Capacitance, interfacial

The differential interfacial capacitance, or simply the interfacial capacitance, is dehned as (Grahame 1947 Delahay 1965 Singh and Uehara 1998) 

The differential capacitance, working in electrochemistry with metallic electrodes, is a magnitude experimentally accessible, measured with relative ease (Grahame 1947 Delahay 1965 Bard and Fanikner 2000). From Equation 3.24, it can be found that the capacitance, as given by the GC theory, is 

FIGURE 3.10 Differential capacitance of the interface Hg/0.001 M NaF. The potentials are measured against a normal calomel electrode. (—0 ) Experimental results ( ), calculated 

Clearly, only the region near the minimum is reasonably predicted by the GC theory, bnt for the remainder of the potential range, the discrepancies are very high. At higher electrolyte concentrations, the discrepancies are even higher. 

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The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

FIG. 18 Simplified equivalent circuit for externally biased ITIES under illumination. The perturbations introduced by the photoreactions in Fig. 11 are contained within the generator term g. Cji and are associated with the interfacial capacitance and the uncompensated resistance. (From Ref. 83. Reproduced by permission of the Royal Society of Chemistry.)... 

FIG. 6 Randles equivalent circuit for the ITIES Zq is the interfacial capacitance, Zy)v are the faradaic impedances of the charge transfer reactions, and is the solution resistance. 

Calculations, which we shall discuss later, show30"32 that the direct contribution of the metal to the interfacial capacitance (from the conduction electrons) increases with the electron density, in... 

For solvents other than water, the model predicts, even in the absence of calculations, that interfacial capacitances in any solvent should increase in the order Hg < In < Ga because of the increasing electron densities.103 This is, in fact, the case for DMSO and acetonitrile as well as for water. From the model used for the... 

Figure 2.9, it can be seen that the interfacial capacitance does show a dependence on concentration, particularly at low concentrations. In addition, whilst there is some evidence of the expected step function away from the pzc, the capacitance is not independent of V. Finally, and most destructive, the Helmholtz model most certainly cannot explain the pronounced minimum in the plot at the pzc at low concentration. The first consequence of Figure 2.9 is that it is no longer correct to consider that differentiating the y vs. V plot twice with respect to V gives the absolute double layer capacitance CH where CH is independent of concentration and potential, and only depends on the radius of the solvated and/or unsolvated ion. This implies that the dy/dK (i.e. straight lines joined at the pzc. Thus, in practice, the experimentally obtained capacitance is (ddifferential capacitance. (The value quoted above of 0.05-0,5 Fm 2 for the double-layer was in terms of differential capacitance.) A particular value of (di M/d V) is obtained, and is valid, only at a particular electrolyte concentration and potential. This admits the experimentally observed dependence of the double layer capacity on V and concentration. All subsequent calculations thus use differential capacitances specific to a particular concentration and potential. 

Based on the discussion above, it seems evident that a detailed understanding of kinetic processes occurring at semiconductor electrodes requires the determination of the interfacial energetics. Electrostatic models are available that allow calculation of the spatial distributions of potential and charged species from interfacial capacitance vs. applied potential data (23.24). Like metal electrodes, these models can only be applied at ideal polarizable semiconductor-solution interfaces (25)- In accordance with the behavior of the mercury-solution interface, a set of criteria for ideal interfaces is f. The electrode surface is clean or can be readily renewed within the timescale of... 

The interfacial capacitance can be determined experimentally as a function of applied... 

Capacitance impedance loop is smaller and its interfacial capacitance of mineral/solution is bigger in the absense of DDTC. But the capacitance impedance loop obviously enlarges and the interfacial capacitance becomes small in the presence of DDTC. With the DDTC concentration increasing, there is no obvious change of the capacitance impedance loop, but its interfacial capacitance increases. 

Consequentally, the interfacial capacitance in the presence of DDTC is smaller than that in absence of DDTC, so mineral hydrophobicity will increase when an organic matter is adsorbing on a mineral electrode. It reasonably explains the experimental appearance in Fig. 4.12. 

The interfacial capacitance increases with the DDTC concentration added. The relationship among potential difference t/ of diffusion layer, the electric charge density q on the surface of an electrode and the concentration c of a solution according to Gouy, Chapman and Stem model theory is as follows. 

Microelectrodes were mentioned previously in Chapter 5, where we saw how their small size increased the faradaic efficiency since the interfacial capacitance Cdi is decreased, itself minimizing the charging currents. Microelectrodes can be purchased relatively cheaply, and in a variety of types, e.g. hemispherical and flat circular rings or bands, with a wide range of diameters. Such electrodes were discussed previously in Section 5.3. 

Au(lll) and Au(210) electrodes have been investigated [20] using electrochemical immitance spectroscopy in aqueous solutions of HGIO4 and KF in the doublelayer potential region, in order to identify and explain frequency dispersion of interfacial capacitance. At negative potentials, the behavior closest to the ideal dispersionless behavior has always been observed. In KF solutions, at positive potentials, dispersion on both electrodes may be attributed... 

Investigation of thiol- and disulfide-modified oligonucleotides with either 25 or 10 bases, or base pairs immobilized on polycrystaUine and Au(lll) electrodes has also been carried out [171]. In these studies, several techniques were employed, including X-ray photoelectron spectroscopy, cyclic and differential pulse voltammetry, interfacial capacitance data, and in situ STM. 

In addition to the use of open-circuit photopotentials, the variation in interfacial capacitance with electrode potential can be utilized to determine the flatband potential as well as the semiconductor dopant concentration. A discussion of the capacitance-potential response of the semiconductor-electrolyte interface is beyond the scope of this text. The reader is referred to Reference 7 for a more complete discussion of this subject. 

When the electrochemical properties of some materials are analyzed, the timescale of the phenomena involved requires the use of ultrafast voltammetry. Microelectrodes play an essential role for recording voltammograms at scan rates of megavolts-per-seconds, reaching nanoseconds timescales for which the perturbation is short enough, so it propagates only over a very small zone close to the electrode and the diffusion field can be considered almost planar. In these conditions, the current and the interfacial capacitance are proportional to the electrode area, whereas the ohmic drop and the cell time constant decrease linearly with the electrode characteristic dimension. For Cyclic Voltammetry, these can be written in terms of the dimensionless parameters yu and 6 given by... 

In contrast, as discussed earlier in Section 3.2.1, studies of the interfacial capacitance allow the effect of the applied potential on the adsorption thermodynamics to be elucidated. For example, as discussed above, cyclic voltammetry reveals that the dependence of the surface coverage T on the bulk concentration of 20H-AQ is accurately described by the Langmuir isotherm over the concentration range 20 nM to 2 iM. However, since adsorption is reversible in the anthraquinone system, the effect of changing the potential at which the monolayer is formed on the surface coverage, or the adsorption thermodynamics, cannot be investigated by ex situ... 

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. 

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