Self-diffusion studies

In Section IV, from the studies on diffusion towards self-affine fractal interface, the surface fractal dimension as determined by the electrochemical method is characterized as being self-similar, even though the rough surfaces and interfaces show the self-affine scaling property. Finally, in Section V, we exemplified the application of fractal geometry in electrochemical systems in view of the characterization of rough surfaces and interfaces by the surface fractal dimension. 

Figure 10. Three-dimensional AFM images of (a) Pt/polished AI2O3, (b) Pt/etched Ni, and (c) Pt/unpolished AI2O3 electrodes. Reprinted from J. -Y. Go et al., A study on ionic diffusion towards self-affine fractal electrode by cyclic voltammetry and atomic force microscopy, J. Electroanal. Chem., 549, p. 49, Copyright 2003, with permission from Elsevier Science.

The first part of this review deals with the synthesis and characterization of dendritic aliphatic polyesters based on 2,2-bis(dimethylol)propionic acid (bis-MPA) and 1,1,1 -tris(hydroxyphenyl)ethane (THPE), as core molecule. The convergent growth approach described earlier was applied. We also present H NMR self-diffusion studies of dendrimers of first, second, and third generation. 

The techniques used for the characterization of the dendrimers Dl, D2, and D3 were H NMR, C NMR, and SEC. Self-diffusion studies were made by pulsed-field spin echo H NMR. The simplicity of the H NMR and C NMR spectra indicates high purity of Dl, D2, and D3. 

Molecular self-diffusion studies by pulsed-field spin echo H NMR turned out to be a convenient method to estimate the hydrodynamic radii of dendrimers of different generations. 

In polymers, the field-gradient spin-echo methods of measuring self-diffusion have been useful in three more or less distinct areas, the diffusion of polymers in their own melt and in concentrated solutions, in dilute and semidilute solutions, and the diffusion of penetrants and diluents in polymer hosts. A fourth category, the diffusion of bulky or flexible molecules in polymer hosts, is useful for subject matter not closely associated with the first and third category. It should be noted that the work reviewed here represents only a small fraction of the diffusion studies in polymers, including those using other NMR methods. 

Self-Diffusion Studies. Diffusion kinetics were determined, as previously described (14 17, 18), with the appropriate scaling down in sample size for enzyme experiments. The tracer used was 65Zn as supplied by the Radiochemical Center, Amersham, and was determined in solution by... 

Soderman et al. [8] gave an overview of NMR self diffusion studies of emulsion systems. They stated that a log-normal distribution function gives a better fit than a normal distribution. Several examples are given including margarine and hydrocarbon gel emulsions. 

The self-diffusion of the individual components is strongly affected by the formation of micelles in the solution. This applies to the surfactant, the counterion, the water, and to solubilized molecules. As illustrated in Fig. 2.11 for sodium dodecyl sulfate, surfactant and counterion diffusion are very weakly dependent on concentration below the CMC while a marked decrease in the micellar region is observed for the surfactant and a less marked one for the counterion37. Water diffusion shows a stronger concentration dependence below the CMC than above it. Self-diffusion studies using radioactive tracers have been performed to obtain information on CMC, on counterion binding, on hydration and on intermicellar interactions and shape changes. 

The methods described so far for studying self-diffusion are essentially based on an observation of the diffusion paths, i.e. on the application of Einstein s relation (eq 3). Alternatively, molecular self-diffusion may also be studied on the basis of the Fick s laws by using iso-topically labeled molecules. As in the case of transport diffusion, the diffusivities are determined by comparing the measured curves of tracer exchange between the porous medium and the surroundings with the corresponding theoretical expressions. As a basic assumption of the isotopic tracer technique for studying self-diffusion, the isotopic forms are expected to have... 

In principle, any of the techniques described for studying self-diffusion may be applied to both single- and multicomponent systems. So far, however, most selfdiffusion measurements of multicomponent systems have been carried out by PFG NMR. Such measurements are possible by applying a set of samples with deuterated compounds with only one species (namely that to be measured) in the protonated form [98], by simultaneously considering different nuclei (e.g. H and 19F [79]), and by Fourier transform PFG NMR [91,92]. 

The application of NMR to the study of diffusion in zeolites involves the refinement and extension of methods originally developed to study self diffusion in liquids and low melting solids. The method is restricted to species such as hydrocarbons which contain a sufficiently high density of atoms such as H with unpaired nuclear spins. Authoritative reviews of the application of NMR to the study of adsorbed molecules have been given by Pfeifer(22,23) and only a brief outline is included here. 

The maximum deviations from stoichiometry in CdTe have been found to be about 1017 excess Te or Cd atoms per cc., and in PbTe about 4 X 1018 excess Pb and 1019 excess Te atoms per cc. Because these deviations from a 1 to 1 stoichiometry are so small (5 X 10-4 or less), they cannot be studied by chemical analysis, x-ray diffraction, or density measurements. Rather the extent of nonstoichiometry and the nature of the defects must be inferred from such quantities as obtained from electrical, optical, magnetic, and self-diffusion studies. 

Liu and Ruckenstein [Ind. Eng. Chem. Res. 36, 3937 (1997)] studied self-diffusion for both liquids and gases. They proposed a semiem-pirical equation, based on hard-sphere theory, to estimate self-diffusivities. They extended it to Lennard-Jones fluids. The necessary energy parameter is estimated from viscosity data, but the molecular collision diameter is estimated from diffusion data. They compared their estimates to 26 pairs, with a total of 1822 data points, and achieved a relative deviation of 7.3 percent. 

To reveal ionic transport behavior through self-diffusion studies [22], we choose four different ionic liquids l-ethyl-3-methylimidazolium tetrafluoro-borate (EMIBF4), l-ethyl-3-methylimidazolium l ii(trifluoromethylsulfonyl)imide (EMITFSI), 1-butylpyridinium tetrafluoroborate (BPBF4), 1-butylpyridinium, and Z7w(trifluoromethylsulfonyl)imide (BPTFSI) (Scheme 5.1). The ionic liquids are comprised of two different cations and anions, and they allow us to visualize the dependence of ionic transport behavior on structural variety from the comparative self-diffusion behavior. 

Results of Self-Diffusion Experiments. Self-diffusion coefficient studies with fused salts really began to gather momentum after radioisotopes became... 

McCall, D. W., Douglass, D. C., and Anderson, E. W. (1963). Self-diffusion study by means of nuclear magnetic resonance spin-echo technique. Ber. Bunsenges. Phys. Chem. 67, 336-340. 

According to Eqs. (4)-(6), the molecular mean square displacements and thus the self-diffusion coefficients may be determined from the slope of a semilogarithmic plot of the PFG NMR signal F versus (Sg) The observation time of self-diffusion is the separation between the two field gradient pulses, t. Owing to their relatively large gyromagnetic ratio and to their natural abundance of 1, protons provide very suitable conditions for NMR self-diffusion studies, but C 44), F 45), and Xe 46-48) resonances have also been used successfully in recent PFG NMR studies of zeolites. 

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