Double layer, capacitance/capacitor charging

Double layer capacitance Excess charge in an electrode surface is compensated by a build-up of opposite-charged ions (Helmholtz layer), creating an electrical double layer. This layer is mathematically treated as a parallel plate capacitor. Typical values are on the order of tens of micro farads per cm. ... 

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. 

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... 

The final point we would like to emphasize is that the diffusion layer should never be confused with the double layer. The double layer arises because the charge on the electrode is counterbalanced by ions of opposite charge that are specifically adsorbed at the electrode surface. Such a construction resembles a capacitor and gives rise to double-layer capacitance, which will be described in detail later on. The thickness of the double layer is only a few A, much smaller than 6. 

An ideally polarizable electrode behaves as an ideal capacitor because there is no charge transfer across the solution/electrode boundary. In this case, the equivalent electrical model consists of the solution resistance, R, in series with the double-layer capacitance, Cdi. An analysis of such a circuit was presented in Section I.2(i). 

In the present system with the copper-2% zinc electrodes, all three processes of protein adsorption, charge transfer, and Faradaic oxidations and reductions are possible. The peaks observed in the anodic and cathodic processes are related, respectively, to oxidations and reductions of the electrode. Copper oxides, chlorides, basic chlorides, phosphates, etc., as well as zinc products, are probable compounds for these electrochemical reactions. Increased Faradaic processes and charge transfer processes with protein solutions are factors for increasing the j-U profiles at U s less than +0.3 V. Since the sweep rate is a constant here, the capacitance of the double layer must increase for the protein solutions, if the increase in j is not all due to Faradaic processes One analog of the electrical double layer capacitance incorporates three capacitors in series (44). Hence... 

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