion in zeolites and zeolitic adsorbents has been achieved largely through the researches of Pfeifer, Karger, and their co-workers at the Karl Marx University in Leipzig,... 

In recent years, in addition to theoretical developments, e.g., reptationW and tube theories,(i3,i4) iYiqyq have been many new analytical techniques,5) such as electron-induced X-ray fluorescence, the NMR field gradient method, forced Rayleigh scattering (FRS), forward recoil spectrometry (FRES), photon correlation spectroscopy, Rutherford back scattering. 

We start by summarizing the pulsed field gradient method and then describe two relevant topics the first deals with droplet size determination of emulsions and the second deals with the characterization of concentrated emulsions. The former is a well-developed area, which has been used for a long time not only by the present author, while the latter constitutes a novel field for the application of the method. We present some (very) preliminary data from such a system. 

With these technique it can also be demonstrated in the two phase regions that both phases with their different structures are really coexisting. This result can be supported by self-diffusion measiuements with the pulsed NMR field gradient method from which the existence of bicontinuous phases and their topology can be concluded [73, 98]. 

At this point, it must be mentioned that not only spin diffusion but also self diffusion of molecules can be studied by NMR [11, 13]. The available magnetic resonance techniques, relaxation and field-gradient methods, are discussed in Sec. 13.3.3 of Chap. VII of this Volume. 

Dynamic processes that can be investigated by NMR include both the motions of individual molecules, e.g., conformational dynamics and molecular rotations, and collective motions, e.g., director fluctuations in nematic systems, layer undulations in smectic systems, or density modulations in columnar phases of discotic systems. Self-diffusion can be measured by NMR relaxation or field gradient methods, as discussed in Sec. 13 of Chap. VII of this Volume. Table 1 gives an overview of the time scales accessible by the most common experimental techniques and examples of the type of motion that can be studied. 

The temperature dependent H, H, and chemical shifts of NH3 and ND3 have been calculated.The pressure and temperature dependence of self diffusion in fluid ammonia have been investigated using the NMR pulsed field gradient method. Substituent effects on the P chemical shifts of PX2Y, X, Y = F, OH, NH2, CH3, BH2, BeH, Li, H, have been analysed. The quadrupole spin relaxation of in NNO in collision with various molecules has been determined.chemical shifts and some /( P N) values have been reported for three classes of compounds containing P-N bonds. The relations of P chemical shift with degree of substitution and substituent have been determined for cyclotriphosphazenes. and NMR spectroscopy has... 

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