Dielectric data, representations

C. M. Roth and A. M. Lenhoff, "Improved parametric representation of water dielectric data for Lifshitz theory calculations,"). Colloid Interface Sci., 179, 637-9 (1996), present another set of parameters for water. 

It is known that in some cases the modulus representation M (oo) of dielectric data is more efficient for dc-conductivity analysis, since it changes the power law behavior of the dc-conductivity into a clearly defined peak [134]. However, there is no significant advantage of the modulus representation when the relaxation process peak overlaps the conductivity peak. Moreover, the shape and position of the relaxation peak will then depend on the conductivity. In such a situation, the real component of the modulus, containing the dc-conductivity as an integral part, does not help to distinguish between different relaxation processes. 

A fuller theoretical analysis of vdW interactions requires recourse to Lifshitz theory [8[. Lifshitz theory requires a description of the dielectric behavior of materials as a function of frequency, and there are several reviews for the calculation of Hamaker functions using this theory. The method described by Hough and White (H-W) [95], employing the Ninham-Parsegian [96] representation of dielectric data, has proved to be most useful. The nonretarded Hamaker constant (for materials l and 2, separated by material 3) is given by... 

In the analysis of the relaxation data we often need to represent the dielectric as a combination of pure resistances and capacitances. The manner of their connection in the dielectric is also assumed. It is through the use of such circuit representation that the dielectric data are analysed. 

A good example of the analysis of the dielectric data using modulus representation is that of the CKN glass (0.4 Ca(N03)2 0.6 KNO3 glass), which is widely cited in the literature. It is shown in Figure 7.03. 

Let us refer in the discussion to a representation of the dielectric data in the time domain, as expressed by the time dependent dielectric function e(t). Figure 6.7 depicts its general shape in a schematic drawing. The a-process and the normal mode show up as two subsequent steps located at the times Tq and Tnm) with heights corresponding to the relaxation strengths Aca and Afnm ... 

Despite some doubts cast on the applicability of the method for this task,37,38 a combined study of ionic motion using electrical relaxation and RMN relaxations suggests that the complex modulus is the most appropriate representation of dielectric data for analysis of ionic conductivity relaxation as in the present case. The points made by Elliot and Roling as well by others authors to discredit the dielectric modulus representation have been refuted and are summarily discussed in a review article, where the authors have answered all the unnecessary criticism on the use of the electric modulus. The representation of the macroscopic data to describe the microscopic motion of the movement of the ions has been also well described, as in the present case, by Ngai et al. ... 

It is hoped that the more advanced reader will also find this book valuable as a review and summary of the literature on the subject. Of necessity, compromises have been made between depth, breadth of coverage, and reasonable size. Many of the subjects such as mathematical fundamentals, statistical and error analysis, and a number of topics on electrochemical kinetics and the method theory have been exceptionally well covered in the previous manuscripts dedicated to the impedance spectroscopy. Similarly the book has not been able to accommodate discussions on many techniques that are useful but not widely practiced. While certainly not nearly covering the whole breadth of the impedance analysis universe, the manuscript attempts to provide both a convenient source of EK theory and applications, as well as illustrations of applications in areas possibly u amiliar to the reader. The approach is first to review the fundamentals of electrochemical and material transport processes as they are related to the material properties analysis by impedance / modulus / dielectric spectroscopy (Chapter 1), discuss the data representation (Chapter 2) and modeling (Chapter 3) with relevant examples (Chapter 4). Chapter 5 discusses separate components of the impedance circuit, and Chapters 6 and 7 present several typical examples of combining these components into practically encountered complex distributed systems. Chapter 8 is dedicated to the EIS equipment and experimental design. Chapters 9 through 12... 

Complex dielectric, modulus, and impedance data representations... 

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)...

For our purpose, it is convenient to classify the measurements according to the format of the data produced. Sensors provide scalar valued quantities of the bulk fluid i. e. density p(t), refractive index n(t), viscosity dielectric constant e(t) and speed of sound Vj(t). Spectrometers provide vector valued quantities of the bulk fluid. Good examples include absorption spectra A t) associated with (1) far-, mid- and near-infrared FIR, MIR, NIR, (2) ultraviolet and visible UV-VIS, (3) nuclear magnetic resonance NMR, (4) electron paramagnetic resonance EPR, (5) vibrational circular dichroism VCD and (6) electronic circular dichroism ECD. Vector valued quantities are also obtained from fluorescence I t) and the Raman effect /(t). Some spectrometers produce matrix valued quantities M(t) of the bulk fluid. Here 2D-NMR spectra, 2D-EPR and 2D-flourescence spectra are noteworthy. A schematic representation of a very general experimental configuration is shown in Figure 4.1 where r is the recycle time for the system. 

The high frequency limit of for this second process is therefore n. The result of the fit is shown in Table III where the mean values of the various parameters and their associated 95% confidence intervals are given. Considering the small amplitude of the second dispersion both in absolute t rms and in relation to the main dispersion the parameters 6m, n and Y are quite well defined, and therefore it may be concluded that the double Debye representation is an acceptable description of the dielectric behaviour of water up to around 2THz. Other alternative interpretations are clearly possible but no attempt has been made here to follow these up at this stage. What is clear is that a small subsidiary dispersion region in the far infrared is necessary to account for all the presently available permittivity data, and that such a dispersion is centred around 650GHz and has an amplitude of about 2.4 in comparison with that of the principal dispersion which is approximately 75. 

In accordance to the data reported in the literature for bulk hyperbranched polyesters [34,35], three relaxation processes are also observed in thin POHOAc films, (Fig. 23) the alpha relaxation process, representing the dynamic glass transition, the beta process, attributed to the relaxation of the ester groups, and the gamma relaxation process, originating from fluctuations of the —OH end groups. The latter two, which are broad and not well-separated from one another, are only distinguishable in the temperature representation of the dielectric spectra (inset, Fig. 23). 

These observations underlie many of the empirical functions commonly used to describe dielectric loss peaks, for instance, the ones proposed by Cole and Cole (100), Davidson and Cole (101), and Havriliak and Negami (102). In the time domain, the empirical KWW relaxation function 0(t) oc exp[—(t/t) ] often provides a reasonable description of experimental data (103). Since the response function is calculated as the negative derivative of 0(t), it behaves as a power law for short times. Moreover, the ubiquitous occurrence of power laws in (dielectric) spectra explains why log-log representations often are preferable power laws present themselves as straight lines when a log-log scale is used. 

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