Dispersion of the dielectric constant

An alternative approach that was used in the past was to treat the photoelectrochemical cell as a single RC element and to interpret the frequency dispersion of the "capacitance" as indicative of a frequency dispersion of the dielectric constant. (5) In its simplest form the frequency dispersion obeys the Debye equation. (6) It can be shown that in this simple form the two approaches are formally equivalent (7) and the difference resides in the physical interpretation of modes of charge accumulation, their relaxation time, and the mechanism for dielectric relaxations. This ambiguity is not unique to liquid junction cells but extends to solid junctions where microscopic mechanisms for the dielectric relaxation such as the presence of deep traps were assumed. 

Studies of the dispersion of the dielectric constant, especially those of Oncley 81), 83), 84), have yielded most of the data now available on the relaxation times of proteins. Measurements already obtained, expressed as T values in water at 25°, range from about tO" sec. for insulin, to about 250 10 sec. for the longer relaxation times of edestin and horse serum y-pseudoglobuKn. Relaxation times between 10 and 10" sec. have been determined for a nmnber of peptides and amino acids. Thus a range of more than 10 in relaxation times has been covered in studies already reported. Further extension of the method to longer relaxation times, involving measurements at lower frequencies, is now being carried on by Dr. Oncley and his associates. 

Fig. 7. Schematic diagram of anomalous dispersion of the dielectric constant the specific conductivity...

There has been much controversy in the past several years concerning the relation of the dispersion of the dielectric constant to the molecular dipole-moment correlation function (see Titulaer and Duetch, 1974). Fatuzzo and Mason (1967) have shown that the autocorrelation function of the net dipole moment of a sphere imbedded in a medium of the same dielectric constant is related to the frequency-dependent dielectric constant by... 

DISPERSION OF THE DIELECTRIC CONSTANTS OF /TRIGLYCINE SULFATE/ IN THE VERY FAR INFRARED. 

First of all, the model of the solvent was materially improved. In 1969 Dogonadze and Kuznetsov took into account the spatial correlation of the polarization fluctuations in the medium. In Refs. 43-46 the frequency dispersion of the dielectric constant was also taken into account, t Using this model, Vorotyntsev et performed quantum mechanical calculations of the... 

A lot of efforts have been done to improve overall performance, namely the transmission speed and bandwidth. Unfortunately the large dispersion of the dielectric constant from microwave to optical frequency produces a delay between optical and electrical RF signals that travel in the material, putting intrinsic limitations on the possibility of improvements. 

There are other physical measurements which reflect molecular mobility and can be related to relaxation times and friction coefficients similar to those which characterize the rates of viscoelastic relaxations. Although such phenomena are outside the scope of this book, they are mentioned here because in some cases their dependence on temperature and other variables can be described by reduced variables and, by means of equation 49 or modifications of it, free volume parameters can be deduced which are closely related to those obtained from viscoelastic data. These include measurements of dispersion of the dielectric constant, nuclear magnetic resonance relaxation, diffusion of small molecules through polymers, and diffusion-controlled aspects of crystallization and polymerization. 

The dispersion of the dielectric constant has been rather extensively used to study the pressure dependence of relaxation processes and the derivative dT/dP)r as in Table 11 -III, because it is so much easier to make dielectric measurements than mechanical measurements under high confining pressures." " ... 

The demonstration here given of the predominant role of counter-ion repulsion in the limitation of the fluctuations in the distribution of counterion have also interesting implication for the interpretation of the dispersion of the dielectric constant. In Oosawa s theory, the relaxation time Tj, associated with the A th fluctuation is ... 

Fig. 11. Effect of dielectric constant of dispersed particle on the ER effect in a polymer gel. The increment in shear storage modulus induced by an ac electric field of 0.4 kV/mm is plotted as a function of the real part of the dielectric constant of the particle...

At optical frequencies in the absence of dispersion (absorption), the dielectric constant equals the square of the refractive index ... 

FIG. 11.6 Dispersion curves of the dielectric constant (s ) and dielectric absorption (s") in the regions of electrical, infrared and optical frequencies. 

Surface plasmons (SPs) are surface electromagnetic waves that propagate parallel along a metal/dielectric interface. For this phenomenon to occur, the real part of the dielectric constant of the metal must be negative, and its magnitude must be greater than that of the dielectric. Thus, only certain metals such as gold, silver, and aluminum are usually used for SPR measurements. The dispersion relation for surface plasmons on a metal surface is ... 

The measurements of the Debye-Falkenhagen effect are generally made with reference to potassium chloride the results for a number of electrolytes of different valence types have been found to be in satisfactory agreement with the theoretical requirements. Increase of temperature and decrease of the dielectric constant of the solvent necessitates the use of shorter wave lengths for the dispersion of conductance to be observed these results are also in accordance with expectation from theory. 

In order to induce the proton ordered XI phase, some thermal treatments are required. Typically we kept the sample at 45K for 12 hours for nucleation and then it was annealed at 65K for a few days. Even after the heat treatment, samples do not always undergo the proton ordering transition. So, before the measurements of Raman spectra, we measured the temperature dependence of the dielectric constant at several low frequencies (20, 30, 60,100, 200,400 Hz). In addition to the dispersions around 160 and 230K(Fig. 1(a)), if a sample shows a clear dispersion around 90K as shown Fig. 1(b), it has enough high proton mobility and we found empirically that the proton ordering phase transition occurred with much higher probability. 

Another point worth mentioning is the use of the metal long-wavelength dielectric function. No dispersion was allowed in the model. The wave-vector dependence of the dielectric constant is important at close proximity to the surface as was already remarked in the context of the image calculations. This approximation may be reasonable away from the surface, distances for which the LFE is most appropriate. 

This means of course, that at such frequencies the effect of the permanent moment has vanished, and that only the part of the dielectric constant due to deformation of the atoms and molecules remains. According to this theory non-polar substances, for which fi equals zero, should not show anomalous dispersion, and this is borne out by experiment. The effect will become evident at frequencies at which the product, o>t, has an appreciable value, From equation (28) for the time of relaxation, t, anomalous dispersion should appear at relatively lower frequencies (a) if the molecules have large radii, r, (b) if the viscosity, 77, is high, and (c) if the temperature is low, all of which have been observed experimentally. Since equation (27) is complex it follows that the dielectric constant, D, has a real and an imaginary part. Debye lias shown that the real part, Df, which corresponds to the measured dielectric constant, follows the equation... 

At lower frequencies (Debye dispersion region), charge transport is limited by the minority carriers which form a bottleneck/ Applied field and current are no longer in phase this results in a polarization and rise of the dielectric constant from its high-frequency value. The conductances of the different defect types act as though in series. The minority carrier determines the over-all conductivity. 

Figure 18, Frequency dependence of the a-c conductivity and of the dielectric constant after Steinemann (140), (1) Pure ice, (2) Slightly impure ice, (a) Conductivity, (b) Dielectric constant. Curves for pure ice closely follow Equations 12a and 14, except for an incipient low-frequency dispersion that may result from very slight impurity content or from electroae polarization. Debye dispersion between 10 and 10 cps. As the impurity content increases (curves 2), the low-frequency dispersion (Steinemann s F dispersion) becomes more prominent and tends to coalesce with the Debye dispersion. Interpretation then becomes difficult. At still higher concentrations, the two dispersions separate again (see Ref. 140). A slight anisotropy of the dielectric constant, observed by Decroly et al. (34) for measurements parallel and perpendicular to the c axis of single crystals, has not been considered...

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