Permittivity complex

Just like compliance, the permittivity is complex and can be resolved into real and imaginary components  

The Physical Chemistry of Materials Energy and Environmental Applications 

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Principles in Processing Materials. In most practical apphcations of microwave power, the material to be processed is adequately specified in terms of its dielectric permittivity and conductivity. The permittivity is generally taken as complex to reflect loss mechanisms of the dielectric polarization process the conductivity may be specified separately to designate free carriers. Eor simplicity, it is common to lump ah. loss or absorption processes under one constitutive parameter (20) which can be alternatively labeled a conductivity, <7, or an imaginary part of the complex dielectric constant, S, as expressed in the foUowing equations for complex permittivity ... 

Dielectric measurements were used to evaluate the degrees of inter- and intramolecular hydrogen bonding in novolac resins.39 The frequency dependence of complex permittivity (s ) within a relaxation region can be described with a Havriliak and Negami function (HN function) ... 

Knowledge of complex permittivities of appropriate electrolyte solutions is useful in assessing interactions of microwave radiation with biological tissues. A full study and analysis of complex permittivities of sodium chloride solutions as a function of concentration, temperature, and microwave frequency (207) has laid the foundations for a similar investigation of calcium salt solutions. 

The Impedance Analyzer was controlled by a 9836 Hewlett-Packard computer which also controlled the time-tempe ture of the press. Measurements at frequencies from 5 to 5 x 10 Hz were taken at regular Intervals during the cure cycle and converted to the complex permittivity. Further details of the experimental procedure has been given elsewhere [10]. 

Measurements of capacitance C and conductance G were used to calculate the complex permittivity e = e -ie"... 

The dielectric measurements were carried out in a plate capacitor and frequency dependences of complex permittivity e = e — is (e and e" being its real and imaginary part, respectively) were determined [33] in the range /= 20 Hz- 200 kHz. 

The dielectric behavior of nonionized PAAm network and a ionized P(AAm/MNa) network with xMNa = 0.03 in deionized-water-acetone mixtures was also studied [33]. High values of complex permittivity e were found for both networks (Fig. 19). For the PAAm network, the dependence of both component e and e" on acetone a is continuous. On the other hand, for the ionized network the jumpwise decrease in swelling at the transition is accompanied by a jumpwise increase in the values of both components of e at all... 

A jumpwise volume change in the transition correlates with a jumpwise change in the shear equilibrium modulus, the refractive index, the stress-optical coefficient and in the components of complex permittivity e and complex modulus G. ... 

In particular, VF2/F3E copolymers have also been the subject of extensive research [6,17,96]. As an example to illustrate the dielectric behavior of these copolymers, the temperature dependence of the real and the imaginary part of the complex permittivity at two different frequencies (1 and 100 kHz) are shown in Figs. 23a and 23b respectively. The measurements correspond to the 60/40 copolymer. The data have been collected by using a sandwich geometry with gold evaporated electrodes [95]. Frequencies of 103 and 106 Hz have been used by employing a 4192 A HP Impedance Analyzer. From inspection of Fig. 23b... 

As an example of the Curie transition for other VF2/F3E compositions, measurements of e and e" as a function of temperature and f = 1 kHz are shown in Figs. 25a and 25b. The complex permittivity function of polymeric materials has been shown to follow the Havriliak-Negami phenomenological equation [99] ... 

Fig. 25a, b. Temperature dependence of a. the real part, e and of b. the imaginary part, e" of the complex permittivity for copolymers with different compositions... 

ASTM D2520, 2001. Standard test methods for complex permittivity (dielectric constant) of solid insulating materials at microwave frequencies to 1650°C. 

Mathematical equations, presented by Maxwell in 1864, are able to predict the behavior of microwave radiation s interaction with any type of food in any geometry. In order to do this, a single pair of parameters describing the electrical (or dielectric) properties of the food are required. This pair of parameters is known as the complex permittivity, or as is more commonly called in the United States, the complex dielectric constant. This parameter pair is defined as ... 

ASTM 1986. Standard Methods Qf Test for Complex Permittivity (Dielectric Constant) of Solid Electrical Insulating Materials at Microwave Frequencies and Temperatures 1q 1650°C. Document D 2520-86 (Reapproved 1990). Philadelphia, PA. American Society for Testing and Materials (ASTM). 

We do not know theoretical descriptions other than ours of the dielectric/FIR spectra applicable for water in the range from 0 to 1000 cm-1, which were made on a molecular basis in terms of complex permittivity s(m). 

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 liquid-state theory—in particular, that capable of describing the wideband spectra s = s — if of the complex permittivity and of absorption... 

A brief list of basic assumptions used in the ACF method precedes the detailed analysis of the results of calculations. The derivation of the formula for the spectral function is given at the end of the section. The calculations demonstrate a substantial progress as compared with the hat-flat model but also reveal two drawbacks related to disagreement with experiment of (i) the form of the FIR absorption spectrum and (ii) the complex-permittivity spectrum in the submillimeter wavelength region. We try to overcome these drawbacks in the next two sections, to which Fig. 2c refers. 

However, the so-corrected hat-curved model still does not give a perfect agreement with the experiment, since it does not allow us to eliminate the second drawback (ii), namely, disagreement with experiment of the calculated complex permittivity in the submillimeter wavelength region. 

Employing the additivity approximation, we find dielectric response of a reorienting single dipole (of a water molecule) in an intermolecular potential well. The corresponding complex permittivity jip is found in terms of the hybrid model described in Section IV. The ionic complex permittivity A on is calculated for the above-mentioned types of one-dimensional and spatial motions of the charged particles. The effect of ions is found for low concentrated NaCl and KC1 aqueous solutions in terms of the resulting complex permittivity e p + Ae on. The calculations are made for long (Tjon x) and rather short (xion = x) ionic lifetimes. 

We have introduced the effective complex susceptibility x ( ) = X,( )+ X ) stipulated by reorienting dipoles. This scalar quantity plays a fundamental role in subsequent description, since it connects the properties and parameters of our molecular models with the frequency dependences of the complex permittivity s (v) and the absorption coefficient ot (v) calculated for these models. 

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