Complex permittivity composite model

There appears some disagreement of the calculated complex permittivity e (v) with the experimental data [17, 42] recorded in the submillimeter wavelength range—that is, from 10 to 100 cm-1. It is evident from Fig. 15 and more clearly from Fig. 16 that a theoretical loss is less in this spectral interval than the experimental one. The reason of such a discrepancy can be explained as follows. Some additional mechanism of dielectric loss possibly exists in water. Such a mechanism will be studied in Sections VII, IX, and X, where we shall propose composite molecular models of water. 

We shall combine the (A) and (B) mechanisms within a composite HC-HO model capable of describing the complex permittivity e (v) and absorption coefficient a(v) of liquid H20 and D20. The theory will be given in a simple analytical form. We shall see that such a modeling could give an agreement with... 

We employ the linear response theory based on a phenomenological molecular model of water. In the proposed composite HC-HO model the complex permittivity is represented as the sum... 

Figure 35. Frequency dependence in the submillimeter wavelength region of the real (a, b) and imaginary (c, d) parts of the complex permittivity. Solid lines Calculation for the composite HC-HO model. Dashed lines Experimental data [51]. Dashed-and-dotted lines show the contributions to the calculated quantities due to stretching vibrations of an effective non-rigid dipole. The vertical lines are pertinent to the estimated frequency v b of the second stochastic process. Parts (a) and (c) refer to ordinary water, and parts (b) and (d) refer to heavy water. Temperature 22.2°C.

Wagner (1914) gave an approximate treatment of the important practical case where a very highly insulating dielectric suffers from inclusions of conductive impurities. Taking the model where the impurity (relative permittivity e2, conductivity a2) exists as a sparse distribution of small spheres (volume fraction f) in the dielectric matrix (relative permittivity e, negligible conductivity), he derived equations for the components of the complex relative permittivity of the composite ... 

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