Capacitance Response

Porous carbons and nanotubes have attracted considerable attention in relation to such practical issues as hydrogen storage, lithium batteries, and supercapacitors. In general, the electrochemical behavior of porous carbons and CNTs solely consists of double-layer charging processes with small or zero contribution of faradaic pseudocapacitance of surface oxide functionalities. This is in sharp contrast with the rich electrochemistry of fullerenes. 

Electrochemical capacitors based on carbon materials can be divided into doublelayer capacitors, where only a pure electrostatic interaction between ions and charged electrode surfaces occur, and supercapacitors, based on the occurrence of faradaic pseudocapacitance reactions (see Chapter 10). It is generally assumed that the charge is mainly stored, in porous carbons, in the double layer at the electrode/electrolyte 

FIGURE 7.13 CV of CNTs A/CoSi700 modified by electrodeposited polypyrrole in contact with 1 M H2SO4. Potential scan rate, 2 mV/sec. (From Frackowiak and Beguin, 2002. Carbon 40, 1775-1787, with permission from Elsevier.) 

For an ideal carbonaceous double-layer capacitor (see Chapter 10), the change in the number of electrons transferred per one carbon atom. An, is (Kavan et al., 2004) 

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The use of conventional electrochemical methods to study the effect of metal adatoms on the electrochemical oxidation of an organic adsorbate may be in some cases of limited value. Very often, in the potential region of interest the current due to the oxidation of an organic residue is masked by faradaic or capacitive responses of the cocatalyst itself. The use of on-line mass spectroscopy overcomes this problem by allowing the observation of the mass signal-potential response for the C02 produced during the oxidation of the adsorbed organic residue. 

The measurements utilise one-sided pn junction (p+n or pn ) and Schottky diodes, which possess a voltage modulated space charge region near the p/n and metal/semiconductor interface, respectively [8], The common feature of capacitance transient techniques is that the electronic properties of deep levels are determined by monitoring the transient high-frequency differential capacitance response of the diode as the electron occupancy of metastably charged deep levels located within the space charge... 

Deposits with extremely low porosities or an interconnected network of fine crystalline grain boundaries would be expected to show some loss of phase shift at low frequencies (i.e., a less than fully capacitative response) as the real resistance of the flaws becomes detectable, Fig. 19B. The value of RP obtained is inversely proportional to the corrosion rate. 

Figure 44 shows the variation in/b for different defect area fractions. The value of /b ranges from 103 to 10s Hz for defect area percentages of 0.001 to 0.05%, respectively (119). The ability to measure small defect area fractions is compromised by incomplete resolution of the resistive plateau, which occurs when Rf0 is large and C is small fb measurements are also limited at high frequencies by the use of potentiostatic control. This normally imposes an upper limit of 10s Hz. A further limitation occurs for thick coatings whose capacitive response shifts the breakpoint to low frequencies where it is difficult to identify confidently and may fall in a range where the EIS data are affected by electrode... 

As was expected from the signal-to-noise analysis, the effects of the several variables on the capacitive responses were much poorer structural predictors. Classification accuracies ranged between 60.0 and 75.6%. 

An interesting sidelight of the organic structural classification study was that herbicidal activity could also be predicted 6). The nitrodiphenylethers could be divided into compounds which were strong herbicides and those compounds which showed little or no herbicidal activity. Both Faradaic and capacitive responses could be used to separate these classes for over half the experimental conditions examined. As was found in the classification of structure, capacitive factorial features performed somewhat better than Faradaic factorial features. It also appeared that classifications of herbicidal activity using Faradaic factorial features could be improved considerably by working at high pH and without surfactant present. The information content of Faradaic or capacitive variable effects data could be improved by variations in % ethanol. 

If the potential on the semiconductor has imposed on it an a.c. component, then the effect is to change the accumulated charge in the depletion layer according to eqn. (38). Assuming that no faradaic current is passing, i.e. the semiconductor is deep in depletion, the capacitive response of the semiconductor layer may be approximated as... 

Conversely, a purely capacitive response is completely out of phase with the perturbation wave. The capacitive impedance response varies continuously and inversely with frequency and has no real component. In the complex plane, an ideal capacitance (C) appears as a vertical line that does not intercept the real axis. 

The impedance response of the R-RC circuit in Figure 4a is illustrated on a complex plane plot in Figure 4b. At low frequencies, the data approach the real axis at R + Rp (pathway 2), and the capacitive response is illustrated by the arc in the data. The frequency at the apex of the arc (to ) corresponds to the characteristic relaxation time (f ) of the circuit ... 

Nernst applied the electrical bridge invented by Wheatstone to the measurement of the dielectric constants for aqueous electrolytes and different organic fluids. Nemst s approach was soon employed by others for measurement of dielectric properties and the resistance of galvanic cells. Finkelstein applied the technique to the analysis of the dielectric response of oxides. Warburg developed expressions for the impedance response associated with the laws of diffusion, developed almost 50 years earlier by Fick, and introduced the electrical circuit analogue for electrolytic systems in which the capacitance and resistance were functions of frequency. The concept of diffusion impedance was applied by Kruger to the capacitive response of mercury electrodes. ... 

Figure 12.17 compares the capacitance response of the sihcon/fluoride solution interface at pH 1.3 with the potential-modulated microwave response. The shoulder in the capacitance curve due to svface states is absent from the microwave reflectance curve. The Mott-Schottky plot for ARm extends to the flatband potential, whereas the plot of 1/C deviates in the region where the surface-state capacitance becomes important. Comparison of the capacitance and microwave responses allows deconvolution of the surface-state capacitance (Schlichthorl and Peter, 1994 and 1995). 

The Role of Ion Identity. Some families of ions (e.g., alkali metals) show considerable differences in their capacitance response for a given concentration, particularly for potentials away from the potential of zero charge, with shifts of the potential of zero charge being observed in some... 

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