Capacity-potential curves

Figure 5. Capacity-potential curves of gold at various temperatures in the frozen electrolyte (taken from ref.16, with permission of the Electrochemical Society,...

The right hand side of Fig. A.4.6 is contained in Fig. 3.3. Capacity measurements can readily be made at solid electrodes to study adsorption behavior. For a review see Parsons (1987). As Fig. A.4.7 illustrates, capacity potential curves of three low-index phases of silver, in contact with a dilute aqueous solution of NaF, show different minimum capacities (corresponding to the condition o = 0) and therefore remarkably different potentials of pzc. The closest packed surface (111) has the highest pzc and the least close-packed (110) has the lowest pcz these values differ by 300 mV. Such complications observed with single crystal electrodes, seem likely to have their parallel at other solid surfaces. For example, it is to be expected that a crystalline oxide will have different pzc values at its various types of exposed faces. 

Capacity-potential curves for three low-index planes of silver in contact with aqueous 0.01 M NaF at 25 °C. 

The effect of the supporting electrolyte on the fpzc of Au electrodes indicates specific affinity of either cations or anions of the dissolved salt to the given surface. For example, the studies performed by Hamelin [34] have shown the effect of the supporting electrolyte on the double-layer capacity - potential curves (see Table 3). 

Some conclusions pertaining to adsorption of 1-pentanol riboflavin and thioctic acid on Au electrode have been drawn from differential capacity-potential curves [274]. It has been found, for instance, that adsorption of these compounds obeys the Langmuir isotherm. Moreover, the free energies of adsorption have been determined. 

Would Eq. (6.261) for the total differential capacity be able to reproduce the experimental capacity curves Let us have a look again at one of the complete capacity-potential curves shown in Fig. 6.65(b) and illustrated in Fig. 6.106 in this section. This is not a simple curve. It breaks out into breaks and flats, and it has a complicated fine structure that depends upon the ions that populate the interphasial region. Whereas there is a region of constant capacity at potentials more negative than the electrocapillary maximum, there is also a "hump in the capacity-potential... 

Fig. 6.106. The lateral-repulsion model for the explanation of the capacity-potential curve.

In the absence of specific adsorption and dipolar contributions, there is no excess charge in the whole double layer when positive and negative ions are equally distributed at the plane of closest approach qM and A02 will be both zero. The corresponding electrode potential is the potential of zero charge (pzc) which can be evaluated from the minimum in the differential capacity—potential curve for a metal electrode in contact with a dilute electrolyte [6]... 

Bockris et al. [87, 290, 291] have recently reported results of a comprehensive program of surface characterization of a large number of perovskite oxide electrodes in oxygen evolution investigations. Anodic and cathodic oxygen reactions were studied in detail as a function of the solid-state surface properties of these materials. Capacity-potential curves were analysed in terms of the Mott-Schottky treatment and indicated that the potential distribution in the oxide corresponds to a depletion of electrons at the oxide electrode surface in the potential region where oxygen reduction... 

The results of the measurements with intrinsic, p-, and n-type germanium (N = 3.5 x 10 cm 3, Np = 7, 5 x l(r cm ) in IN KOH at 25° and 45°C are shown in Figs. 3-5. The circular frequency, w =2irf, used for the measurement is indicated at each curve. Ail measurements were made with and without illumination of the electrodes. The capacity-potential curve... 

Efimov and Erusalimchik (10) have criticized the results of Bohnenkamp and Engell (9), They state that the capacity values of the minimum of the capacity-potential curve reported by Bohnenkamp and Engell are too. small, compared with (heir own measurements, and assume that this is due to a poor contact at the reverse side of the germanium electrodes and an inadequate preparation of the surface. We tested the contact on the reverse side with the help of a sample contacted at both sides and found no capacitive component large enough to in-... 

Zviagin and Liutovich (11) found similar minimum values for p-type Si as we did for the Ge samples. The theoretical curve of the Russian authors is calculated on the assumption that the minority carriers are depleted. This is possible for a p-type semiconductor only in the case of cathodic polarization. Since the Russian authors did not take into account the possibility of enrichment of the minority carriers, they did not get a distinct minimum of the theoretical capacity-potential curve. We found the minimum for n-type Ge under reverse bias, i. e., under anodic current. This result is to be expected (in contrast to a common rectifier) as long as the resistance across the phase boundary (R ) is high compared to the recombination rate or the rate orformation of free carriers. It is to be expected, in other words, as long as the electrochemical potential of the free carriers remains nearly constant across the space charge up to the surface. The Russian authors point out that the measured capacity is not equal to the space charge capacity, but should be related to it. This relationship is indicated by the measured frequency dependence of the measured impedances. It is in agreement with our assumption that the... 

It will be useful to emphasize the practical aspects of the problem which are twofold the solution side and the metal side. On the solution side at the interphase, a level of impurities which does not interfere with dl measurements over the time scale of a mercury-drop lifetime, which is 4 s, could completely hinder observations of significant current-potential curves [i( )] or meaningful differential capacity-potential curves [C(E)] at a solid metal electrode which will stay 2, 3, or 4 h in the same solution. Not only must the water, salts, and glassware be kept clean, but also the gas used to remove oxygen and the tubing for the gas. Of course, conditions are less drastic for studies of strong adsorption than in the case of no adsorption also bacteria develop less in acid solutions than in neutral ones (which cannot be kept uncontaminated more than one or two days). This aspect will not be discussed in this chapter. 

In this work, the main aim has been to determine the steady-state behaviour behaviour by measuring the current-potential curve. In general, the steady state is the most important characteristic of an electrode reaction. Fortunately, most known electrochemical reactions have a steady state and are variations of the redox type of reaction. As shown above, the steady current-potential curve can be exactly interpreted for redox reactions. In order carry out a complete analysis, it is essential to measure the components of the steady state by impedance-potential measurements. In addition, impedance delivers information about the charging processes as they appear in the high-frequency double layer capacity-potential curve. This last parameter is the parameter which should connect electrochemistry and surface science. The unfortunate fact is that it is still not very well understood. 

Fig. 5. Analysis of the experimental steady-state current—potential and impedance-potential data from E = — 650 mV to E = —150 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 3.0 M sulphuric acid at 65°C. (a) Steady state current-potential curve. The potentials are the measured potentials, (b) High-frequency double layer capacity-potential curve. The potentials are the measured potentials.

However, the active dissolution of titanium depends markedly on temperature in acid solution. At lower temperatures, the picture is not so clear. It is necessary to have a quantitative measure of the rate of the hydrogen reaction and the titanium dissolution reaction. The complete set of current-potential and impedance-potential data has been tested against the theory given above. The best strategy seems to be to fit to a single electrode reaction and then to look for deviations from the expected behaviour for a perfect redox reaction. A convenient way of doing this is to represent the electrochemical data as a standard rate constant-potential curve in conjunction with a double layer capacity-potential curve [21]. 

Fig. 6. Analysis of the experimental steady-state current-potential and impedance-potential data from E = -1300 mV to E = -600 mV for a titanium rotating-disc electrode (45 Hz) in a solution of 2 M perchloric acid, (a) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10-5cm s and E° = —246 mV. The Tafel slope bc = 120 mV and the measured ohmic resistance was 0.3 ohm cm2. The potentials are the "true potentials, (b) Standard rate constant-potential curve calculated for the hydrogen evolution reaction on titanium assuming that DA = 7.5 x 10-5 cms-1 and E° = — 246mV. The Tafel slope bc = 211 mV and the measured ohmic resistance was 0.3 ohm cm2. The potentials are the "true potentials, (c) High-frequency double layer capacity-potential curve obtained from the impedance data. The potentials are the measured potentials.

The electrochemical behaviour of stainless steel has not been worked out completely, although the measured data are available. However, one aspect of the behaviour, based on the measured double layer capacity data, seems to be susceptible to interpretation. The capacity-potential curves are determined by the state of the metal surface and by the ionic environment. In this work, it has been assumed that the ionic environment is a constant. This means that the double layer capacity-potential curves should reflect the nature of the metal surface just as, say, an electron energy spectrum in surface science. Stainless steel has a complicated electrochemical behaviour. In previous work [22] an attempt has been made to compare the double layer capacity curves measured during dissolution and passivation of the stainless steel with that of the pure components. It seems that all the data in the high frequency regime can be fitted to eqn. (70) with the Warburg coefficient set equal to zero. 

Fig. 10. Double layer capacity-potential curves for different metal rotating-disc electrodes (45 Hz rotation speed) in the given acid solutions, (a) Nickel in 1M HC104 (b) electropolished nickel in 1M HC104 (c) nickel in lM HC1 (d) chromium in 1M HC104 (e) iron in 1M HC104 and (f) stainless steel (304 L) in 1M HC104.

The graphs [Fig. 17(a) and (b)] show the large increase in standard rate constant as the potential goes negative, suggesting that the palladium electrode is much more active for the deposition reaction at potentials less than about 100 mV. This effect is also reflected in Fig. 17(c) and (d) in which the double layer capacity-potential curves are reproduced. These show that the double layer capacity sharply increases with negative potential. The main reason for this effect is, undoubtably, an area increase as palladium metal is deposited. Figure 17(e) and (f) show the associated log current-potential curves (corrected for ohmic resistance). These curves are also reproduced by calculation from the measured impedance-potential curves. 

Fig. 17. Analysis of current-potential and impedance-potential data for the active deposition-dissolution of palladium in solutions of 1M hydrochloric acid + 0.01 M PdCl2 (A) and 0.1 M hydrochloric acid + 0.91 M perchloric acid + 0.01 M PdCl2 (B). (a) Standard rate constant-potential curve calculated according to the reaction scheme (78) using experimental data obtained for palladium in solution A with the parameters i>a = 220 mV, 6C = 60 mV, and E° = 575 mV. (b) Standard rate constant-potential curve calculated according to the reaction scheme (78), using experimental data obtained for palladium in solution B with the parameters i>a = 220 mV, bc = 60 mV, and ° = 575 mV. (c) Double layer capacity-potential curve for solution A. (d) Double layer capacity-potential curve for solution B. (e) Current-potential curve for solution A. (f) Current-potential curve for solution B.

Fig. 20. Typical result of measuring the characteristics of dissolution of a dental amalgam (Dispersalloy, electrode 37 HD) in 2/3 strength Ringer s solution. The measurements are almost in the steady state at 60 s per potential point, (a) Charge transfer-potential curve (b) Current-potential curve, also showing the return potential sweep and (c) double layer capacity-potential curve.

The capacity of the double layer depends strongly on the solvent but there is a qualitative similarity in the shape of capacity-potential curves in all solvents including water. Early measurements seemed to indicate qualitative differences between water and such non-aqueous solvents as methanol, ethanol and ammonia which have featureless capacity curves in contrast to the characteristic humped curves found in water. However, more recent studies have shown that capacity humps occur commonly in solvents of widely differing types. They are found in solvents of high and medium dielectric constant and probably have a common origin in field reorientation of solvent dipoles. 

Cmin is measured at the minimum on the cathodic branch of the capacity-potential curve for 0.1 Af KPF solutions exc t where otherwise stated, t Measured along axis of the dipole assuming a planar molecule. 

Fig.l. Differential capacity-potential curves at the HMDE in 0.5 M LiCl04 (20 % ethanol) with rhamnolipid-concentrations (1) 0 (2)... 

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