Dielectric constant-temperature curve

Apart from an occasional reference to polymers, the equations developed in Sections IV and V are general and not necessarily limited to long-chain molecules. However, their application to small molecules is handicapped by the lack of information on Dg, though y can usually be estimated reasonably well because of the preponderance of x-ray data on small molecules. Smyth has reviewed, quite extensively, the dielectric properties of polar solids. In his work he attributed the low values of e to solidification, which usually fixes the molecule with such rigidity in the lattice that little or no orientation of the dipoles in an externally applied field is possible. Therefore the orientation polarization is zero, and the dielectric constant depends on the same factors as those in the nonpolar molecular solid. The dielectric constant temperature curves of these polar molecules show curves of great discontinuity at the melting point, for in... 

In the range of frequencies where dipole movement is finite but incomplete there is some internal friction as the movement of dipoles fails to keep in step with the change in field. This causes loss of electric power and some building up of heat in the dielectric. This can be characterized by various parameters such as power factor and loss factor. The peak in the power factor-frequency curves coincides with the point of inflection in the dielectric constant-frequency curves and is also shifted by raising the temperature (Fig. 4.4). 

At large distances the curve of Fig. 8b is a plot of — (c2/ r)> where t is the macroscopic dielectric constant of the solvent at the temperature considered. For small values of r the curve deviates from this value but at every point the slope of the curve must represent the mean intensity of the mutual attraction or repulsion at the particular temperature considered. If the curve of Fig. 86 for dissociation in solution is to be useful, every point on this curve must belong to the same temperature T. That is to say, when we consider any change in the distance r between the ions, we are interested in an isothermal change in r. 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

It should be noted that the properties of a CTC depend to a considerable degree on the conditions of their preparation. Temperature increase, in particular, favors the accumulation of complete charge transfer states in a CTC. In the case of a CTC obtained in solution, the increase of dielectric constant of the solvent has the same effect. The method of preparation of a CTC also affects the kinetic curves of the accumulation and depletion of complete transfer states arising at protoirradiation. 

Most people assume all X7Rs are the same. They actually think it is a specific material, and that all vendors with an X7R capacitor on hand are equivalent competitors. That is simply not true. Even a given vendor can have several X7R formulations with dielectric constants ranging from 1000 to 7000. X7R only refers to a material with a TCC of 15% over -55°C to 125°C. And that too, only with zero applied volts (or close to it). Take a look at Figure 4-6. These are curves extracted and superimposed (rather painfully) from the Epcos database of MLCCs. You can clearly see that all these are labeled X7R, but their temperature profile visibly falls into two main categories. So, if somebody says to you the... 

Plotting ixbase VS. pH gives a sigmoidal curve, whose inflection point reflects the apparent base-pAi, which may be corrected for ionic strength, I, using Equation 6.11 in order to obtain the thermodynamic pATa value in the respective solvent composition. Parameters A and B are Debye-Hiickel parameters, which are functions of temperature (T) and dielectric constant (e) of the solvent medium. For the buffers used, z = 1 for all ions ao expresses the distance of closest approach of the ions, that is, the sum of their effective radii in solution (solvated radii). Examples of the plots are shown in Figure 6.12. 

The effect of exciplex dissociation (process MC) on the over-all kinetics of molecular fluorescence decay has been examined by Ware and Richter34 for the system perylene-dimethylaniline in solvents with dielectric constants (e) varying from 2.3 to 37. In low dielectric media (e = 2.3-4) the perylene fluorescence response may be fitted to a two-component exponential curve and exciplex emission is also observed, whereas in more polar solvents (e > 12) exciplex fluorescence is absent (at ambient temperatures) and the molecular fluorescence decays exponentially. These observations are consistent with both an increase in exciplex stability toward molecular dissociation with solvent polarity (Eq. 13) and the increased probability of dissociation into solvated ions... 

If we measure the dielectric constant as a function of temperature, then, it should be a linear function of 1 /T and from the constants of the curve we can find both the electronic polarizability ao and the dipole moment... 

Phase transitions may be detected by the corresponding anomaly in the temperature dependence of the quadrupole coupling constant. For example, in monomethylamine a phase transition occurs at 80 °K and a hysteresis loop has been observed in the frequency vs. temperature curve with a broadening of the lines just before the transitions 24> This transition has been confirmed by the N.M.R. study of the proton line width and by the dielectric behavior, but no precise explanation has been given. 

FIG. 11.3 Complex dielectric functions of poly(vinyl acetate). (A) Dielectric loss s"[T) as a function of temperature for three frequencies. (B) Temperature dependence of the dielectric constant s (v) (top panel) and the dielectric loss s"(v) (bottom panel) of the complex dielectric function curves from right to left in the temperature range from 377 to 313 K with steps of 4 K and 312.5,311.5,310.5,310 K. (C) 3D plot of the dielectric loss s"[ ,T). The author is much indebted to Prof. M. Wubbenhorst (KU Leuven) for his illustrative measurements on PVAC, especially for the benefit of this book. 

Fig. 9 Longitudinal dielectric constant of DyV04 vs. temperature, experimental (solid curve) and theoretical (dot-dash curve). The influence of the external pressure P = 10cm is shown by the dashed curve...

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