Inner-layer capacity

M) were typically used for such a comparison to eliminate the influence of possible differences in the inner-layer capacities. However, C of different solid metals, as well as of liquid Ga, In(Ga), and Tl(Ga) alloys have shown such a large variation that this approach can hardly be considered as appropriate. It should be noted that the error in C, which for solid electrodes is much higher than for liquid electrodes, increases with the decrease ofcei further, as shown later (Section II.2 (iv)), the effects of surface crystallographic inhomogeneity also prove especially appreciable.24 67 74... 

Leikis et al,223 used the Parsons-Zobel method to obtain the roughness factor fpz for pc/Ag electrodes. It was found that /pz 1.2, which was explained by the geometric inhomogeneity of the pc-Ag electrode surface. A more detailed analysis is given in Section II.2. Thus it should be noted that in the case of pc electrodes with appreciable differences of EamQvalues for the various planes (AEff o > 100 mV), it is impossible to obtain the true roughness coefficient, the actual Ea=0, and the inner-layer capacity. 

Data for the pc-Au/DMF + LiC104 interface have been collected by Borkowska and Jarzabek.109 The value of ffa0was found to be 0.27 V (SCE in H20) and the roughness factor / = 1.3 (Table 8). Unlike Hg, Bi, In(Ga), and Tl(Ga) electrodes and similarly to the Ga/DMF interface, the inner-layer capacity for pc-Au in DMF depends weakly on a, and thus the effect of solvent dipole reorientation at pc-Au is less pronounced than at In(Ga), Bi, and other interfaces. 

In a very extensive and thorough study of silver electrodes in a nonadsorbing KPFg electrolyte, Valette determined the inner-layer capacities of Ag(lll), Ag(lOO), and Ag(llO) to be equal to 77,92, and 112//F... 

Surface and Double-layer Properties Valette [19] has analyzed earlier experimental data on the inner-layer capacity at PZC for Ag(lll), Ag(lOO), and Ag(llO) surfaces in order to estimate the surface area and capacitance contributions of superficial defects for real electrodes, as compared to ideal faces. Considering the application of surface spectroscopy techniques to single-crystal Ag electrodes, one should note that anisotropy of the SHG response for metal electrode allows one to analyze and correlate its pattern with interfacial symmetries and its variations by changing nonlinear susceptibility and the surface structure. Early studies on Ag(lll) single-crystal electrodes have... 

Setting as = 0 we obtain A = 1/Cn, where C is the Helmholtz or inner-layer capacity.72 By definition, this is the first-order correction to the Gouy-Chapman theory. Setting as = -aM with as = zeNs, from Eqs. (71) and (72) we obtain for the dipole moment ... 

Naneva and Popov et al. [4, 5] have studied Cd(OOOl) grown electrolytically in a Teflon capillary in NaF aqueous solu-hon. A value of pz,- equal to —0.99 V (versus saturated calomel electrode (SCE)) was evaluated from minimum potential (Timin) on the differential capacity C-E curves obtained in dilute electrolyte. The zero charge potential was found to be prac-hcally independent of the crystallographic orientation. The pzc and the inner layer capacity of Cd(OOOl) single crystals were determined in KF solution as a function of temperature [5]. The positive values of indicated that the water... 

By measuring the change in with charge density on the metal, the metal s contribution to the inner layer capacity can be estimated. Thus,... 

Significant changes in inner layer behavior are observed when water is replaced by a non-aqueous solvent in which electrolytes are soluble. In the case of the Hg methanol interface, a deep minimum is observed on the inner layer capacity curve at negative charge densities [35]. In the case of the amide solvents [35], a variety of behaviors is observed. The protic solvents, formamide, and A-methyl formamide, possess capacity maxima at negative charge densities (fig. 10.22). The other fea-... 

Differentiating equation (10.7.9) with respect to dAm< ), one obtains an equation for the solvent contribution to the inner layer capacity ... 

Fig. 10.24 A plot of inner layer capacity due to the solvent, Csoiv against electrode charge density, a , according to the two-state model (a) and three-state model (b). The values of the parameters for the two-state model are zj = 0.48 run, p = 3.0 debye (1.0 x 10 C m), Ej = 9.0, T = 298 K, Uri = —5kT, 11 2 = 0 the parameters are the same for the three-state model except that zj = 0.30 nm and Cr3 = —7kT.

The equations for the potential drop and inner layer capacity C are the... 

It follows that d ln gni/[d(dAi is a minimum when din m/d(dAm (j>) = 0, that is, when = Nd- The inner layer capacity curve calculated with the parameters chosen previously for the two-state system and with a low value of U p is also shown in fig. 10.24. As predicted, a minimum occurs at the position of the maximum on the curve for the two-state system. At charge densities sufficiently far from the minimum, maxima are observed. The three-state model is able to account for inner layer capacity curves in a variety of solvents such as methanol, ethylene carbonate, and dimethylformamide [35]. 

The inner-layer capacity existing on the metal side of the oHp is high in this range of potential. 

When there is no adsorption, only solvent molecules are present in this layer. Then the variation of the inner-layer capacity vs. charge density gives information on the metal-solvent interactions [see Section V.3(i). The short-range interactions change the solvent properties. 

Although, obviously, there is a continuous change of structure and composition in the dl, from the metal surface to the bulk of the solution, the model which has explained successfully many results for mercury, was assumed to be valid for other metals. In the case of no adsorption this model leads to the conclusion that the variations of the inner-layer capacity C with charge density cr should be independant of the concentration of the ions in solution. In the case of no adsorption, there are only solvent molecules on the metal side of the oHp. Only for water are there available results on metal crystal faces. 

As adsorption of a nonionic substance at a metal electrode proceeds by replacement of solvent molecules at the surface by the adsorbate, following the G-C-S model, it is sufficient to consider the inner-layer capacity ... 

For the inner-layer capacity and its variations with charge density at the metal surface, results are very scarce and much debated. It seems that, in aqueous solutions without specific adsorption, C is maximum not far from zero-charge density (Figs. 28-30) on single-crystal metal faces, the general shape of the curve would include only one maximum and would be nearly symmetrical. 

In the determination of R by the Valette-Hamelin method [59] the inner layer capacity, Cinner, is calculated for the different values of the charge densities, cr, at constant electrolyte concentration, postulating that the Cinner vs. a curve has to be monotonically close to a zero charge potential value. This condition is obtained by adjusting the R value. 

The inner-layer capacity can be further analyzed to express its dependence on specific... 

The observed capacitance, C, is a series combination of the inner layer capacity, C and the diffuse layer capacity. Equation (5.36) predicts an inverted parabolic dependence between and 02- Furthermore, the capacity at the minimum decreases with decreasing concentration and is centred symmetrically about the potential of zero charge for a z z valent electrolyte. Consequently, the diffuse layer contribution only becomes apparent in dilute solutions, as is shown for NaF solutions in Fig. 5.5. As the inner layer contains only solvent molecules, its capacity is independent of NaF concentration so that once C is known as a function of potential then the capacity curves at all other concentrations can be calculated. This has been confirmed experimentally. Similar equations have been... 

The slope of the curve in Fig. 7 gives the reciprocal of the inner layer capacity Cf, which is defined by Also, the differential capacity c i is given by a series... 

Fig. 8. Inner layer capacity as a function of the surface charge density in aqueous phase for the interface between TBATPB(NB) and LiCl(W) at various electrolyte concentrations. The concentration of LiCl was 0.02 (o), 0.05 (a), 0.1 ( ), 0.2 (O), 0.5 (v), and 1.0 ( ) mol dm when the concentration of TBATPB was 0.1 mol dm and the concentration of TBATPB was 0.05 ( ) and 0.17 (a) mol dm" when the concentration of LiCl was 0.1 moldm" ...

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