Variation of capacitance

Electrochemically polished and chemically treated Cd(0001), Cd(10T0)t Cd(l 120), Cd(lOTl), and Cd(ll2l) electrodes have been studied by impedance and cychc voltammetry by Lust et al.152 153 249 664 665 a slight variation of capacitance (3 to 6%) has been observed with v. In the case of chemically treated electrodes, a somewhat higher (5 to 10%) dependence of C on v has been explained by the geometric roughness of the electrode surface. 

Fig. 9.27 shows the variation of capacitance as a function of the surface area from which it may be concluded that in principle it is possible to obtain double-layer supercapacitors having specific capacitance of the order of 100 F/g so that values of practical capacitance density as high as 30 F/g can be predicted. 

The ratio of the alternating variation of capacitance ACs t) to the static value of capacitance Cso without time dependence is given as [3]... 

Considering the effect up to EA, the ratio of the alternating variation of capacitance ACs underneath the tip to the static capacitance Cso is given by... 

Fig. 5.40 Variation of capacitance with temperature for (a) Class I COG, (b) Class II X7R and (c) Class III Z5U dielectrics.

Te and Cu monolayers on gold, as well as Ag and Bi monolayers on platinum were obtained by cathodic underpotential deposition and investigated in situ by the potentiodynamic electrochemical impedance spectroseopy (PDEIS). PDEIS gives the graphical representation of the real and imaginary interfacial impedance dependencies on ac frequency and electrode potential in real-time in the potential scan. The built-in analyzer of the virtual spectrometer decomposes the total electrochemical response into the responses of the constituents of the equivalent electric circuits (EEC). Dependencies of EEC parameters on potential, especially the variation of capacitance and pseudocapacitance of the double layer, appeared to be very sensitive indicators of the interfacial dynamics. 

Fig. 15 shows the variation of capacitance determined by cyclic voltammetry as a function of the potential sweep rate. It is clear that the presence of an ordered mesoporous network facilitates the formation of the double layer, especially at high potential sweep rates, that results in a higher capacitance for the mesoporous carbon. Upon gasification of the two carbons with CO2 for obtaining an almost equivalent increment of specific siuface area (carbons MCI and ACl in Table 2), the mesoporous carbon shows a larger increase of capacitance (Fig. 15). 

TABLE 1 The variation of capacitance values with conduction processes (Sinclair, 1995 Irvine etal., 1990)... 

Energy The variation of capacitive energy, also called internal energy of the spring, is given by... 

Construction The variation of capacitive (electrostatic) energy is given in an equivalent way from individual variations of poles and from the variation of dipole this is the embedding principle ... 

Construction Two poles are associated in the building of this dipole. The variation of capacitive energy (or work) of a dipole is the sum of variations of capacitive energy of the two poles ... 

Energy In this energetic variety (said to be corpuscular for making short), the variation of capacitive energy is given by the product of the energy-per-corpuscle by the variation of the number... 

The isolation of the system with respect to the exterior makes the variation of capacitive energy equal to zero, which, by taking into account the equality of angles and therefore of their variations, is translated by zeroing the sum of dipolar torques... 

On another hand, the variation of capacitive energy is the same in the system whatever the considered level, dipole or multipole. 

This subject has been already studied in Chapter 6 (about dipoles) in case study C5 First-Order Chemical Reaction in steady-state conditions. The embedding principle allows one to relate the poles (representing the species) to the dipole (representing the reaction) by stating that the variation of (capacitive) energy can be written indifferently in terms of poles or of dipole variations ... 

The variation of capacitive energy of the ion population is given by two terms of the Gibbs... 

The variation of capacitive energy of these four poles (an electrodynamical one and a thermal one for each side) is given by the following Gibbs equation ... 

A translated effort allows one to express the amount of capacitive energy in one variety in terms of state variables of another variety. For instance, the variation of capacitive energy in the a variety can be expressed as the product of a b-effort times a b-basic quantity variation ... 

The starting point as usual is the writing of a Gibbs equation expressing the variation of capacitive energy as the sum of the variations of three energy varieties hydrodynamics, physical chemistry, and thermics ... 

By deriving the definition of enthalpy and replacing the variation of capacitive energy with its Gibbs expression, the following variation of enthalpy is obtained ... 

Now, by comparing this energy variation with the variation of capacitive energy given in Equation K2.20 established by assuming a constant n, the differential energetic ratio can be identified with ratios between heat capacities and gas constant [the Mayer relationship (Equation K2.21) has been used for the second equality] ... 

Variation of capacitance with bias voltage analogous to the effect with p-n junctions has been observed. 

Figure 24 shows the differential capacitance versus bias voltage at various frequencies for a devices with a relatively thick polyacetylene layer (150 nm). Accumulation is seen at bias voltages below about +10 V, and at the lowest frequency shown (50 Hz), the value of capacitance in accumulation is close to the value of Q. There is no indication for the onset of inversion at even the lowest frequency used, and the variation of capacitance in the depletion regime is well modelled by equation 27, as shown in figure 25. The slope of the linear redon of (C/Ci) versus bias voltage gives a value of Na, which for this structure is... 

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