Capacitance electric double-layer

Two models of surface hydrolysis reactions and four models of the electrical double layer have been discussed. In this section two examples will be discussed the diprotic surface group model with constant capacitance electric double layer model and the monoprotic surface group model with a Stern double layer model. More details on the derivation of equations used in this section are found elsewhere (3JL). ... 

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions. The measured capacitance ranges from about two to several hundred microfarads per square centimeter depending on the stmcture of the double layer, the potential, and the composition of the electrode materials. Figure 4 illustrates the behavior of the capacitance and potential for a mercury electrode where the double layer capacitance is about 16 p.F/cm when cations occupy the OHP and about 38 p.F/cm when anions occupy the IHP. The behavior of other electrode materials is judged to be similar. 

Fig. 7. (a) Simple battery circuit diagram where represents the capacitance of the electrical double layer at the electrode—solution interface, W depicts the Warburg impedance for diffusion processes, and R is internal resistance and (b) the corresponding Argand diagram of the behavior of impedance with frequency, for an idealized battery system, where the characteristic behavior of A, ohmic B, activation and C, diffusion or concentration (Warburg... 

The capacitance. The electrical double layer may be regarded as a resistance and capacitance in parallel see Section 20.1), and measurements of the electrical impedance by the imposition of an alternating potential of known frequency can provide information on the nature of a surface. Electrochemical impedance spectroscopy is now well established as a powerful technique for investigating electrochemical and corrosion systems. 

The model more generally accepted for metal/electrolyte interfaces envisages the electrical double layer as split into two parts the inner layer and the diffuse layer, which can be represented by two capacitances in series.1,3-7,10,15,32 Thus, the total differential capacitance C is equal to... 

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y, whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the face j.262,263 In the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc electrode and depends on the average charge density <7pc = R ZjOjOj [Fig. 10(b)]. The capacitance Cj al is obtained by the equation... 

The electrical double-layer structure at Ga/DMF, In(Ga)/DMF, and Tl(Ga)/DMF interfaces upon the addition of various amounts of NaC104 as a surface-inactive electrolyte has been investigated by differential capacitance, as well as by the streaming electrode method.358 The capacitance of all the systems was found to be independent of the ac frequency, v. The potential of the diffuse layer minimum was independent of... 

Ga, In(Ga), Tl(Ga), and Hg in A-methylformamide + NaC104 solutions have been studied by the impedance method.359 The capacitance of the electrical double-layer for all electrodes in the frequency range 200 Hz < v < 5000 Hz was independent of v. The values of Ea=Q were usually... 

The electrical double layer has been studied at the interface of acidified (pH = 3) KCIO4 and K2SO4 solutions in contact with an Sn solid drop electrode with an additionally remelted surface (SnDER).616 The E, is independent of ctl as well as of the electrolyte. Weak specific adsorption of CIO4 at SnDER is probable around <7 = 0. This view is supported by the high value of/pz for SnDER/H20 + KCIO4 (fpz = 1 -27). A value of fpz = 0.99 for SnDER/H20 + K2S04 indicates that the surface of SnDER is geometrically smooth and free from components of pseudo-capacitance.616... 

The electrical double layer at BiDER/PrOH and BiDER/2-PrOH interfaces with the addition of various electrolytes (LiC104> Lil, LiSCN, KSCN) has been studied using impedance.691-693 The Emj was independent of cei and v. A weak dependence of C on v has been found at cucio4 < 0- 1 M and at a > -0.03 C m 2, and the equilibrium differential capacitance C o has been obtained by linear extrapolation of C vs. tu,/2 to co1/2 = 0. Parsons-Zobel plots at a = 0 are linear, with/pz = 1.01 0.01. The values of cf have been obtained according to Grahame and Soder-... 

The existence of Galvani potentials between two different conducting phases is connected with the formation of an electric double layer (EDL) at the phase boundary (i.e., of two parallel layers of charges with opposite signs, each on the surface of one of the contacting phases). It is a special feature of such an EDL that the two layers forming the double layer are a very small (molecular) distance apart, between 0.1 and 0.4nm. For this reason EDL capacitances are very high (i.e., tenths of pF/cm ). 

III. NEGATIVE DIFFERENTIAL CAPACITANCE AND ELECTRICAL DOUBLE LAYER STABILITY... 

In the equivalent electric scheme of the entire electrochemical cell (Figure 1.5b), we note, starting from the working electrode, the presence of a capacitance, Cd, in parallel with an impedance, Zf, which represents the Faradaic reaction. The presence of the supporting electrolyte in excess indeed induces the formation of an electrical double layer, as sketched in... 

Diprotic Surface Groups. Most of the recent research on surface hydrolysis reactions has been interpreted in terms of the diprotic surface hydrolysis model with either the triple layer model or the constant capacitance model of the electric double layer. The example presented here is cast in terms of the constant capacitance model, but the conclusions which are drawn apply for the triple layer model as well. 

In recent several years, super-capacitors are attracting more and more attention because of their high capacitance and potential applications in electronic devices. The performance of super-capacitors with MWCNTs deposited with conducting polymers as active materials is greatly enhanced compared to electric double-layer super-capacitors with CNTs due to the Faraday effect of the conducting polymer as shown in Fig. 9.18 (Valter et al., 2002). Besides those mentioned above, polymer/ CNT nanocomposites own many potential applications (Breuer and Sundararaj, 2004) in electrochemical actuation, wave absorption, electronic packaging, selfregulating heater, and PTC resistors, etc. The conductivity results for polymer/CNT composites are summarized in Table 9.1 (Biercuk et al., 2002). 

To learn that the use of microelectrodes is a valuable means of decreasing the capacitive effects of the electric double-layer. 

The area of an electrode is finite and essentially constant. Similarly, the thickness of the electric double-layer does not vary by a large amount. As an empirical rule, we find that the double-layer capacitance has a value in the range 10-40 pF cm, where F is the SI unit of capacitance, the farad. Note that a capacitance without an area is not particularly useful - we need to know the complete capacitance. 

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