The double-layer capacitance at electrode interfaces
An important class of electrochemical capacitors utilizes the co-called double-layer capacitance that arises at all electrode interfaces with electrolyte solutions or ionic melts. The concept and model of the double layer arose in the work of von Helmholtz (1853) on the interfaces of colloidal suspensions and was subsequently extended to surfaces of metal electrodes by Gouy, Chapman, and Stern, and later in the notable work of Grahame around 1947. Models of the double layer are shown in Figure 2, with their capacitor-like structures.
Helmholtz envisaged a capacitor-like separation of anionic and cationic charges across the interface of colloidal particles with an electrolyte. For electrode interfaces with an electrolyte solution, this concept was extended to model the separation of "electronic" charges residing at the metal electrode surfaces (manifested as an excess of negative charge densities under negative polarization with respect to the electrolyte solution or as a deficiency of electron charge density under positive polarization), depending in each case, on the corresponding potential difference between the electrode and the solution boundary at the electrode. For zero net charge, the corresponding potential is referred to as the "potential of zero charge".
In response to positive or negative electric polarization of the electrode relative accumulations of cations or anions develop, respectively, at the solution side of the charged electrode. If, for energetic reasons, the ions of the electrolyte are not faradaically dischargeable (that is no electron transfer can occur across the interface ("ideally polarizable electrode", for example a mercury electrode, Grahame 1947 and Parsons 1954), then an electrostatic electrical equilibrium is established at the interface resulting in a "double layer" of separated charges (electrons or electron deficiency at the metal side and cations or anions at the solution side of the interface boundary), negative and positive, across the interface.
The difference of potential extends beyond the immediate layer of solvated ions in the compact, capacitor-like (Helmholtz) region, out into solution, so that a further diffuse region capacitance (the diffuse-layer capacitance "Cdiff") arises. It combines with that of Helmholtz's region "CH" in series. (See the Appendix for further details.)
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