Capacity of double layer

Cd differential capacity of double layer Cj integral capacity of double layer Cs capacity in RC series combination... 

Fig. 8. Differential capacity of double layer calculated by Grahame. The curve for IM NaF from Fig. 10 has served as a basis for calculating the capacity of the molecular condenser.

Fig, 10, Differential capacity of double layer between mercury and aqueous solutions of NaF, T 25 a... 

In recent years, many types of double-layer capacitors have been built with porous or extremely rough carbon electrodes. Activated carbon or materials produced by carbonization and partial activation of textile cloth can be used for these purposes. At carbon materials, the specific capacity is on the order of 10 J,F/cm of trae surface area in the region of ideal polarizability. Activated carbons have specific surface areas attaining thousands of mVg. The double-layer capacity can thus attain several tens of farads per gram of electrode material at the surfaces of such carbons. 

Relaxation methods for the study of fast electrode processes are recent developments but their origin, except in the case of faradaic rectification, can be traced to older work. The other relaxation methods are subject to errors related directly or indirectly to the internal resistance of the cell and the double-layer capacity of the test electrode. These errors tend to increase as the reaction becomes more and more reversible. None of these methods is suitable for the accurate determination of rate constants larger than 1.0 cm/s. Such errors are eliminated with faradaic rectification, because this method takes advantage of complete linearity of cell resistance and the slight nonlinearity of double-layer capacity. The potentialities of the faradaic rectification method for measurement of rate constants of the order of 10 cm/s are well recognized, and it is hoped that by suitably developing the technique for measurement at frequencies above 20 MHz, it should be possible to measure rate constants even of the order of 100 cm/s. 

According to El-Mashri et al.,190 the A106 A104 ratio determines the hydration capacity of anodic oxides. Tetrahedral sites are hydrated easily to form a boehmite-like structure, which is known to be composed of double layers of Al-centered octahedra, weakly linked by water molecules to other layers.184 As the oxide formed in H3P04 contains about 70% tetrahedral aluminum bonds, its hydration ability should be higher than that of the oxide formed in tartrate solution. However, this has not been found in practice, which is interpreted by El-Mashri et al. as being due to some reduction of A104 by incorporated phosphate species. 

There is an upper limit to the frequency range useful for kinetic studies due to the presence of double-layer capacity and ohmic resistance [53]. In practical cases, the limit is ca. 10 kHz. Then, from eqns. (64) and (65), it follows that, for p values to be obtained with reasonable accuracy, the condition p > ca. 5 x 10-4 s1/2 should be met. This corresponds to a standard rate constant of ca. 3 cm s 1. 

Figure 3.4 gives examples of real electrocapillary curves and differential capacity curves. Double layer models have to explain the shape of these curves. 

The diffuse layer capacity is an important quantity often used in the analysis of double layer capacity data. In the absence of specific adsorption, the diffuse layer capacity is defined as... 

Passivation of cathodes in hexamethylphosphotriamide has been studied in greater detail. Measurements of double-layer capacity have revealed that cathodic polarization of electrodes in alkali metal salt solutions or the enrichment of the bulk of these solutions in solvated electrons leads to passivation which decreases the capacity... 

Figure 4.5.54. Time dependency of double layer capacity (Cji) obtained with a least square fit of the measured impedance spectra at open circuit potential.

Figure 5.14 Measurement of double layer capacity by galvanostatic transient method switch-on and switch-off of current.

A double layer, consisting of a ferroelectric ceramic and a liquid crystal layer, therefore represents for a.c. voltage pulses the series connection of a nonlinear and linear capacity. By suitably dimensioning the capacities of both layers, the voltage across the liquid crystal layer can be increased much stronger than linear with the total voltage applied across the double layer, as shown in Fig. 56. By this method... 

The stabilization activity results from the capacity of the layered double hydroxides to react with the HCI formed during the degradation of PVC. The reaction between the layered double hydroxides and the HCI occurs in a two-step process (3) ... 

Of all the numerous methods devised for the measurement of double layer capacity, the most popular and most accurate has been the measurement of the impedance of the cell using an a.c. bridge. Figure 53 shows a schematic... 

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