Capacitance frequency dependence

Figure 5 presents the capacitance-frequency dependence from impedance spectroscopy measurements for CS48 and CS15 in acidic and organic medium. In the low frequency region (from ImHz to lOOmHz) nearly a complete penetration of the ions into the pores is allowed and the quite stable values indicate the domination of the capacitive behavior at the electro 1 ytc/carbon interface. All the curves show a typical drop of... 

Figure 23-13 Capacitance-frequency dependence of capacitors based on template carbons (a) CS48 in 1 mol/L H2SO4, (b) CS15 in Imol/L H2SO4, (c) CS48 in TEABF4, (d) CS15 in TEABF4. The frequency is expressed in logarithmic scale. (Adapted from Ref. [88].)...

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

A constant phase element (CPE) rather than the ideal capacitance is normally observed in the impedance of electrodes. In the absence of Faradaic reactions, the impedance spectrum deviates from the purely capacitive behavior of the blocking electrode, whereas in the presence of Faradaic reactions, the shape of the impedance spectrum is a depressed arc. The CPE shows power law frequency dependence as follows129 130... 

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. 

The Capacitance of the Double Layer. It has been seen that the impedance of the double layer is frequency dependent Taking a frequency of 1 kilocycle, and a capacitance value of 50 pF cm, one has... 

Capacitive reactance is a frequency-dependent quantity, decreasing with increasing frequency. Typically, double-layer capacitances for aqueous solutions are 10-100 nF/cm2. Thus the capacitive reactance for a 1-cm2 electrode with a 10-fxF capacitance at an applied frequency of 104 rad/s (1.6 kHz) is... 

It might seem more convenient to eliminate the calculation by employing a bridge with a series R-C balancing arm as in Figure 6.246. However, the parallel combination is used more frequently because the parallel capacitance required to compensate a series capacitance of 100 /iF at 1000 Hz with a resistance Rs - 1000 0 is only about 300 pF. Small capacitances can be obtained with high accuracy and less frequency dependence (and less cost) than large ones. 

First of all, membrane capacitance of nerves has a negative frequency dependence below 300 Hz, namely capacitance increases with frequency in this region. This is a behavior which cannot be explained by a simple RC circuit and indicates the presence... 

The origin of the frequency dependent membrane capacitance is not well understood, although it is likely to be due to membrane proteins. However, there are a variety of proteinous components in the membrane and most of them are not directly related to ionic channels. Therefore, it is virtually impossible to physically separate the capacitance due to gating proteins from capacitances due to other proteins. However, if the frequency dependent capacitance is related to gate proteins, the capacitance must change with an increase or decrease in the membrane potential. It is known that ionic channels are not tightly closed at the resting state (membrane potential near -60 mV). 

From these observations, it became apparent that the frequency dependent capacitance must be due, at least partially, to gating particles, and, in particular, to those of sodium channels. If the capacitance change shown in Figure 6 is indeed due to sodium channels, then the change must be affected by TTX, which is known to block sodium channels selectively. Figure 7 shows the membrane capacitance at various potentials. As can be seen, TTX effectively eliminates the voltage dependence of... 

The capacitance and the series resistance have values which are not constant over the frequency spectrum. The performances may be determined with an impedance spectrum analyzer [70], To take into account the voltage, the temperature, and the frequency dependencies, a simple equivalent electrical circuit has been developed (Figure 11.10). It is a combination of de Levie frequency model and Zubieta voltage model with the addition of a function to consider the temperature dependency. 

On the Frequency Dependence of Differential Capacitance of Diamond Electrodes. 233... 

The above-described situation is but an exception rather than the rule. Generally, the diamond electrode capacitance is frequency-dependent. In Fig. 12 we show a typical complex-plane plot of impedance for a single-crystal diamond electrode [69], At lower frequencies, the plot turns curved (Fig. 12a), due to a finite faradaic resistance Rp in the electrode s equivalent circuit (Fig. 10). And at an anodic or cathodic polarization, where Rf falls down, the curvature is still enhanced. At higher frequencies (1 to 100 kHz), the plot is a non-vertical line not crossing the origin (Fig. 12b). Complex-plane plots of this shape were often obtained with diamond electrodes [70-73],... 

It goes without saying that the frequency dependence of capacitance, which follows from the complex-plane plots of the type shown in Fig. 12, manifests itself in a frequency-dependent slope of Mott Schottky plots (Fig. 13) [78], The complications in calculating Na thus involved will be discussed at length in Section 5.3 below. 

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