Complex permittivity empirical formula

Starting with the important example of ordinary water, we choose temperatures 22.2°C and 27°C. We compare our theory with the recorded FIR spectra [42, 56] of the complex permittivity/absorption. At low frequencies we use for this purpose an empirical formula [17] by Liebe et al. these formulas were given also in Section IV.G.2.a. The values of the employed molecular constants are presented in Table VI and the fitted parameters in Table VII. The Reader may find more information about experimental data of liquid H2O and D2O in Appendix 3. 

Figs. 32a-c illustrate the absorption spectra, calculated, respectively, for water H20 at 27°C, water H20 at 22.2°C, and water D20 at 22.2°C dotted lines show the contribution to the absorption coefficient due to vibrations of nonrigid dipoles. The latter contribution is found from the expression which follows from Eqs. (242) and (255). The experimental data [42, 51] are shown by squares. The dash-and-dotted line in Fig. 32b represents the result of calculations from the empirical formula by Liebe et al. [17] (given also in Section IV.G.2) for the complex permittivity of H20 at 27°C comprising double Debye-double Lorentz frequency dependences. 

The theory of wideband complex permittivity of water described in the review drastically differs from the empirical double Debye representation [17, 54] of the complex permittivity given for water by formula (280b). Evolution of the employed potential profiles, in which a dipole moves, explored by a dynamic linear-response method can be illustrated as follows ... 

Studies of dielectric spectra of water in a range of temperatures present a fundamental physical problem that has also important practical applications. Experimental investigation of these spectra has a rich history. We refer here only to a few works. In Downing and Williams [22] and Zelsmann [21] tables for optical constants of water were presented for the temperature T = 300 K and for a wide T-range, respectively. In recent publications by Vij et al. [32] and Zasetsky et al. [33] in addition to original investigations the results of many other works are also discussed. In work by Liebe et. al. [19] a useful empirical double Debye-double Lorentz formula for the complex permittivity e(v, T) is suggested. 

Similarly to above glassy systems, the disordered ferroelectrics, polymers and composites are also characterized by slow relaxation processes. Their quantitative measure is complex dielectric permittivity, which can be described by generalized Debye law [29-31] in the form of the following empirical formulas ... 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

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