Low-Frequency Capacitance

An interesting incidental effect observed when an inhibitor is present in such a great excess that it forms a separate phase is the appearance of a large low-frequency capacitance loop which we attribute to precipitation (physical adsorption). This effect, however, plays no role in the experiments discussed above, since they all deal with aqueous single-phase solutions. 

CLF low frequency capacitance of the polymer layer (F) d diameter of circular probe (cm)... 

Miller [34] mentioned this time constant as the factor of merit of the capacitor. At this frequency, half of the low-frequency capacitance CLF is reached. For/greater than CLF, and for higher frequencies, C < CLF. 

Similar conclusions were derived from the work of Kek, Pejovnik, and Mo-gensen [43] who were the first to use AC-impedance spectroscopy for the detailed investigation of Pt, Au, and Ni films deposited in YSZ and exposed to mildly reducing environments (Fig. 20c-e). The low-frequency capacitance of the metal/YSZ interface is up to 300 pF cm-2, manifesting the presence of a double layer at the metal/gas interface even under mildly reducing conditions ( -1% H2) (Fig. 20c,d). This double layer is stabilized even on Au by prolonged anodic polarization (Fig. 20e). 

Helmholtz capaeitance limiting high frequency capacitance in PEIS limiting low frequency capacitance in PEIS space charge capacitance... 

Compared to field effect, the analysis of low frequency capacitance versus voltage measurements to yield a density of gap states in a-Si H is rather straightforward. Such stupes were first presented by Dohler and Hirose... 

This fundamental surface sensitivity for current transient measurements also applies to TSC and low frequency capacitance measurements. The latter case follows from the fact that the low frequency capacitance is proportional to the total barrier current that flows through the external circuit as a result of small voltage changes. The capacitance DLTS and TSCAP methods, on the other hand, are largely insensitive to surface effects. Thus features in current DLTS that do not appear in the corresponding capacitance DLTS spectra are likely candidates for states localized near the barrier interface. 

Low-frequency capacitances can be calculated from the following equation ... 

It has been shown in this work that for sample thickness L the screening length, /, by carriers, the low frequency value of the capacitance is inversely proportional to 1. By increasing the concentration of carriers, one can first extend to higher frequency the region where large, low frequency capacitances are observed and, second, decrease /, thus obtaining capacitors of enormous capacity - supercapacitors. 

Figure 6.13. (A) Conduction mechanisms in electrostatic assembled it-stacked materials (1) electron hopping involving the ruthenium and (2) M and M sites, (3) electronic conduction through the porphyrin it-stacks, and (4) hole transfer to a Ru(II) complex followed by electronic conduction through the porphyrin it-stack (B) Randles type equivalent drcuit proposed for the films (C) Nyquist diagrams of a modified electtrode (F = 3.5 X 10 molcm ) at 0.72 and 0.92 V and (D) low-frequency capacitance vs. potential and charge-transfer resistance vs. thickness (inset), for electrostatic assembled CoTRP/ZnTPPS films.

As a final note to this section, instead of the interpretation of the low frequency capacitative region as a faradaic, redox pseudocapacitance, Jakobs et al [104] described Region B as a porous capacitor region. The impedance of a porous capacitor depends on frequency as... 

The complex plane plots for different ratios of CaJCpore, where Cpore = s, are presented in Fig. 9.7. With the increase of the importance of the external flat surface there is a decrease in the low-frequency resistance, and the low-frequency capacitance is the total capacitance of the porous and flat surface ... 

Hence at low frequencies for an oxidized film, we note that total low-frequency capacitance is given by... 

Hence the high-frequency impedance of a reduced nonconducting polymer and the low-frequency capacitance of an oxidized polymer both depend linearly on layer thickness (via the N factor). The linear dependence of capacitance on thickness is of considerable diagnostic importance in model verification, since we usually expect the total capacitance of a thin film to be inversely proportional to film thickness. We can explain the prediction in Eqn. 438 by noting that low-frequency capacitance is confined to pore walls, which has its major axis orientated at right angles to the electrode surface. Thus the deeper the pore, the more capacitors there are in parallel in the pore wall and consequently the greater the total capacitance. 

FIGURE 1.87. Variation of low-frequency capacitance C/, with layer thickness for a Cl -doped poly(pyrrole) film in 0.1 M NaCl, applied potential, 400 mV. 

K is the conductivity of the electrolyte, C the low-frequency capacitance of a pore, n the number of pores, h their height and r their radius. This model does not take account of the variation of the capacitance with the voltage. 

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