Dielectrics complex capacitance

A complex capacitance can be expressed as the product of the complex dielectric constant, e, and a geometrical constant, Cq, of the sample ... 

Remember 16.4 Like the admittance representation, the complex-capacitance representation emphasizes values at high frequency and is often used for solid-state and dielectric systemsfor which information is sought regarding system capacitance. 

The characteristic frequency evident as a peak for the imaginary part of the complex-capacitance in Figures 16.12(b) and 16.13(b) has a value corresponding exactly to fc = 27tReC) only for the blocking system. As found for data presentation in admittance format, the presence of a Faradaic process confounds use of graphical techniques to assess this characteristic frequency. Like the admittance format, the complex capacitance is not particularly well suited for analysis of electrochemical and other systems for which identification of Faradaic processes parallel to the capacitance represents the aim of the impedance experiments. It is particularly well suited for analysis of dielectric systems for which the electrolyte resistance can be neglected. 

Example 16.2 Complex Capacitance of Dielectrics Find an expression for the complex capacitance for the electrical circuit shown in Figure 16.9 and discussed in Example 16.1. Identify the limits and characteristic frequencies. 

Example 16.1 Admittance of Dielectrics Example 16.2 Complex Capacitance of Dielectrics Example 16.3 Evaluation of Double-Layer Capacitance... 

The connection between the impedance and dielectric measurements can be seen easily for only relatively simple examples. In Figure 7-8c the complex capacitance plot for the same equivalent circuit is similar to typical dielectric response dielectric only in the low-frequency region. The plot of the magnitude of the complex impedance, also shown in this panel, is known as the Bode plot. 

Complex permittivity is used when the material is considered as a dielectric (an insulator) with losses. The capacitor is characterized with a complex capacitance or a complex permittivity ... 

Dielectric properties can be measured by any instrument that provides the frequency-dependent impedance Z or complex capacitance C in the relevant frequency range. Broadband dielectric spectroscopy (BDS) is nowadays able to cover a frequency range fiom 10 Hz up to 10 ° Hz with affordable instrumentation, typically combining fi quency response analyzers (FRA), bridges, and networic analyzers at the radio fi quencies. A comprehensive overview about dielectric techniques, instrumentation, and modeling is given in Kremer and Schonhals (2002). 

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... 

Let s consider the dielectric spectrum in Fig. 13 in the vicinity of the TE mode antiresonance frequency. Here the complex capacitance C ([Pg.608]

The above dielectric (or complex capacitance) notation and Debye dispersion (Eq. 1-15) have often been used to describe a single bulk-media dielectric relaxation process in organic and polymeric (lossy) systems where at least two components with resistive and capacitive features exist [9, p. 33]. The permittivity of a lossy dielectric with negligible parallel DC conductance can be expressed on the basis of the Havriliak-Negami model (Eq. 1-16). Equivalent circuits representing a Debye model for lossy dielectric, where C, g = C g e, Cg - C j, R 1 /G [1, p. 65, p. 216], are shown in Figure 5-3. 

Figure 7.43 shows the plots of other system functions, the complex admittance G = Z S the complex dielectric modulus M = jwZ and the complex capacitance K = M . In particular we can see that when M is used the roles of R and are exchanged compared to the Z plot, so this plot is particularly suitable for analysis of capacitances, although the information content is, in principle , the same for all system functions. The significance of the admittance plot consists in the fact that, for a parallel connection of R and C (and suflBciently high frequencies), the real part is identical with the sample conductance. 

Dielectric losses arise from the direct capacitive coupling of the coil and the sample. Areas of high dielectric loss are associated with the presence of axial electric fields, which exist half way along the length of the solenoid, for example. Dielectric losses can be modeled by the circuit given in Figure 2.5.3. The other major noise source arises from the coil itself, in the form of an equivalent series resistance, Rcoii. Exact calculations of noise in solenoidal coils at high frequencies and small diameters are complex, and involve considerations of the proximity and skin depth effects [23],... 

Frequency-dependent measurements of the materials dielectric impedance as characterized by its equivalent capacitance, C, and conductance, G, are used to calculate the complex permitivity, e = d — id, where co = 2nf, f is the measurement frequency, and C0 is the equivalent air replacement capacitance of the sensor. 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

When applying an alternating electric field to a polymer placed between two electrodes, the response is generally attenuated and the output current is out of phase compared with the input voltage. This response stems from the polymer s capacitive component and its conductive or loss component, as represented by a complex dielectric permittivity measured frequencies f, and temperatures T ... 

The methodology for the calculation of the complex relative permittivity for the dipolar relaxation mechanism is founded on the calculation of the dielectric response function, f(t), for a depolarization produced by the discharge of a previously charged capacitor. In Figure 1.29a, a circuit is shown where a capacitor is inserted in which a dipolar dielectric material is enclosed in the parallel plate capacitor of area, A, and thickness, d, with empty capacitance C0 = Q0/U0 = 0(A/d), and E0 = U0ld. In Figure 1.29b, the corresponding depolarization process is shown. 

For thin polystyrene films annealed for 12 hours at 150 °C in high vacuum (10-6 mbar) and measured in a pure nitrogen atmosphere the dynamic glass transition was characterized using two experimental techniques capacitive scanning dilatometry and Broadband Dielectric Spectroscopy. Data from the first method are presented in Fig. 15a, showing the real part of the complex capacity at 1 MHz as a function of temperature for a thin PS film of 33 nm. 

Several parameters are used to characterize the interaction of microwave radiation and matter the complex permittivity (e ), the dielectric constant O ). and the loss tangent (tan S). The dielectric constant, i-. can be thought of in a straightforward manner, as shown in Figure 5.15. Two parallel plates have a given capacitance, Co, when there is no material between them a vacuum. When the vacuum is replaced by a nonconducting medium, a dielectric, the new capacitance, C, is greater than Cq. The dielectric constant, e, is the ratio of these two capacitances ... 

The electrical properties of polyelectrolyte complexes are more closely related to those of biologically produced solids. The extremely high relative dielectric constants at low frequencies and the dispersion properties of salt-containing polyelectrolyte complexes have not been reported for other synthetic polymers. Neutral polyelectrolyte complexes immersed in dilute salt solution undergo marked changes in alternating current capacitance and resistance upon small variations in the electrolyte concentration. In addition, their frequency-dependence is governed by the nature of the microions. As shown in... 

Careri et al. (1986), using the framework of percolation theory, analyzed the explosive growth of the capacitance with increasing hydration above a critical water content (Fig. 14). The threshold for onset of the dielectric response was found to he 0.15 h for free lysozyme and 0.23 h for the lysozyme—substrate complex. In the percolation model the thresh-... 

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