Sigmoidal dielectric model

Fi. 4.30 A sigmoidal dielectric model smoothly varies the effective permittivity from SO to 1 as shown. 

This model has been, and still is, widely used especially for some specific applications. An older use is in the description of dielectric saturation effects around ions. The origin is the Debye model, not completely satisfying and thus subjected over the years to many variants. The spherical symmetry of the problem suggests the use of a distance dependent function s(r). The functions belonging to this family are often called sigmoidal functions because their spatial profile starts from a low value and increases monotonically to reach... 

From the theoretical point of view, no complete theories exist able to relate the microscopic orientation fluctuations of permanent dipoles to macroscopic dielectric properties of macromolecules in solution. A phenomenological understanding of the (j shape is possible by considering the plane rotator model which possesses a sigmoidal power spectrum decreasing when the frequency is increased. On the hypothesis that, in the interval (m, co + rfm), the emitted noise by the fluctuating permanent dipoles corresponds to a noise resistance such as... 

The results of the D-B and H-H models, as shown in a comparison of Figures 4-7 with Figures 32-35 are very similar. In both cases a = 0.6 and approximately independent of either the K or the shape parameter The )3 parameter changes in a sigmoidal pattern from about 0.35 to 1.0 for the D-B model and from 0.35 to about the 0.7-0.8 range for the H-H model. In other words, both the D-B and the H-N models predict the shape of the dielectric relaxation process to have nearly the same dependence on sphere diameter or segment asymmetry and both models have very different starting points. 

Jayaram et al. performed a systematic study of the effects of electrostatic interactions on the counterion condensation around DNA. They used a 20-mer of electrically neutral sodium-DNA, with the DNA fixed in its canonical B form. The mobile counterions were placed randomly in a 50 A radius cylinder around the DNA, and the solvent was modeled as a dielectric continuum. Four dielectric treatments, ranging from Coulombic interactions with constant dielectric to a dielectric saturation model with a modified Coulombic potential introducing dielectric discontinuity, were studied. The dielectric saturation model used a modified Hingerty sigmoidal function... 

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