Double layer, capacitance/capacitor thickness

The final point we would like to emphasize is that the diffusion layer should never be confused with the double layer. The double layer arises because the charge on the electrode is counterbalanced by ions of opposite charge that are specifically adsorbed at the electrode surface. Such a construction resembles a capacitor and gives rise to double-layer capacitance, which will be described in detail later on. The thickness of the double layer is only a few A, much smaller than 6. 

The simplistic approach that capacitance should be related with the electrodes surface area comes flum the analogy with vacuum (air) capacitors where capacitance originates ftom a double layer of nanometer thickness over a flat surface. By contrast, high surfece... 

The interior has a well-defined electrical capacitance with respect to the outside. Double layers are formed in the electrolyte/membrane interphase both internally and externally. The measured intracellular potential includes the potential of these charged double layers (Section 7.5). A double layer has a thickness on the order of 0.1—10 nm, and the cell membrane is approximately 7 nm. The total measured BLM capacitance, double layers included, is about 1 pF/cm. The charge q necessary to obtain a voltage U across a capacitor is q — CU [coulomb]. With a cell radius of 2 pm, the membrane area is A = 4Tcr = 50 X 10 [m ]. With v = 60 mV, the charge is q = 0.5 pC. Because a... 

It is often found that the double-layer capacitance or a coating capacitance does not behave like an ideal capacitor, experimentally manifested in the complex plane plot by a depressed semicircle whose center lies below the real axis. This behavior is usually attributed to some distribution (or dispersion) in some physical property of the system (e.g., the porous surface of the metal or the varying thickness or composition of a coating) and is modeled by the use of a constant phase element (CPE) [30]. 

The complete ac equivalent circuit of an EIS is complex, as it involves components such as the bulk resistance and space-charge capacitance of the semiconductor, the capacitance of the gate insulator, the interface impedance at the insulator-electrolyte interface, the double-layer capacitance, the resistance of the bulk electrolyte solution and the impedance of the reference electrode [58-60]. However, considering usual values of insulator thickness ( 30-100 nm), the ionic strength of the electrolyte solution (>10 -10 M) and low frequencies (<1000 Hz), the equivalent circuit of an EIS structure can be simplified as a series connection of insulator capacitance and space-charge capacitance for the semiconductor, which is similar to the MIS capacitor [58-60]. Therefore, the capacitance of the EIS structure may be expressed in terms of the electrolyte solution/ insulator interface potential (cp) as ... 

Interesting porous structures are achieved by anodic activation of glassy carbon (GC) in 3 M H2SO4 at -1-1.98 V vs. SCE. The porous layers are well contacted by the pristine GC basis behind this layer [240,434]. Application in electrochemical double layer capacitors seems to be straightforward. However, maximum capacitances are otily about 1 F/cm. This is due to the limitation of the layer thickness. In comparison to Ae maximum in Fig. 24 in the same electrolyte, namely 200 F/cm, this means a layer thickness of only 50 pm. Thicker layers become instable due to scaling. 

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. 

Based on the above discussion, there are a number of factors that affect the double-layer behavior and the corresponding EDL capacitance, such as the concentration and size of ions, the ion-specific adsorption, the ion-solvent interaction, and the solvent in the electrolytes. The thickness of the EDL is typically on the order of several angstroms in aqueous solution. Since the distance separating the charges in an EDL is extremely small, the specific capacitance (capacitance normalized by the effective surface area) of EDL can reach a very high value in the aqueous electrolyte. In contrast, the specific capacitance of a typical parallel-plate capacitor is quite small... 

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. 

The thickness of the Helmotz double layer, which is about a few nanometers, over an extensively developed area, means that a significantly greater quantity of charge can be accumulated compared to classical capacitors. It is possible to obtain a capacitance of several thousand Farads for one unit element. 

The capacitance is defined as the charge divided by the voltage, and for a parallel plate capacitor the capacitance is equal to eco/t, where t is the distance between the plates. We can therefore see from Eq. (4.42) that the electrical double layer can be treated as a parallel plate capacitor with a thickness of l/K. 

In general, the Helmholtz layer can be treated as a linear capacitor. In a theoretical model of the electric double-layer, the compact Helmholtz layer is generally treated as an ideal capacitor with a fixed thickness (d), and its capacitance is considered unchanging with the potential drop across it. Therefore, fhe capacifance of fhe Helmholtz layer can be treated as a constant if fhe femperafure, fhe dielectric constant of the electrolyte solution inside the compact layer, and its thickness are fixed. However, if the specific ion adsorpfion happened on the electrode surface, the dielectric constant of the electrolyte solution inside the compact layer may be affected, leading to non-linear behavior of the Helmholtz layer. This will be discussed more in a later section. 

---