Dielectric spectroscopy description

Fig. 4.5 Scaling representation of the spin-echo data at Q nax- Different symbols correspond to different temperatures. Solid line is a KWW description (Eq. 4.8) of the master curve, a Polyurethane at Qmax=l-5 A L The shift factors have been obtained from the superposition of the NSE spectra. (Reprinted with permission from [127]. Copyright 2002 Elsevier), b Poly-(vinyl chloride) at Qmax=l-2 A L The shift factors have been obtained from dielectric spectroscopy. (Reprinted with permission from [129]. Copyright 2003 Springer, Berlin Heidelberg New York)...

Following the general plan of our chapter, we will discuss here a universal view of scaling which is widely employed in modem dielectric spectroscopy. We will show how this concept can be applied to the description of disordered materials and how these ideas can be useful in the determination of the topological parameters of these systems. 

Equations (1.23a), (1.23b) and (1.23c) are, respectively, Cole-Cole (C-C) (0Davidson-Cole (D-C) (0Havriliak-Negami (0empirical laws. The calculations of permittivity on the base of Eq. (1.22) with relaxation function corresponding to KWW law (see Eq. 1.20) yield Eq. (1.23c) with y8 = a - [30]. Expression (1.23c) delivers pretty good description of experimental data obtained by dielectric spectroscopy, radiospectroscopy and quasielastic neutron scattering. It can be shown, that the physical mechanism, underlying the expressions (1.23) is the distribution of relaxation times in a system. Namely, Equation (1.23) can be derived by the averaging of simple Debye response (1.21) with properly tailored distribution function of relaxation times F(x) ... 

Description of the Experimental Set-up for Simultaneous Small and Wide Angle X-ray Scattering and Dielectric Spectroscopy (SWD)... 

The particular choice of the authors was rather to put emphasis on experimental techniques that are either specifically relevant or powerfiil with respect to ferroelectric polymers and fenoelectrets or represent recent experimental developments and trends. In this sense, room was given to nonlinear dielectric properties that can be probed by nonlinear dielectric spectroscopy and various types of hysteresis experiments. Besides a systematic description of piezoelectric and inverse piezoelectric techniques, we have added dielectric resonance spectroscopy as an all-round approach yielding elastic, piezoelectric, and dielectric properties of polymer electrets in a single dielectric measurement. 

A brief description of relationships between dielectric spectroscopy and molecular motions follows from the reviews by Adachi, et al.(2) and Watanabe(3). The... 

Historically, the bulk lubricant has been studied by dielectric spectroscopy and interpreted according to the Debye relaxation theory [3,4]. In impedance terms the system can also be represented according to a theory of colloidal dispersions or polycrystalline media composed of spheres of vastly different conductivities, where the contaminants become a more conductive phase suspended inside the less conductive additive/base oil matrix [6, 34]. Alternatively, when the contaminants are absent, the polar additives can be considered as a conductive discontinuous phase suspended inside insulating continuous base oil. Initially the description of the impedance representation of the fresh, uncontaminated oil will be provided, and then the effects of oxidative degradation and contaminants will be discussed. 

The reflectivity of bulk materials can be expressed through their complex dielectric functions e(w) (i.e., the dielectric constant as a function of frequency), the imaginary part of which signifies absorption. In the early days of electroreflectance spectroscopy the spectra were often interpreted in terms of the dielectric functions of the participating media. However, dielectric functions are macroscopic concepts, ill suited to the description of surfaces, interfaces, or thin layers. It is therefore preferable to interpret the data in terms of the electronic transitions involved wherever possible. 

It should, however, be noted that there exist rather complex and nontransparent descriptions made [15] in terms of the absorption vibration spectroscopy of water. This approach takes into account a multitude of the vibration lines calculated for a few water molecules. However, within the frames of this method for the wavenumber1 v < 1000 cm-1, it is difficult to get information about the time/spatial scales of molecular motions and to calculate the spectra of complex-permittivity or of the complex refraction index—in particular, the low-frequency dielectric spectra of liquid water. 

The extension of continuum models to complex environments is further analyzed by Ferrarini and Corni Frediani, respectively. In the first contribution the use of PCM models in anisotropic dielectric media such as liquid crystals is presented in relation to the calculation of response properties and spectroscopies. In the second contribution, PCM formulations to account for gas-liquid or liquid-liquid interfaces, as well for the presence of a meso- or nano-scopic metal body, are presented. In the case of molecular systems close to metal bodies, particular attention is devoted to the description of the surface enhanced effects on their spectroscopic properties. 

An innovative approach due to Haider et al. [113] may help to sidestep the challenges involved in explicit molecular dynamics simulation and obtain information on these slow dynamics. The authors use the results of dielectric reflectance spectroscopy to model the IL as a dielectric continuum, and study the solvation response of the IL in this framework. The calculated response is not a good description of the subpicosecond dynamics, a problem the authors ascribe to limited data on the high frequency dielectric response, but may be qualitatively correct at longer times. We have already expressed concern regarding the use of the dielectric continuum model for ILs in Section IV. A, but believe that if the wavelength dependence of the dielectric constant can be adequately modeled, this approach may be the most productive theoretical analysis of these slow dynamics. 

TVn efficient description of ion pairing is based on the chemical model of electrolytes. Chemical models of electrolytes take into account local structures of the solution due to the interactions of the ions and solvent molecules. The underlying information stems from spectroscopic, kinetic, and electrochemical experiments, as well as from dielectric relaxation spectroscopy. The postulated structures include ion pairs, higher ion aggregates, and solvated and selectively solvated ions [183]. 

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