Double layer, capacitance/capacitor

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. 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

Figure 1-13 displays the experimental dependence of the double-layer capacitance upon the applied potential and electrolyte concentration. As expected for the parallel-plate model, the capacitance is nearly independent of the potential or concentration over several hundreds of millivolts. Nevertheless, a sharp dip in the capacitance is observed (around —0.5 V i.e., the Ep/C) with dilute solutions, reflecting the contribution of the diffuse layer. Comparison of the double layer witii die parallel-plate capacitor is dius most appropriate at high electrolyte concentrations (i.e., when C CH). 

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). 

The double-layer consists of ions juxtaposed with the electrode, so it resembles a plate capacitor (e.g. see Figure (5.3)) - we will describe this in terms of its double-layer capacitance, Cji (cf Chapter 5). 

The relationship between the fractional surface coverage 9 and the double-layer capacitance C may be better understood in terms of the following model. The doublelayer capacitance at the electrode in the presence of adsorption can be viewed as consisting of two capacitors connected in parallel. One capacitor corresponds to the electrode areas that are unoccupied (free) and the other to the electrode areas that are occupied (covered) with adsorbate (13-15). These two condenser-capacitors have different dielectrics and thus different capacitances. The capacitance of a parallel combination of capacitors is equal to the sum of the individual capacitances. 

Recently supercapacitors are attracting much attention as new power sources complementary to secondary batteries. The term supercapacitors is used for both electrochemical double-layer capacitors (EDLCs) and pseudocapacitors. The EDLCs are based on the double-layer capacitance at carbon electrodes of high specific areas, while the pseudocapacitors are based on the pseudocapacitance of the films of redox oxides (Ru02, Ir02, etc.) or redox polymers (polypyrrole, polythiophene, etc.). 

A double layer carbon capacitor consists of an anode and cathode of 1 g each of carbon cloth (S.S.A. = 2500m2g 1), the electrolyte being sulphuric acid. With reference to [3] make and justify an estimate of the capacitance of the cell. 

Finally, the basic equivalence of the two measuring techniques should be appreciated. Although there are many ways to approach such a comparison, the following simplified explanation will, we hope, give a more intuitive feeling for the relationship between EIS and PR measurements. As stated above, both techniques rely on the frequency dependence of the impedance of the double-layer capacitance in order to determine the polarization resistance. EIS uses low frequencies to force the capacitor to act like an open circuit. PR measurements use a slow scan rate to do the same thing. To make comparisons, the idea of equivalent scan rate is useful. Suppose that a particular electrochemical system requires EIS measurements to be made down to 1 mHz in order to force 99% of the current through Rp. What would the equivalent scan rate be for PR measurements A frequency of 1 mHz corresponds to a period of 1000 s. If the sine wave is... 

After application of a potential step of magnitude = 2 - Ei, the exponential decay of the current with time depends on the double-layer capacitance (Cd) and the solution resistance (Rs) (-> resistance, subentry - solution resistance), i.e., on the time constant r = RsCd- Consequently, if we assume that Cd is constant and the capacitor is initially uncharged (Q = 0 at t = 0), for the capacitive charge (Qc) we obtain... 

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