Minimum capacitance

Frumkin was the first to give a qualitative consideration of the electrochemical properties of pc electrodes.10,20 70 He noted that the charge fixed value of the potential E and this may change the form of the capacitance curve near the diffuse-layer capacitance minimum. Important results were obtained in a pioneering paper by Valette and Hamelin.67 They compared experimental capacitance curves for a pc-Ag electrode and its three basic faces. They found that the capacitance of a pc-Ag electrode can be obtained by the superposition of the corresponding Cj, E curves for individual faces exposed at the pc surface, i.e. 

A weighted sum of C,E curves for the faces was found to be similar to the C,E curve for a pc electrode. According to Valette and Hamelin,67 all main Ag faces [(111), (100), and (110)] are exposed on the surface, their fractions 0j on the surface being 0.31, 0.23, and 0.46, respectively. These authors demonstrated that the diffuse-layer capacitance minimum potential E a of a pc-Ag electrode was only slightly less negative (30 mV) than the pzc of the Ag(110) face, i.e., for the face with the more negative value of EamQ. The diffuse-layer capacitance minimum for pc-Ag was wider and less deep than for the Ag faces. 

Mathematical simulation of C, E curves shows that the shape of the diffuse-layer capacitance minimum depends on the difference of Eamo in individual faces and their fractions, as well as on the shape of partial Cj, E curves (Fig. 9). 

The results of experimental capacitance studies at two plane model pc-Bi electrodes were in agreement with these conclusions.2 266 Thus it has been shown that the potential of the diffuse-layer capacitance minimum for a pc electrode does not correspond to the zero charge potential of the whole surface, i.e., Zfipj Oat E n-... 

The idea in these papers67,223,224 was to identify the potential of the capacitance minimum in dilute electrolyte solutions with the actual value of Ea=o (i.e., <7ge0m( min) = Ofor the whole surface) and to obtain the value of R as the inverse slope of the Parsons-Zobel plot at min.72 Extrapolation of Cwom vs- to Cgg0m = 0 provides the inner-layer capacitance in the / C geom, and not C ea as assumed in several papers.67,68,223,224 In the absence of ion-specific adsorption and for ideally smooth surfaces, these plots are expected to be linear with unit slope. However, data for Hg and single-crystal face electrodes have shown that the test is somewhat more complicated.63,74,219,247-249 More specifically,247,248 PZ plots for Hg/... 

Japaridze et al.m 323 have studied the interface between Hg and a number of vicinal and nonvicinal diols such as 1,2-, 1,3-, 2,3- and 1,4-butanediol (BD), ethanediol (ED), and 1,3-propanediol. KF and LiC104 were used as surface-inactive electrolytes. The potential of zero charge was measured by the capacitance method against an SCE in water without correction for the liquid junction potential at the solvent/H20 contact (such a potential drop is estimated to be in the range of 20 to 30 mV). The potential of the capacitance minimum was found to be independent of the electrolyte concentration while capacitance decreased with dilution. Therefore, Emin was taken to measure E . These values are reported in Table 4. 

Cu crystallizes in the fee and its melting point is 1356 K. The experimental data for single-crystal Cu/H20 interfaces are also controversial. 567 570,572 57X The first studies with Cu(l 11), Cu(100), and Cu(l 10) in surface-inactive electrolyte solutions (NaF, Na2S04) show a capacitance minimum at E less negative than the positive limit of ideal polarizability of Cu electrodes (Table 11). depends on the method of surface... 

Therefore some indirect methods have been worked out to determine the value of ff=0.154,259 In particular (1) salting out of organic compounds from a surface-inactive electrolyte solution, (2) F"" for 1-pentanol or other organic compounds with a high attractive interaction constant a, and (3) dependence of the capacitance minimum on thiourea concentration. It should be noted that indirect estimates based on TU adsorption give... 

Dependence of capacitance minimum on cm- TU, thiourea. Potential of adsorpdon-desofption peak for ihCjHuOH (0.1 M). Salting out... 

Figure 3.10 illustrates the same trends in terms of capacitances. In this example the asymmetry of the electrolyte has been varied at fixed concentration. In this plot the trends are more pronounced than in fig. 3.9. The new feature is that the capacity minimum no longer coincides with the zero point of the diffuse layer potential, but is shifted in the direction where the multivalent ion is the co-ion. (In fig. 3.9 the same can be seild of the position of the minimum slope.) The value y (min) where the capacitance minimum is located can be obtained by differentiating [3.5.34] with respect to y leading to the condition... 

Identification of the capacitance minimum with the PZC clearly suggests that the PZC depends upon the crystal face exposed to the solution. The capacitance of a model poly crystalline electrode, with the assumption that the surface was 46% (110), 23% (100) and 31% (111) is also shown. The PZC in this case is close to that of the (110) surface. The situation is more complicated with a real polycrystalline electrode surface with exposed high-index planes and defect sites. 

In accordance with the Stern-Grahame model of the EDL structure the values of C are determined by both the diffuse and compact-layer properties, the latter being dependent on the metal properties. However, in very dilute solutions of a surface-inactive electrolyte the dominant contribution to C near the p.z.c. (at the capacitance minimum) is given by the diffuse layer, C = Cgc(0, c). Therefore the ratio of capacitances in these conditions should be close to the RF for the surface of the solid metal M ... 

Potentials of zero charge of the interface can be found reliably by the same independent methods that are used at the metal-water interface. These include finding the differential capacitance minimum of the electric double layer, from electrocapillary curves, with a flowing-electrolyte electrode, with the vibrating boundary method, with radiotracers, or by measuring the second harmonic... 

Mathematical simulation of Cpc, E curves shows that the shape of the diffuse-layer capacitance minimum depends on the difference of Ea=o for individual faces, exposed on the PC electrode surface, and their fractions, as well as on the shape of partial Cj, E curves (Fig. 3). The results of experimental capacitance studies at two-plane model PC Bi electrodes were in agreement with these conclusions [5, 15, 16]. Thus it has been shown that the potential of the diffuse-layer capacitance minimum for a PC electrode with noticeable difference in Eu=o values for various planes does not correspond to the PZC of the whole surface and JZy 0 at... 

Fe crystallizes in the body-centered cubic (bcc) system. Fe(lOO) and Fe(lll) singlecrystal faces were grown at 750 780 from FeBr2 in pure H2 atmosphere and reduced for 1 h at E = —0.95 V (SCE) in the working solution (pH = 2.5). A diffuse-layer capacitance minimum was observed with Emm practically independent of Cel (Table 5). The PZ plot was linear with R somewhat higher than unity. The inner-layer capacitance decreases from Fe(lll) to Fe(lOO) as the atomic density of the face increases [56]. 

In contrast to y, the value of C can be measured not only for liquid electrodes but also for solid ones. Usually, the specific adsorption of ions increases the capacitance of the EDL, whereas the adsorption of organic molecules decreases it. In the framework of a simplified model of the double layer as a capacitor, this corresponds to varying the distance between the capacitor plates and decreasing the permittivity. In dilute solutions of a surface-inactive 1,1-electrolyte, a capacitance minimum appears in the vicinity of pzc (see curve 1 in Fig. 4). The position of this minimum is determined by the potential Eq = 0. In solutions with relatively high (>0.1 M) concentrations of surface-inactive electrolytes, this minimum of C, Fo-curve disappears, but the pzc position stiU corresponds to Fq = 0 (curve 2 in Fig. 4). Numerical integration of these C, Fo-curves... 

For nonsymmetrical surface-inactive electrolytes, the minimum of C shifts from the pzc. If, in the absolute magnitude the anion charge is higher than the cation charge, the minimum shifts from pzc to more negative values, and vice versa. Specific adsorption of ions also induces a shift of the capacitance minimum from the pzc. Moreover, when the specific adsorption is sufficiently pronounced, no minimum appears in the C, fo Curves,... 

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