Double layer, capacitance/capacitor capacity

The energy capacity of ECs arises from either double-layer capacitance for electric doublelayer capacitors (EDLCs) or pseudocapacitance for redox capacitors [2, 3]. The energy storage mechanism of EDLCs is based on non-faradic phenomena in electric double layer formed at an electrode/electrolyte interface. In regard to electrode active materials for EDLCs, carbon materials such as activated carbons have been most widely used [4] because of their reasonable cost, good electrical conductivity, and high specific surface area. However, there is a limitation in their specific capacitance the gravimetric capacitance of most carbon materials does not linearly increase with an increase in the specific surface area above 1,200 m g [5]. 

It is instructive to compare this to the capacitance of a plate capacitor o A/d. Here, A is the cross-sectional area and d is the separation between the two plates. We see that the electric double layer behaves like a plate capacitor, in which the distance between the plates is given by the Debye length The capacity of a double layer — that is the ability to store charge — rises with increasing salt concentration because the Debye length decreases. 

An important quantity with respect to experimental verification is the differential capacitance of the total electric double layer. In the Stern picture it is composed of two capacitors in series the capacity of the Stem layer, Cgt, and the capacitance of the diffuse Gouy-Chapman layer. The total capacitance per unit area is given by... 

The second meaning of the word circuit is related to electrochemical impedance spectroscopy. A key point in this spectroscopy is the fact that any -> electrochemical cell can be represented by an equivalent electrical circuit that consists of electronic (resistances, capacitances, and inductances) and mathematical components. The equivalent circuit is a model that more or less correctly reflects the reality of the cell examined. At minimum, the equivalent circuit should contain a capacitor of - capacity Ca representing the -> double layer, the - impedance of the faradaic process Zf, and the uncompensated - resistance Ru (see -> IRU potential drop). The electronic components in the equivalent circuit can be arranged in series (series circuit) and parallel (parallel circuit). An equivalent circuit representing an electrochemical - half-cell or an -> electrode and an uncomplicated electrode process (-> Randles circuit) is shown below. Ic and If in the figure are the -> capacitive current and the -+ faradaic current, respectively. 

Double-layer capacity (Capacitance) — The excess charge stored on both sides of the double layer depends on the -> electrode potential, therefore the double layer can be represented by a capacitor in equivalent circuits. In general, this capacitor in nonlinear, i.e., the stored charge is not proportional to the potential. Hence two different capacities can be defined ... 

Capacitive effects. The presence of a protective layer on the surface of a metallic cluster decreases the capacity of the cluster. For a planar metal electrode, the electrical double layer comprised of the charge on the surface of the electrode and the ions of opposite charge in the solution (or the solvent dipoles) can be modeled as a parallel plate capacitor with capacity Cpp in Farads (F) given by... 

The most important metric for all types of capacitors is charge storage ability. This is described in terms of capacity (coulombs per gram) or capacitance (capacity per volt, F/g or F/cm ). Strictly speaking, capacitance and specific capacitance refer to charge per volt accumulated in the double layer... 

The gavanostatic transient method can be used to measure the double layer capacity and the ohmic drop in the electrolyte between the working and reference electrodes. Figure 5.14 shows the initial variation of the potential resulting from a current step. During this period, diffusion is of little importance because its time constant is usually much larger. The electrode acts like a capacitor connected in parallel with a resistance, where the capacitor represents the double layer capacity and the parallel resistance corresponds to the transfer resistance of the electrode reaction (Section 3.5). The applied current I is the sum of the capacitive current Iq given by (5.94) and the faradaic current I-p described by the Butler-Volmer equation ... 

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