Capacitor dielectric response

Equation 1.79 is the basis for a measurement method of the dielectric response function /ft). Upon connecting the switch of the circuit shown in Figure 1.28, a polarization current, ipolft), through the capacitor can be recorded, according to the following equation... 

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. 

From audio frequencies (below which there are worries that are due to conductance and electrochemical reactions at the charged plates) to microwave frequencies (above which electronics are not fast enough), a capacitor is actually a practical device, not just a conceptually convenient picture for measuring dielectric response and energy absorption. At higher frequencies—IR, visible, UV—this information comes from absorption and reflection of electromagnetic waves (see Fig. LI.6). (Dielectric responses are discussed in great detail in Level 2, Subsection L2.4.A.)... 

Rather than continue so formally, consider dielectric susceptibilities in terms of illustrative models. Conceptually the simplest picture of a dielectric response is that in an electric circuit. Think about a capacitor as a sandwich of interesting material between two parallel conducting plates (see Fig. L2.22). 

Recent work by Bao et al. has shown that P(VDF-TrFE) synthesized via reductive dechlorination from P(VDF-CTFE) exhibits ferroelectric relaxor behavior at high temperature ( 100°C) with a melting point near 200°C [111]. This result is important as it provides another avenue to study the relaxor phenomena which are still not completely understood. The high melting point coupled with the high dielectric response of these materials at high temperature makes them attractive for use in high-temperature capacitors. 

The overall admittance (Equation 2.3) for a parallel resistor-capacitor (RC) circuit is given by the sum of the conductance (l/R) and capacitance contributions, where the resistance (R) represents the dissipative component of the dielectric response, while the capacitance (C) describes the storage component. The impedance function for that circuit is... 

Dielectric analysis (DEA) measures changes in the properties of a polymer as it is subjected to a periodic (or alternating) electric field. In DEA a sample is placed between two electrodes. The traditional electrode geometry used for thermoplastics is a parallel-plate capacitor. The parallel-plate electrode measures the bulk dielectric response of the material subjected to a sinusoidal voltage applied to the electrodes. The electrodes typically are formed by vapor deposition or sputtering of a metal onto the polymer surfaces. A more contemporary dielectric electrode geometry is the interdigitated comb type of electrode which is particularly well... 

Domansky K, Liu J, Wang LQ, Engelhard MH, Baskaran S (2001) Chemical sensors based on dielectric response of functionaUzed mesoporous silica films. J Mater Res 16 2810-2816 Endres HE, Drost S (1991) Optimization of the geometry of gas sensitive interdigital capacitors. Sens Actuators B 4 95-98... 

A common approach to model the dielectric response, typically used for impedance spectroscopy, is based on equivalent circuits consisting of a number of resistors, capacitors, constant phase elements, and others. Alternatively, the dielectric response can be modeled by a set of model relaxation functions like the Debye function or more generalized (semiempirical) Cole-Cole, Cole-Davidson, or Dissado-Hill equation (Kremer and Schonhals 2002). 

Method involves placing a specimen between parallel plate capacitors and applying a sinusoidal voltage (frequencies ranging from 1 mHz to 1 MHz) to one of the plates to establish an electric field in the specimen. In response to this field, a specimen becomes electrically polarized and can conduct a small charge from one plate to the other. Through measurement of the resultant current, the dielectric constant and dielectric loss constant for a specimen can be measured. The sharp increases in both the dielectric constant and the dielectric loss constant during a temperature scan are correlated with the occurrence of Tg... 

Now let us examine what would happen to the response of the dielectric if we put an alternating voltage on the capacitor of frequency co. If CO is low (a few Hz) we would expect the material to respond in a similar manner to the fixed-voltage case, that is d (static) = e(co) = e(0). (It should be noted that eo, the permittivity of free space, is not frequency-dependent and that E(0)/eo = H, the static dielectric constant of the medium.) However, if we were to increase co to above microwave frequencies, the rotational dipole response of the medium would disappear and hence e(co) must fall. Similarly, as we increase co to above IR frequencies, the vibrational response to the field will be lost and e(co) will again fall. Once we are above far-UV frequencies, all dielectrics behave much like a plasma and eventually, at very high values, e(co)lto = 1. 

The objective of this monograph is to describe and interpret the time dependence of the electrical response of dielectrics. Interpretation is difficult because the observable relationship between polarization and field is simple in the cases relevant for dielectric relaxation and because the measurements have relatively little information content. The response of the dielectric can be described by a set of linear differential equations and many models can be described which correspond to the same differential equations. When the dielectric relaxation of a given material has been measured the investigator is in the position of a man presented with a black box which has two terminals. He may apply alternating fields of various kinds and he may heat the box but he is not allowed to look inside. And he finds that the box behaves as if it contained a combination of capacitors and resistors. 

Dielectric test methods are used to measure the cure of epoxy adhesives between two conducting electrodes. This method is especially appropriate for metal-to-metal joints because the substrates themselves can be used as the electrode. The adhesive is treated as a capacitor during the test. Its response (dielectric constant, dissipation factor, etc.) over a range of electrical frequencies is measured as a function of curing time. 

The LF measurements (a) are provided by means of impedance/admittance analyzers or automatic bridges. Another possibility is to use a frequency response analyzer. In lumped-impedance measurements for a capacitor, filled with a sample, the complex dielectric permittivity is defined as [3]... 

Experimental Methods.— The initial fleeting excursions from frequency domain into time domain (for example, ref. S) appear to have been made because, at that time, steady-state measurements at very low frequencies ( 10 Hz) were unsatisfactory. Step-up, step-down, and ramp voltages were variously applied to capacitors containing dielectric samples, and the tranaent current i(/), or charge q t), responses monitored over a wide range of times such approaches have been reviewed. Although it is now quite feasible to make steady-state measurements at very low frequencies. 

The current response i t to a unit voltage step of a unit vacuum capacitor filled with a dielectric material, is related to the complex relative permittivity (e ) of the dielectric by the Fourier transform... 

Commercial submicron BT particles were modified for the study of the preferred crystal phase relationship to the corresponding dielectric properties. The results reveal that the crystal phase of the BT particles in the nanometer size range relates to the impurities incorporated in the BT crystal lattice. The responsible impurity has been identified as hydroxyls. BT is considered to meet the demands for current and future capacitor applications by modifying submicron BT particles. 

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