Double layer capacitance Charging

Murray and co-workers have also demonstrated that the variation in Au-core sizes leads to a transition from metal-like double layer capacitive charging for larger sized particles to redox-like charging for smaller particles ranging between 1.1 nm and 1.9 nm diameter [105] (Figure 20.8). Gold particles stabilized with short chain alkanethiolate monolayers have been used in this study. The capacitance of the clusters is calculated using the concentric sphere capacitance model ... 

Figure 14.3.18 Equivalent circuit for an electroactive monolayer. Rfi = solution resistance, = double-layer capacitance, = charge-transfer resistance, and Cads capacitance of the adsorbed layer.

PDEIS is a new technique based on fast measurements of the interfacial impedance with the virtual instruments [3] that benefits from the efficient synchronization of direct hardware control and data processing in the real-time data acquisition and control [4], The built-in EEC fitting engine of the virtual spectrometer divided the total electrochemical response into its constituents those result from different processes. Thus, just in the electrochemical experiment, we come from the mountains of raw data to the characteristics of the constituent processes - the potential dependencies of the electric double layer capacitance, charge transfer resistance, impedance of diffusion, adsorption, etc. The power of this approach results from different frequency and potential dependencies of the constituent responses. Because of the uniqueness of each UPD system and complex electrochemical response dependence on the frequency and electrode potential, the transition from the PDEIS spectrum (Nyquist or Bode plot expanded to the 3D plot... 

Figure 4.26 Equivalent circuit used for the simulation of a metal deposition process on a stepped surface (Ref. , p. 35). electrolyte resistance, Cdi double layer capacitance, charge transfer resistance, ad-atom charge transfer resistance, ad-atom surface diffusion resistance, R ad-atom incorporation resistance, ad-atom adsorption capacitance, and step half-width. (Reproduced with permission from Ref. [59], 1996, Wiley-VCH.)...

A quick method to estimate the safe charge-injeetion limit of the electrode is to measure the electrode potential as a function of the injected charge [21]. At low charge-injection levels, the electrode potential increases linearly with increasing charge injection as the double-layer capacitance charges. However, with the onset of electrolysis, any additional charge is consumed by hydrolysis and the electrode potential reaches a plateau. 

Fig. 20.25 (a) Randles circuit and (b) the corresponding complex plane plot. Rn,Ca, / ci. and Z are the (uncompensated) series resistance, double-layer capacitance, charge transfer resistance, and Warburg impedance, respectively. 

Figure Bl.28.8. Equivalent circuit for a tliree-electrode electrochemical cell. WE, CE and RE represent the working, counter and reference electrodes is the solution resistance, the uncompensated resistance, R the charge-transfer resistance, R the resistance of the reference electrode, the double-layer capacitance and the parasitic loss to tire ground.

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions. The measured capacitance ranges from about two to several hundred microfarads per square centimeter depending on the stmcture of the double layer, the potential, and the composition of the electrode materials. Figure 4 illustrates the behavior of the capacitance and potential for a mercury electrode where the double layer capacitance is about 16 p.F/cm when cations occupy the OHP and about 38 p.F/cm when anions occupy the IHP. The behavior of other electrode materials is judged to be similar. 

From an electroanalytical point of view, the double-layer capacitance is a nuisance resulting in the charging current, which has no analytical value. 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

This does not imply that this double layer is at its point of zero charge (pzc). On the contrary, as with every other double layer in electrochemistry, there exists for every metal/solid electrolyte combination one and only one UWr value for which this metal/gas double layer is at its point of zero charge. These critical Uwr values can be determined by measuring the dependency onUWR of the double layer capacitance, Cd, of the effective double layer at the metal/gas interface via AC Impedance Spectroscopy as discussed in Chapter 5.7. 

FIG. 7 Simplified equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdi), impedance of base electrolyte transfer (Zj,) and electron-transfer impedance (Zf) is coupled in series with the uncompensated resistance (R ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)... 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

This impedance response, in general, is similar to that elicited from an Armstrong electrical circuit, shown in Figure 3, which we represent by Rfl+Cd/(Rt+Ca/Ra). Rfl is identified with the ohmic resistance of the solution, leads, etc. Cj with the double-layer capacitance of the solution/metal interface Rfc with its resistance to charge transfer and Ca and Ra with the capacitance and resistance... 

Very often, the electrode-solution interface can be represented by an equivalent circuit, as shown in Fig. 5.10, where Rs denotes the ohmic resistance of the electrolyte solution, Cdl, the double layer capacitance, Rct the charge (or electron) transfer resistance that exists if a redox probe is present in the electrolyte solution, and Zw the Warburg impedance arising from the diffusion of redox probe ions from the bulk electrolyte to the electrode interface. Note that both Rs and Zw represent bulk properties and are not expected to be affected by an immunocomplex structure on an electrode surface. On the other hand, Cdl and Rct depend on the dielectric and insulating properties of the electrode-electrolyte solution interface. For example, for an electrode surface immobilized with an immunocomplex, the double layer capacitance would consist of a constant capacitance of the bare electrode (Cbare) and a variable capacitance arising from the immunocomplex structure (Cimmun), expressed as in Eq. (4). 

The preceding derivation has assumed implicitly that the double-layer charging current is negligible in front of the Faradaic current or that it can be eliminated by a simple subtraction procedure. In cases where these conditions are not fulfilled, the following treatment will take care of the problem under the assumption that the double-layer capacitance is not affected appreciably by the Faradaic reaction but may nevertheless vary in the potential range explored. The first step of the treatment then consists of extracting the Faradaic component from the total current according to (see Section 1.3)... 

We have used voltammetric measurements in the absence of the electroactive species to quantitatively evaluate this heat-sealing procedure. The magnitude of the double layer charging current can be obtained from these voltammograms [25,68-70], which allows for a determination of the fractional electrode area (Table 1). This experimental fractional electrode area can then be compared to the fractional pore area calculated from the known pore diameter and density of the membrane (Table 1). In order to use this method, the double layer capacitance of the metal must be known. The double layer capacitance of Au was determined from measurements of charging currents at Au macro-disk electrodes of known area (Fig. 6, curve A). A value of 21 pF cm was obtained. 

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