Dielectric concentration profiles

One of the drawbacks of ellipsometry is that the raw data cannot be directly converted from the reciprocal space into the direct space. Rather, in order to obtain an accurate ellipsometric thickness measurement, one needs to guess a reasonable dielectric constant profile inside the sample, calculate A and and compare them to the experimentally measured A and values (note that the dielectric profile is related to the index of refraction profile, which in turn bears information about the concentration of the present species). This procedure is repeated until satisfactory agreement between the modeled and the experimental values is found. However, this trial-and-error process is complicated by an ambiguity in determining the true dielectric constant profiles that mimic the experimentally measured values. In what follows we will analyze the data qualitatively and point out trends that can be observed from the experimental measurements. We will demonstrate that this... 

NMR spectroscopy shares its ability to provide information about the elementary steps of diffusion and the resulting concentration profiles with other spectroscopic techniques like IR [45,46], neutron [47-49] and dielectric [50, 51] spectroscopy. With respect to its ability to follow molecular diffusion paths between himdreds of nanometers up to hundreds of micrometers, however, it is unique. Measurements of this type are based on the apphcation of an inhomogeneous magnetic field. In the technique, being so far the most... 

The dielectric response of metal-PI structures was supposed to be determined by water diffusion into the PI under the metallization. Therefore, a numerical system was simulated, consisting of a partially masked surface exposed to the ambient gas and where the in-diffusing species is consumed by a chemical reaction. Fig. 5 defines the problem ometry. Concentration profiles were calculated using standard finlte-difKrence methods in two dimensions. It is noteworthy to remark that all simulations were performed... 

Notice that now the dielectric constant has disappeared from this relation. This means that the electrostatic contribution in a solvent of high dielectric constant like water, is now much smaller than in the primitive model, and that the hard core term plays a much larger role in the makeup of the concentration profile near the electrode. 

Figure 48 The cation concentration profiles for the systems of Figure 46 with (circles) and without (no circles) the local dielectric coefficient correction.

The transfer matrix formalism enables us to find the modal field profile in the case of an arbitrary arrangement of annular concentric dielectric rings. However, we are especially interested in structures that can confine the modal energy near a predetermined radial distance, i.e. within the defect. 

Pore size and dielectric constant s of water in pores exhibit a strong effect on proton distributions, as studied in Eikerling. Model variants that take into account the effect of strongly reduced s near pore walls ° and the phenomenon of dielectric saturation ° 2° lead to nonmonotonous profiles in proton concentration with a maximum in the vicinity of the pore wall. 

More recently, Yang and Thompson implemented this type of sensor in FI manifolds, which they consider ideal environments for relating the sensor s hydrodynamic response to the analyte s concentration-time profile produced by the dispersion behaviour of sample zones. Network analysis of the sensor generates multi-dimensional information on the bulk properties of the liquid sample and surface properties at the liquid/solid interface. The relationship between acoustic energy transmission and the interfacial structure, viscosity, density and dielectric constant of the analyte have been thoroughly studied by using this type of assembly [171]. 

The results for the density profiles (in mole/dm3 unit) are shown in Fig. 8. Comparing the results to Fig. 7 of [41] (where a similar geometry was used but without dielectric boundaries), it can be seen that the presence of dielectric inhomogeneity has a large effect on the charge distribution in the channel. In our earlier study [41] both the Ca++ and Na+ ions were concentrated in the center of the filter. On the contrary, our present results indicate that the Ca++... 

The potential profile is the least reliable feature of the GC model. Certainly, Monte Carlo calculations in which the ions are represented as charged hard spheres in a dielectric continuum show that the GC potential profile is seriously in error at high electrolyte concentrations. However, it is sometimes used at very low concentrations to obtain an approximate idea of potential variation in the diflhse layer. 

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