Potentials and Capacitances

Similarly the difference in potential between E and Eo is RTlF)(bJb), and the charge is again FALb, giving 

By solving the transport equations, we can show that when there is complete Donnan exclusion, the resistance describing the motion of an 

Similarly the resistance describing the motion of the electrons in the polymer is given by Eqn. 11  

Note that while Rx for ionic motion decreases monotonically with oxidation as more counterions are incorporated, Rg for electronic motion passes through a minimum at 50% oxidation when the number of AjB pairs exchanging electrons is at a maximum. 

When the resistive rail is electronic motion in the polymer, we find 

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Hiratsuka et al102 used water-soluble tetrasulfonated Co and Ni phthalocyanines (M-TSP) as homogeneous catalysts for C02 reduction to formic acid at an amalgamated platinum electrode. The current-potential and capacitance-potential curves showed that the reduction potential of C02 was reduced by ca. 0.2 to 0.4 V at 1 mA/cm2 in Clark-Lubs buffer solutions in the presence of catalysts compared to catalyst-free solutions. The authors suggested that a two-step mechanism for C02 reduction in which a C02-M-TSP complex was formed at ca. —0.8 V versus SCE, the first reduction wave of M-TSP, and then the reduction of C02-M-TSP took place at ca. -1.2 V versus SCE, the second reduction wave. Recently, metal phthalocyanines deposited on carbon electrodes have been used127 for electroreduction of C02 in aqueous solutions. The catalytic activity of the catalysts depended on the central metal ions and the relative order Co2+ > Ni2+ Fe2+ = Cu2+ > Cr3+, Sn2+ was obtained. On electrolysis at a potential between -1.2 and -1.4V (versus SCE), formic acid was the product with a current efficiency of ca. 60% in solutions of pH greater than 5, while at lower pH... 

During a number of years we have applied surface orientated analytical methods to the study of protein adsorption on solid surfaces. These Investigations Include in situ studies with elllpsometry, surface potential and capacitance measurements (1.2) We have applied spectroscopic techniques like infra- ed reflection absorption spectroscopy (IRAS, 3-5) and ESCA (5-7) to investigate details in the Interaction between organic molecules and surfaces. Spectroscopic techniques have also been used to... 

The second technique involves using a four probe apparatus, similar to that described by Cahan and Wainright. The membrane sample is placed in an PTFE apparatus which is equipped with two platinum strips in contact with the film, as shown in Fig. 1.115. Two platinum electrodes in a fixed geometry (distance of 1.026 cm) were placed on the surface of the film to measure the membrane potential and capacitance. Conductivity measurements could be obtained by utilizing complex impedance plots, which employ a circuit diagram... 

The relationships between the electrode potential and capacitive current (/g = d2/df) in the three most important cases are as follows. 

Fig. 1. Scheme of experimental setup. L.G., light guide F., light filter P.C.H., perspex cell holder O, outside I, inside T.C., Teflon cell M, membrane. One pair of electrodes used for measuring potential and capacitance second pair used for applying current. 

In a broad sense a parallel combination of charge transfer resistance and CPE elements, in series with finite diffusion element typically represent the circuit. When potential modulation is introduced, charge-transfer-related impedances decrease with increases in electrochemical potential and capacitance for the metal-polymer interface. The capacitance is usually nonideal due to film or electrode porosity [13] and typically is represented by the CPE element. If the film is formed as a reflective boundary, the angle is sometimes different from -90° because of inhomogeneity of the film and distributed values for diffusion coefficients. If two films are formed on the electrode, two RI CPE semicircles are often observed. 

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. 

For the impedance of the resistance and capacitance in series, the current will lead the potential phase angle by... 

The capacitance. The electrical double layer may be regarded as a resistance and capacitance in parallel see Section 20.1), and measurements of the electrical impedance by the imposition of an alternating potential of known frequency can provide information on the nature of a surface. Electrochemical impedance spectroscopy is now well established as a powerful technique for investigating electrochemical and corrosion systems. 

Electrochemical tests This group includes the various electrochemical tests that have been proposed and used over the last fifty or so years. These tests include a number of techniques ranging from the measurement of potential-time curves, electrical resistance and capacitance to the more complex a.c. impedance methods. The various methods have been reviewed by Walter . As the complexity of the technique increases, i.e. in the above order, the data that are produced will provide more types of information for the metal-paint system. Thus, the impedance techniques can provide information on the water uptake, barrier action, damaged area and delamination of the coating as well as the corrosion rate and corroded area of the metal. However, it must be emphasised that the more comprehensive the technique the greater the difficulties that will arise in interpretation and in reproducibility. In fact, there is a school of thought that holds that d.c. methods are as reliable as a.c. methods. 

Figure 1-13 displays the experimental dependence of the double-layer capacitance upon the applied potential and electrolyte concentration. As expected for the parallel-plate model, the capacitance is nearly independent of the potential or concentration over several hundreds of millivolts. Nevertheless, a sharp dip in the capacitance is observed (around —0.5 V i.e., the Ep/C) with dilute solutions, reflecting the contribution of the diffuse layer. Comparison of the double layer witii die parallel-plate capacitor is dius most appropriate at high electrolyte concentrations (i.e., when C CH). 

The Hg/dimethyl sulfoxide (DMSO) interface has been studied by electrocapillary and capacitance measurements in a range of temperatures.291,304 Eamo was measured using the streaming electrode method. All potentials were recorded in a nonisothermal cell against a 0.1 M NaCl calomel electrode (CE) in water at 25°C. The potential difference of the cell CE/0.1 M NaC104 (aq.)/0.1 M NaC104 (DMSO)/CE was -0.096 V. This value was used to recalculate the data.312... 

The capacitance is a readily measured interfacial property and it gives qualitative information on the adsorption of species at the electrode surface. Since the surface charge density, q, is a function of the potential and of coverage, the measured capacitance may be expressed as the sum of a true (high frequency) capacitance and an adsorption pseudocapacitance, i.e. q f(E,6) and hence... 

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. 

A constant bias potential is applied across the sensor in order to form a depletion layer at the insulator-semiconductor interface. The depth and capacitance of the depletion layer changes with the surface potential, which is a function of the ion concentration in the electrolytic solution. The variation of the capacitance is read out when the semiconductor substrate is illuminated with a modulated light and the generated photocurrent is measured by means of an external circuit. 

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... 

An EG G PARC 273 Potentiostat/Galvanostat was used in both the electrolysis and the CV experiments, coupled with an HP 7044B X/Y recorder. A Solartron 1255 HF Frequency Response Analyzer and a Solartron 1286 Electrochemical Interface were employed for the a.c. impedance measurements, using frequencies from 0.1 to 65 kHz and a 10 mV a.c. amplitude (effective) at either the open circuit potential (OCP) or at various applied potentials. As the RE can introduce a time delay at high frequencies, observed as a phase shift owing to its resistance and capacitance characteristics, an additional Pt wire electrode was placed in the cell and was connected via a 6.8 pF capacitor to the RE lead [32-34]. 

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