Dielectric permittivity spectroscopy

Some authors have used the designation modulus spectroscopy to denote small-signal measurement of M vs. v or co. Clearly, one could also define admittance and dielectric permittivity spectroscopy. The latter is just another way of referring to ordinary dielectric constant and loss measurements. Here we shall take the general term impedance spectroscopy to include aU these other very closely related approaches. Thus IS also stands for immittance spectroscopy. The measurement and use of the complex (< ) function is particularly appropriate for dielectric materials, those with very low or vanishing conductivity, but aU four functions are valuable in IS, particularly because of their different dependence on and weighting with frequency. 

The dielectric permittivity as a function of frequency may show resonance behavior in the case of gas molecules as studied in microwave spectroscopy (25) or more likely relaxation phenomena in soUds associated with the dissipative processes of polarization of molecules, be they nonpolar, dipolar, etc. There are exceptional circumstances of ferromagnetic resonance, electron magnetic resonance, or nmr. In most microwave treatments, the power dissipation or absorption process is described phenomenologically by equation 5, whatever the detailed molecular processes. 

Static solution permittivity, e(c), and static solvent permittivity, es(c), for solutions of various electrolytes at various concentrations (c) have been obtained by dielectric relaxation spectroscopy [44]. Ion-pairs contribute to permittivity if their lifetime is longer than their relaxation time. However free ions do not contribute to permittivity. Thus,... 

A study has been reported of the complexation of ZnBr2 by Br- (as LiBr) in solvents of low basicity but different dielectric permittivities (propylene carbonate, (MeO)2CO and EtOAc) using Raman spectroscopy and calorimetry.1012 Both the [ZnBr3] and [ZnBr4]2 anions are observed, except in the case of EtOAc, where only the 1 1 complex is formed. The dielectric permittivity has no effect on the AHf of the complexes. 

The dielectric spectroscopy study of conductive samples is very complicated because of the need to take into account the effect of dc-conductivity. The dc-conductivity c>o contributes, in the frequency domain, to the imaginary part of the complex dielectric permittivity in the form of additional function a0/(so ). The presence of dc-conductivity makes it difficult to analyze relaxation processes especially when the contribution of the conductivity is much greater than the amplitude of the process. The correct calculation of the dc-conductivity is important in terms of the subsequent analysis of the dielectric data. Its evaluation... 

The classical approach to the fit parameter estimation problem in dielectric spectroscopy is generally formulated in terms of a minimization problem finding values of X which minimize some discrepancy measure S(, s) between the measured values, collected in the matrix s and the fitted values = [/(co,-, x(7 ))] of the complex dielectric permittivity. The choice of S(e,e) depends on noise statistics [132]. 

The result shows that the dc-conductivity can be computed by using the Hilbert transform applied to the real components of the dielectric permittivity function and subtracting the result from its imaginary components. The main obstacle to the practical application of the Hilbert transform is that the integration in Eq. (48) is performed over infinite limits however, a DS spectroscopy measurement provides values of s (co) only over some finite frequency range. Truncation of the integration in the computation of the Hilbert... 

Samples for dielectric spectroscopy were prepared by sputtering 100 nm of Au in an Ar plasma onto both sides of the freely standing films. Disks 9.5 mm in diameter were punched out of the metallized films. These disks were used to measure both the dielectric permittivity with an HP 4192 Impedance Analyzer and the dissipation factor with a GenRad 1615-A Capacitance Bridge. 

In dielectric relaxation spectroscopy, both components of the permittivity are measured as a function of frequency (see the next section). Figure 2 shows the typical shape of both z logf) and s (log/)> where f=(ol2n is the frequency (in Hz). 

Figure 24 compares the global TSDC spectrum of the analyzed polymer with the imaginary permittivity read at different fi-equencies. The results of dielectric relaxation spectroscopy clearly reveal the existence of two peaks, that tend to converge, for lower fi equencies, to the position of the -10 °C and 8 °C peaks detected by TSDC. Such comparison also allows the two peaks found by dielectric relaxation to be attributed to the a and 5 relaxations [179]. 

Computer controlled systems have been developed that enable investigation of the spatial distribution of impedance within resins and in turn the identification of flaws (62). Water trapped within the composite will cause dielectric permittivity to increase, thus revealing its presence. Detection of voids, variation in the cross section of the adhesive layer, ingress of moisture into a joint structure, and characterization of cure in epoxy resin can be achieved with high frequency dielectric spectroscopy (10" -10 Hz) (63). 

Dielectric spectroscopy is a technique which allows one to evaluate the complex dielectric permittivity e = e — ie" as a function of frequency and temperature, where e is the dielectric constant and e" is the dielectric loss [3,12]. A schematic view of a dielectric spectroscopy experiment is shown in Fig. 21.3. A dielectric sample of thickness d and area A is subjected to an alternating electric field of angular frequency w. Through measurements of the complex impedance of the sample it is possible to experimentally determine e [12,18-20]. Dielectric spectroscopy is a very suitable method to study molecular dynamics in polymers above Tg. In this case, segmental motions of the polymeric chains give rise to the so called cc-relaxation process, which can be observed as a maximum in e" and a step-Uke behavior in e as a function of frequency. Both, the intensity of the a relaxation, and the frequency of maximum... 

Amorphous PET (Rhodia S80 from RhodiaSter, = 45000 g/mol) was prepared by quenching from the molten state as described elsewhere [35]. Broad-band dielectric spectroscopy measurements of the complex dielectric permittivity were performed from 10 Hz to 10 Hz by using a BDS-10... 

Dielectric relaxation spectroscopy can monitor molecular and collective modes for motion of liquid crystalline molecules. In ferrolectric liquid crystals based on chiral tilted smectic phases the complex dielectric permittivity e has, in addition to molecular orientational modes, two contributions from the director fluctuations. 

DieieCtriC Spectroscopy. Dielectric experiments obtain the permittivity e (co) and loss "(< ) of materials that has a permanent dipole moments over a wide range of frequency (129,130). The complex dielectric permittivity ( >) = e ((o) — ie"(co) is given by the one-sided Fourier transform of the normalized dipole moment... 

Abstract The physical principles and basic experimental techniques of impedance spectroscopy, i. e. static or frequency dependent dielectric permittivity measurements of sorbent/sorbate systems are given. These measurements can be used to characterize the state of a sorbent material in industrial adsorption processes. Combined with either manometric or gravimetric measurements of adsorption equilibria leading to calibration curves, permittivity measurements also allow fairly simple and quick measurements of gas adsorption equilibria. Kinetic processes and catalytic reactions inside a sorbent/sorbate system also can be observed. Pros and cons of dielectric measurements are discussed. List of Symbols. References. 

S.2.2.2 High-frequency Dielectric Relaxation Spectroscopy Earlier studies of dielectric relaxation times in aqueous alkali hahde solutions by Kaatze and coworkers [12, 130] were obtained from the complex permittivities as a function of the frequency, but at frequencies up to about 100 GHz only as noted by Buchner [131]. The complex permittivity of conducting solutions has to be corrected for the conductance. The remainder can be expressed as Debye equations ... 

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... 

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