Double-layer capacitors voltage dependence

With a dripping mercury electrode the surface is ideal and the double layer is modeled as a pure, frequency independent capacitor, somewhat voltage-dependent. The capacitance values are very high because of the small double-layer thickness, Cdi is about 20 pF/cm. With solid electrode materials, the surface is of a more fractal nature, with a distribution of capacitive and resistive properties. The actual values are dependent on the type of metal, the surface conditions, the type of electrolyte, and the applied voltage. The capacitance increases with higher electrolyte concentration. The double-layer capacitor is inevitable it is there as long as the metal is wetted. Cdi may dominate the circuit if there are no sorption or electrode reaction processes, or if the frequency is high. 

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

Capacitors can be polarized or non-polarized, depending on the - dielectric. Non-polarized devices have dielectrics consisting of ceramics or polymers (such as polystyrene, polyester, or polypropylene). They are normally box-shaped and their capacity is usually in the range from pF to pF, the maximum voltage up to 1000 V. Polarized capacitors are electrochemical devices the dielectric is an anodic oxide of A1 (pF to 100 mF, potentials up to 1000 V), Ta (capacities pF to 100 pF, potentials up to 20 V), or Nb (- electrolytic capacitor) or a double layer (- supercapacitor, capacities up to some 10 F and potentials up to 2.5 V or 5 V). Aluminum electrolytic capacitors are normally of cylindrical shape with radial or axial leads. Tantalum capacitors are of spherical shape and super capacitors form flat cylinders. 

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. 

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