Electrical double-layer capacitors capacitance properties

MerleL C., M. Salanne, B. Rotenberg, and P. A. Madden. 2013. Influence of solvation on the structural and capacitive properties of electrical double layer capacitors. Electrochimica Acta 101 262—271. 

Double-layer properties of porous carbon materials have been widely investigated in relation to the development of the electrochemical capacitors. For detailed information the reader should consult specialized literature. For porous carbons materials, the double-layer capacitance depends on their specific snrface area [82,83], pore stmcture (notably, the pore size distribntion) [84-87], and their crystalline stmctnre and snrface chemistry [83,88,89], Shi [84] measnred the dc capacitance of varions carbons in a KOH electrolyte and noticed that the overall capacitance may reasonably be described as a sum of the capacitance of micro- and mesopores. Assuming that the electrical double layer propagates into micropores accessible for N2 adsorption, the author estimated the differential donble-layer capacitance per unit of micropore surface area as 15 to 20 p,F/cm. Lower values were reported by Vilinskaya... 

The problem when trying to make an electrical model of the physical or chemical processes in tissue is often that it is not possible to mimic the electrical behavior with ordinary lumped, physically realisable components such as resistors (R), capacitors (C), inductors, semiconductor components, and batteries. Let us mention three examples 1) The constant phase element (CPE), not realizable with a finite number of ideal resistors and capacitors. 2) The double layer in the electrolyte in contact with a metal surface. Such a layer has capacitive properties, but perhaps with a capacitance that is voltage or frequency dependent. 3) Diffusion-controlled processes (see Section 2.4). Distributed components such as a CPE can be considered composed of an infinite number of lumped components, even if the mathematical expression for a CPE is simple. 

The first attempts to achieve such a device were made in the 1970s. The cell had a non-symmetric Ag/RbAg4l5/C structure with a double-layer capacitance at the carbon electrode in the range of 10-40 nF cm" interface area However, due to the redox reaction, the working voltage was too low (<0.7 V) for the electronic devices of the time. Furthermore, the reversibility of the Ag electrode was poor and it was difficult to use fully the surface area of the ultrafine carbon. More recently, double-layer capacitors using acidic solution (H2SO4) as liquid electrolyte were developed by NEC (Nippon Electric Co. Ltd). A liquid electrolyte allows most of the surface area of the carbon electrode to be used. The electrical characteristics of the devices can be classified in relation to the properties of each material as follows. 

The electrical response of such a system is comparable to that of a capacitor. Being of faradic origin and non-electrostatic, this capacitance is distinguished from the double-layer one and is called pseudo-capacitance. In summary, the electrical double-layer formation is a universal property of a polarized material surface, and pseudo-capacitance is an additional property which depends both on the type of electrode material and electrolyte. Compared to the double-layer normalized capacitance ( 10 pF cm ), it has generally a high value (100-400 pF cm ), because it involves the bulk of the electrode and not only the surface. From a practical point of view, pseudo-capacitance contributes to enhancing the capacitance of materials and their energy density. 

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