Self-similarity dielectric relaxation

We have studied a variety of transport properties of several series of 0/W microemulsions containing the nonionic surfactant Tween 60 (ATLAS tradename) and n-pentanol as cosurfactant. Measurements include dielectric relaxation (from 1 MHz to 15.4 GHz), electrical conductivity in the presence of added electrolyte, thermal conductivity, and water self-diffusion coefficient (using pulsed NMR techniques). In addition, similar transport measurements have been performed on concentrated aqueous solutions of poly(ethylene oxide)... 

In the following section the power of the fractional derivative technique is demonstrated using as example the derivation of all three known patterns of anomalous, nonexponential dielectric relaxation of an inhomogeneous medium in the time domain. It is explicitly assumed that the fractional derivative is related to the dimension of a temporal fractal ensemble (in the sense that the relaxation times are distributed over a self-similar fractal system). The proposed fractal model of the microstructure of disordered media exhibiting nonexponential dielectric relaxation is constructed by selecting groups of hierarchically subordinated ensembles (subclusters, clusters, superclusters, etc.) from the entire statistical set available. 

Another most important question in anomalous dielectric relaxation is the physical interpretation of the parameters a and v in the various relaxation formulas and what are the physical conditions that give rise to these parameters. Here we shall give a reasonably convincing derivation of the fractional Smoluckowski equation from the discrete orientation model of dielectric relaxation. In the continuum limit of the orientation sites, such an approach provides a justification for the fractional diffusion equation used in the explanation of the Cole-Cole equation. Moreover, the fundamental solution of that equation for the free rotator will, by appealing to self-similarity, provide some justification for the neglect of spatial derivatives of higher order than the second in the Kramers-Moyal expansion. In order to accomplish this, it is first necessary to explain the concept of the continuous-time random walk (CTRW). 

The idea that a solute changes the structure of the solvent is very old. We have mentioned an application of this idea in Sec. 2.3 to explain some puzzling observations (Chadwell, 1927). The addition of solutes such as ether or methyl acetate to water was found to decrease the compressibility of the system in spite of the fact that the compressibilities of these pure solutes are about three times larger than the compressibility of pure water. Similar attempts to explain the effect of solute on viscosity, dielectric relaxation, self-diffusion, and many other properties have been suggested in the literature. ... 

Based on the experimental observation that self-diffusion of water molecules in ice has an activation energy similar to that of the dielectric and mechanical relaxations ( — 13.5 kcal./mole), some investigators (I2J) see a connection between the formation and migration of valence defects... 

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