Non-ideal capacitor

However, complex systems usually present a distribution of relaxation times and the resulting plot is a depressed semi-circle, which is associated with a non-ideal capacitor or constant phase element (CPE), and its impedance is given by [42] ... 

As was previously indicated, IS measurements can also be used to determined membrane modifications and Figure 9.13 shows Nyquist and Bode plots for PS-Uf and PS-Uf/BSA fouled membranes in contact with a NaCl solution. Here a significant increase in electrical resistance due to membrane fouling can be observed, but the electrolyte contribution hardly differs in both systems. In both cases, the equivalent circuit for the membrane-electrolyte system is given by (R,C,)-(RM that is, a series association of the electrolyte part, formed by a resistance in parallel with a capacitor and the membrane part, which consists of a parallel association of a resistance and a CPE or non-ideal capacitor (RmQm). Fitting the experimental data allows determination of the electrical parameters (resistance, capacitance) for the different NaCl solutions studied and their variation with electrolyte concentration is shown in Figure 9.13c, d, respectively. 

CPE is like a non-ideal capacitor (a capacitor with a constant phase shift lower than 90°). T is a measure of the magnitude of Zcpe n is a. constant parameter (0 < n < 1) representing inhomogeneities in the surface and co is the angular frequency. In the case of n = 1, Zcpe equals a pure capacitor corresponding to the electrode-electrolyte interface capacitance. The parameters n and T depend on the electrode material [3]. 

Figure 2-11 Input Ripple of a Buck Converter Showing the Effect of a Non-ideal Bulk Capacitor...

In general, the Helmholtz layer can be treated as a linear capacitor. In a theoretical model of the electric double-layer, the compact Helmholtz layer is generally treated as an ideal capacitor with a fixed thickness (d), and its capacitance is considered unchanging with the potential drop across it. Therefore, fhe capacifance of fhe Helmholtz layer can be treated as a constant if fhe femperafure, fhe dielectric constant of the electrolyte solution inside the compact layer, and its thickness are fixed. However, if the specific ion adsorpfion happened on the electrode surface, the dielectric constant of the electrolyte solution inside the compact layer may be affected, leading to non-linear behavior of the Helmholtz layer. This will be discussed more in a later section. 

For example, whilst modelling high frequency noise in nanopore devices, Smeets el al. demonstrated the necessity of accounting for non-ideal capacitive behaviour and it has become common since for the generalised device capacitance to be replaced by either a parallel resistor-capacitor unit or a constant phase element [23]. Chien et al. used the circuit shown in Fig. 14 B, replacing C with a CPE, to determine pore resistance and diameter from Bode plots for Si pores. [42]. Pedone et al. used two parallel resistor-CPE units in series with a solution resistance for characterising the electrical properties of a pore-cavity-pore deviee [43]. 

The calomel electrode Hg/HgjClj, KCl approximates to an ideal non-polarisable electrode, whilst the Hg/aqueous electrolyte solution electrode approximates to an ideal polarisable electrode. The electrical behaviour of a metal/solution interface may be regarded as a capacitor and resistor in parallel (Fig. 20.23), and on the basis of this analogy it is possible to distinguish between a completely polarisable and completely non-polarisable... 

Figure 1. The tunneling of a single electron (SE) between two metal electrodes through an intermediate island (quantum dot) can be blocked of the electrostatic energy of a single excess electron trapped on the central island. In case of non-symmetric tunneling barriers (e.g. tunneling junction on the left, and ideal (infinite-resistance) capacitor on the right), this device model describes a SE box .

In examining the properties of the metal solution interfaee, two limiting types of behavior are found, namely, the ideal polarizable interfaee and the ideally non-polaiizable interface. In the former case, the interface behaves as a capacitor so that charge can be placed on the metal using an external voltage source. This leads to the establishment of an equal and opposite charge on the solution side. The... 

When one studies an (almost) ideally polarizable interface, such as the mercury electrode in pure deaerated acids, the equivalent circuit is a resistor Rs and a capacitor Cdi in series. The high accuracy and resolution offered by modern instrumentation allows measurement in such cases in very dilute solutions or in poorly conducting, non-aqueous media, which could not have been performed in the early days of studying the mercury/electrolyte interface. 

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