Dielectric permittivity spectrum

Figure 51 Dielectric permittivity spectrum of the average erythrocyte fitted to the single-shell model. Experimental results are figured by points, and the fitting results by a soHd line. (From Ref 70. With permission from Elsevier Science B.V.)...

Bias-induced reverse piezoelectric response Broadband dielectric spectroscopy (BDS) Dielectric permittivity spectrum Dielectric resonance spectroscopy Elastic modulus Ferroelectrets Electrical breakdown Acoustic method Characterization Dynamic coefficient Interferometric method Pressure and frequency dependence of piezoelectric coefficient Profilometer Quasistatic piezoelectric coefficient Stress-strain curves Thermal stability of piezoelectricity Ferroelectric hysteresis Impedance spectroscopy Laser-induced pressure pulse Layer-structure model of ferroelectret Low-field dielectric spectroscopy Nonlinear dielectric spectroscopy Piezoelectrically generated pressure step technique (PPS) Pyroelectric current spectrum Pyroelectric microscopy Pyroelectricity Quasistatic method Scale transform method Scanning pyroelectric microscopy (SPEM) Thermal step teehnique Thermal wave technique Thermal-pulse method Weibull distribution... 

At low and medium frequencies (/ < IGHz), dielectric spectra are commonly taken in the parallel-plate geometry (cf Fig. 6) that consists of two flat elecfrodes of the area A that sandwich a sheet or film of the material under investigation with thickness d. From the complex capacitance, the dielectric permittivity spectrum can then be derived by... 

Fig. 7 Dielectric permittivity spectrum e (m) and dielectric loss spectra e (m) of a 1 pm thick film of PVDF at selected temperatures...

The first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

Typically, another transparency region exists o>a < co < cox where co, called the optical frequency, denotes the lower bound of the electronic (optical) absorption spectrum. Provided this transparency band is wide (say, co0/cox < 102 typically cox > 1016 s-1 and coa 1013—1014 s 1), one can define the optical dielectric permittivity, sx = 1 +477. ... 

Fig. 4.105. Dielectric absorption spectrum (imaginary part of the complex permittivity, e") of LiBr solutions in acetonitrile at 25 °C. 1, Pure solvent 2, 0.107 M 3,0.194 M 4,0.303 M 5,0.479 M 6, 0.657 M. S and IP indicate the frequency regions of the relaxation processes of solvent and solute. For the sake of clarity, experimental data ( ) are added only for curves 1, 4, and 6 (J. Barthel, H. Hetzenauer, and R. Buchner, Ber. Bunsenges. Phys. Chem. 96 988, 1992).

Keywords aerogels, dielectric permittivity, response function, impedance spectrum, Maxwell-Wagner polarisation... 

The far-infrared (FIR) absorption spectrum of low-viscosity liquids contains a broad peak of resonant character with a resonant frequency and intensity which decreases with increasing temperature [14,15]. Phis phenomenon is known as the Poley absorption. It takes its name from the work of Poley [16], who observed that the difference between the high-frequency dielectric permittivity... 

On the other hand, the second LHM component, i.e., the network of thin wires acts as a quasi-medium with a negative effective dielectric permittivity and can be, in the microwave spectrum, characterized by... 

The Hamaker constant can be evaluated accmately using the continuum theory, developed by Lifshitz and coworkers [40]. A key property in this theory is the frequency dependence of the dielectric permittivity, e( ). If this spectrum were the same for particles and solvent, then A=0. Since the refractive index n is also related to t ( ), the van der Waals forces tend to be very weak when the particles and solvent have similar refractive indices. A few examples of values for for interactions across vacuum and across water, obtained using the continuum theory, are given in table C2.6.3. 

To obtain time-dependent properties, we have to pass firom the basic model to an extended version in which the solute is described thorough a time-dependent Schrodinger equations. In this extended version of the model we have also to introduce the time-dependence of the solvent polarization, which is expressed in terms of a Fourier expansion and requires the whole frequency-spectrum of the dielectric permittivity e(o ) of the solvent. 

Since the volume fractions of free, cpf, and bound, cp, water are both unknown, it is convenient to measure the dielectric permittivity in a frequency range where the dielectric loss of bound water may be safely neglected. The relaxation spectrum of free and bound water for our systems will safely satisfy this requirement at the measurement frequency of 75 GHz. In this case, die complex permittivity of the bound water is equal to its real part, i.e., = s -i-... 

The introduction of dye molecules into the liquid crystalline host does not change the majority of the properties of the host, provided that not too much dye is introduced (not more than 1-2%). The N I transition temperature of the liquid crystal, the viscous and elastic properties, the electrical conductivity (provided the dye is not ionic and does not contain ionic impurities), the dielectric permittivities, (provided the dye molecule does not have a large dipole moment), and even the refractive indices all remain the same. The only significant change in the properties of the crystal is the appearance of absorption bands in the visible region of the spectrum and a slight increase in viscosity [151]. 

Figure 8.10 UV-visible spectra of the equimolar mixture of p-nitrophenyl-aza-phenol with [(PP3)RuH2l in the presence of 8 vol% of CHjCN and CHjCN in THF. c = 0.001 M, 230 K. The spectrum in pure THF is given for reference. The resulting media polarity (in parenthesis) was calculated according to the formula e = (cxhf thf + c,e,)/100, where q is the relative concentration of the ith component (Cj p + q = 100% v/v), and e,- is its dielectric permittivity at 230 K [25].

The electrical impedance, conductivity, real and imaginary part of dielectric permittivity and magnetic permeability have been determined using an Agilent E4991A RF Spectrum Analyzer. The used frequency was in the range from 1 MHz to 3 GHz. The sample thickness varied from 0.5 to 1 mm. The frequency step was 20 Hz. The tests were performed at room temperature (=25°C)... 

Usually, the depolarization current is measured to avoid the dc conductivity contribution. The dielectric relaxation spectrum is then obtained by Fourier transform or approximate formulas, e.g., the Hamon approximation [14]. By carefully controlling the sample temperature and accurately measuring the depolarization current, precision measurements of the dielectric permittivity down to 10" Hz are possible [18]. In fast time domain spectroscopy or reflectometry, a step-like pulse propagates through a coaxial line and is reflected from the sample section placed at the end of the line. The difference between... 

In order to obtain information about molecular dynamics from a dielectric relaxation spectrum, the complex dielectric permittivity is related to the correlation function of the electric dipole moment m, of the ith species and the dipole moment Mj of a small (in comparison with the whole sample) macroscopic volume V surrounding m,. Mj is the sum of permanent dipole moments in this volume Mi N being the number of dipole moments in the volume. The... 

Fig. 4.3. The Jonscher representation of the Dissado-Hills dielectric loss spectrum. So is the static permittivity copH is the principal relaxation rate n and m are the Dissado-Hill parameters. Arrows indicate variations of the loss curve on increasing values of the model parameters.

Dielectric spectroscopy is a valuable tool for studying the conformational and dynamic properties of polar macromolecules. The conformational features can be determined by dielectric relaxation strength measurements, whereas the dielectric spectrum provides information on the dynamics of the macromolecules. Phenomenological and molecular theories of dielectric permittivity and dielectric relaxation of polymers have also been developed to elucidate the experimentally observed phenomena. As Adachi and Kotaka have stressed (see Further reading), experimental information depends on each monomer s dipole vector direction as related to the chain contour. A classification of polar polymers into three categories was introduced by Stockmayer type-A polymers, where the dipole is parallel to the chain contour (Fig. 12.4), type-B, where it is perpendicular to the chain contour, and type-C, where the dipoles are located on mobile side groups. For type-A chains, the global dipole moment of each chain is directly proportional to the chain s end-to-end vector R. 

From the value of the resonant frequency and its change with temperature or other external parameters the permittivity of a dielectric sample and its temperature or field dependence can be determined. In case of superconductors, the temperature dependence of the magnetic field penetration depth can be determined [8], Since the mode spectrum of a resonator is controlled both its physical dimensions and by the material properties, the physical dimensions of all resonator components have to be known with tight tolerances. Relative changes of permittivity or penetration depth can be determine with much higher accuracy than absolute values. 

As a result of these very general considerations, one expects the dielectric response function, as expressed by the complex permittivity, k (oj), or the attenuation function, a(oi), of ordinary molecular fluids to be characterized, from zero frequency to the extreme far-infrared region, by a relaxation spectrum. To first order, k (co) may be represented by a sum of terms for individual relaxation processes k, each given by a term of the form ... 

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