Electrode / electrolyte interface capacitance

CPE is like a non-ideal capacitor (a capacitor with a constant phase shift lower than 90°). T is a measure of the magnitude of Zcpe n is a. constant parameter (0 < n < 1) representing inhomogeneities in the surface and co is the angular frequency. In the case of n = 1, Zcpe equals a pure capacitor corresponding to the electrode-electrolyte interface capacitance. The parameters n and T depend on the electrode material [3]. 

The thickness 51 of a cyclic voltammogram at a fixed UWR value also conveys useful information. It is related to the scan rate u and to the capacitance Cd of the electrode-electrolyte interface via ... 

The traditional treatment of a double layer at electrode-electrolyte interfaces is based on its separation into two series contributions the compact ( Helmholtz ) layer and the diffusive ( dif ) layer, so that the inverse capacitance is... 

Figure 8. Equivalent circuit of a transmission line network representing the ion migration into the pores. R and C denote the resistance of the electrolyte inside a pore and the doublelayer capacitance of the electrode/electrolyte interface, respectively, both of which are taken per unit length.

The electrode/electrolyte interface discussed above exhibits a capacitance whose magnitude depends on the distribution of ions on the solution side of the interface. In relatively concentrated electrolytes, the capacitance of the Helmholtz layer dominates the interfacial capacitance. For most metals, typical Helmholtz capacitances range from 20-60 pF cm-2, and depend substantially on the applied potential, reaching a minimum at the potential of zero charge where there is no excess charge on either side of the interface. 

Here C is the specific differential double layer capacitance. The two terms on the left side of Eq. (4) describe the capacitive and faradaic current densities at a position r at the electrode electrolyte interface. The sum of these two terms is equal to the current density due to all fluxes of charged species that flow into the double layer from the electrolyte side, z ei,z (r, z = WE), where z is the direction perpendicular to the electrode, and z = WE is at the working electrode, more precisely, at the transition from the charged double layer region to the electroneutral electrolyte. 4i,z is composed of diffusion and migration fluxes, which, in the Nernst-Planck approximation, are given by... 

Numerous models of the electrode-electrolyte interface have been developed. The simplest of these is the Helmholtz double-layer model, which posits that the charge associated with a discrete layer of ions balances the charge associated with electrons at the metal surface. The Helmholtz double-layer model predicts incorrectly that the interfacial capacitance is independent of potential. Nevertheless, cvurent models of the charge redistribution at electrode-electrolyte interfaces owe their terminology to the original Helmholtz model. 

Electrochemical capacitors, also called supercapacitors, are very attractive electricity sources because of their high power, very long durability, and intermediate energy between the classical dielectric capacitors and batteries. The performance of a typical electrochemical capacitor is based on the accumulation of charges in the electrical double layer without faradaic reactions (no electron transfer The electrons involved in double layer charging are the delocalized conduction-band electrons of the electrode material. As shown in Fig. 23.9, an electrochemical capacitor contains one positive electrode with electron deficiency and the second one with electron excess (negative). The capacitance C of one electrode due to a pure electrostatic attraction of ions is proportional to the surface area S of the electrode-electrolyte interface, according to the formula (23.3) ... 

As mentioned in the introduction, the electrical nature of a majority of electrochemical oscillators turns out to be decisive for the occurrence of dynamic instahilities. Hence any description of dynamic behavior has to take into consideration all elements of the electric circuit. A useful starting point for investigating the dynamic behavior of electrochemical systems is the equivalent circuit of an electrochemical cell as reproduced in Fig. 1. The parallel connection between the capacitor and the faradaic impedance accounts for the two current pathways through the electrode/electrolyte interface the faradaic and the capacitive routes. The ohmic resistor in series with this interface circuit comprises the electrolyte resistance between working and reference electrodes and possible additional ohmic resistors in the external circuit. The voltage drops across the interface and the series resistance are kept constant, which is generally achieved by means of a potentiostat. 

Enhancement of Capacitance. The agreement between (modified) Verwey-Niessen models and experiment is less satisfactory for lower-polarity organic media (e.g., DCE, as opposed to NB) and for lower electrolyte concentrations [13]. What is the physical origin of the higher experimental capacitances seen for these conditions As noted by Schmickler and co-workers [59], this enhancement of capacitance at the ITIES relative to the classical model stands in contrast to the response of electrode-electrolyte interface, where the capacitance is often found to be lower than the Gouy-Chapman function. 

On the other hand, the noise (i.e., the background current due to the capacitive charging and discharging current at the electrode-electrolyte interface) is proportional to the surface area (A) of the electrode, as given by... 

EDLCs store energy within the variation of potential at the electrode/electrolyte interface. This variation of potential at a surface (or interface) is known as the electric double layer or, more traditionally, the Helmholtz layer. The thickness of the double layer depends on the size of the ions and the concentration of the electrolyte. For concentrated electrolytes, the thickness is on the order of 10 A, while the double layer is 1000 A for dilute electrolytes (5). In essence, this double layer is a nanoscale model of a traditional capacitor where ions of opposite charges are stored by electrostatic attraction between charged ions and the electrode surface. EDLCs use high surface area materials as the electrode and therefore can store much more charge (higher capacitance) compared to traditional capacitors. 

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