Capacitance phase boundary

In summary AC impedance spectroscopy provides concrete evidence for the formation of an effective electrochemical double layer over the entire gas-exposed electrode surface. The capacitance of this metal/gas double layer is of the order of 100-300 pF/cm2, comparable to that corresponding to the metal/solid electrolyte double layer. Furthermore it permits estimation of the three-phase-boundary length via Eq. 5.62 once the gas exposed electrode surface area NG is known. 

The existence of Galvani potentials between two different conducting phases is connected with the formation of an electric double layer (EDL) at the phase boundary (i.e., of two parallel layers of charges with opposite signs, each on the surface of one of the contacting phases). It is a special feature of such an EDL that the two layers forming the double layer are a very small (molecular) distance apart, between 0.1 and 0.4nm. For this reason EDL capacitances are very high (i.e., tenths of pF/cm ). 

Diffusion resistances can occur for Li in the electrode, but also for the salt in the electrolyte (if anion conductivity in the electrolyte is significant). Further effects are due to depletion of carriers at a phase boundary. In such cases, time dependencies of the electrical properties occur (in addition to Rs, effective capacitances Cs also appear). The same is true for impeded nucleation processes. Since any potential step of the electrochemical potential can be connected with current-dependent effective resistances and capacitances, the kinetic description is typically very specific and complex. As the storage processes in Li-based batteries are solid-state processes, the... 

Diffuse layer capacitance — The diffuse layer is the outermost part of the electrical double layer [i]. The electrical double layer is the generic name for the spatial distribution of charge (electronic or ionic) in the neighborhood of a phase boundary. Typically, the phase boundary of most interest is an electrode/solution interface, but may also be the surface of a colloid or the interior of a membrane. For simplicity, we here focus on the metal/solution interface. The charge carriers inside the metal are electrons, which are confined to... 

This model is based on the Gouy-Chapman theory (diffuse double-layer theory). The theory states that in the area of the boundary layer between solid and aqueous phase, independently of the surface charge, increased concentrations of cations and anions within a diffuse layer exists because of electrostatic forces. In contrast to the constant-capacitance model, the electrical potential does not change up to a certain distance from the phase boundaries and is not immediately declining in a linear manner (Fig. 14 a). Diffusion counteracts these forces, leading to dilution with increasing distance from the boundary. This relation can be described physically by the Poisson-Boltzmann equation. 

The constant-capacitance model assumes that the double layer on the solid-liquid phase boundary can be regarded as a parallel-plate capacitor (Fig. 14b). 

Applications that have received attention, and the material properties that enable them, are shown in Figure 27.1. These applications are reviewed in detail in Waser and Ramesh. Decoupling capacitors and filters on semiconductor chips, packages, and polymer substrates (e.g., embedded passives ) utilize planar or low aspect ratio oxide films. These films, with thicknesses of 0.1 to 1 J,m, are readily prepared by CSD. Because capacitance density is a key consideration, high-permittivity materials are of interest. These needs may be met by morpho-tropic phase boundary PZT materials, BST, and BTZ (BaTi03-BaZr03) solid solutions. Phase shifters (for phase array antennas) and tunable resonator and filter applications are also enabled by these materials because their effective permittivity exhibits a dependence on the direct current (DC) bias voltage, an effect called tunability. 

Another example of specific ion adsorption was discussed in terms of the formation of interfacial ion pairs between ions in the aqueous and the organic phase. The contribution of specific ionic adsorption to the interfacial capacitance can be calculated using the Bjerrum theory of ion-pair formation. The results show that a phase boundary between two immiscible electrolyte solutions can be described as a mixed solvent region with varying penetration of ion pairs into it, depending on their ionic size. The capacitance increases with increasing ionic size in the order Ii+ < Na+ < K" " < Rb < Cs" ". Yufei et al. [22] found that significant specific ion adsorption occurs at the interface between two immiscible electrolytes... 

Such a Fermi level shift can result in effects which can easily be confused with capacitive effects . These effects are called by the electrochemists, pseudo-capacitive effects. In solid state electrochemistry they are sometimes also described as an adsorption with partial transfer. To illustrate the point, let us consider the schematic situation depicted in Fig.6, It is familiar to electrochemists. Without entering into the details of the relevant surface levels and densities, we can say, from a thermodynamical viewpoint, that the electrode measures the chemical activity of 0 atoms in a perturbed layer located at the phase boundary. The electrode potential variations are related to the 0-chemical-activity-variations by formula (22). Extending the hypotheses, here, the 0 atoms are supposed to be soluble in the electronic conductor but the direct exchange of oxide ions is regarded as impossible. 

Except for the case of the micropipette electrode for which the conducting electrode material is an electrolyte, the electrodes are built from metals or conducting ceramics like titanium nitride (TIN). Therefore, the boundary between the electrode and the electrolyte forms a phase boundary. Eor a well conducting electrolyte, this phase boundary can be modeled by a capacitance whose dielectric consists of two consecutive water molecule layers. The conducting plates of this capacitor are the electrode and the electrolyte. The two layers are the water dipoles adsorbed on the electrode surface and the hydration envelope of the ions in the vicinity of the... 

Fig. 7.25 The voltage development on polarization of an ion-blocking cell corresponding to Fig. 7.23 with a constant current for To t- - ears as a purely ohmic contribution (IR drop) and the phase boundary process becomes apparent. For times of the order of r (3) the phase boundary process is complete (C elements impermeable). At this time resolution the initial jump becomes I(R o + R ). The bulk polarization is stationary when t t (4) and all capacitive elements are blocked U(t = oo) = R- - + Re n [431].

Deposits with extremely low porosities or an interconnected network of fine crystalline grain boundaries would be expected to show some loss of phase shift at low frequencies (i.e., a less than fully capacitative response) as the real resistance of the flaws becomes detectable, Fig. 19B. The value of RP obtained is inversely proportional to the corrosion rate. 

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