Inner layer capacitance, determined

In addition to the effect of the nonideality of the metal on the electrolyte phase, one must consider the influence of the electrolyte phase on the metal. This requires a model for the interaction between conduction electrons and electrolyte species. Indeed, this interaction is what determines the position of electrolyte species relative to the metal in the interface. Some of the work described below is concerned with investigating models for the electrolyte-electron interaction. Although we shall not discuss it, the penetration of water molecules between the atoms of the metal surface may be related3 to the different values of the free-charge or ionic contribution to the inner-layer capacitance found for different crystal faces of solid metals. Rough calculations have been done to... 

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

Surface Roughness and Shape of Inner-layer Capacitance Curves In 1973, Valette and Hamelin [25, 26] proposed another method to determine the roughness... 

Fig.S The inner-layer capacitance versus electrode charge dependence for the PC Cd electrode at different values of roughness factor (1) 1 (2) 1.08 (4) 1.15 (3) extrapolation by an approximate equation determined between —1.0 and —lOpCcm. ...

Amokrane and Badiali proposed a semiempirical approach to the determination of the solvent contribution C, to the capacitance of the double layer in aqueous and nonaqueous " solutions. They used the relation C = Cf - C m, where Q is the experimentally determined capacity of the inner layer and Cm is the contribution of the metal. The plots ofC, vs. (Tm were presented for various solvents and correlated with their properties.However, the problem of the supporting electrolyte was entirely neglected in the quoted papers. It was shown recently that the height and position of the maximum on the C, vs. Gm plots depend on the type of the supporting electrolyte. Experimental differential capacity data obtained on the Hg electrode in methanol and ethanol containing various electrolytes with nonadsorbing anions (F , PFg, ClOi) indicate that the type as well as concentration of the electrolyte influences the position and the height of the maximum on the C, vs. plots (Fig. 13). 

From their calculations of the surface excess entropy and volume of the electric double layer at a mercury-aqueous electrolyte interface, Hill and Payne (HP) [147] postulated an increase in the number of water molecules in the Stern inner region as the surface charge a of about 30 piC/m2, which is consistent with the results of TC on a silver surface obtained some 30 years later. HP used an indirect method to determine the excess entropy and volume by measuring the dependence on temperature and pressure of the double layer capacitance at the mercury-solution interface. 

Thus, if the semiconductor corresponds essentially to an insulator of the Schottky barrier type, use of Mott-Schottky plots will allow the determination of the capacitance of the inner layer. Utilization of impedance measurements with different frequencies may give rise to the possibility of determining the double layer capacity separate from the inner layer. In this way a map of the double layer, an estimation of the Helmholtz potential difference and the potential difference (pd) in the space charge region may be obtained. The pd in the Helmholtz layer is, however, not only given by the charge on the surface of the polymer, but also by the potential difference due to aggregated layers which form within it, and in particular the solvent dipole layer (70). 

The double-layer capacitance is composed of several contributions. In a geometrical sense the double layer in "supported" systems is represented by the compact "Helmholtz" or "Stem" layer. The electrostatically attracted solvated species reside in the "outer Helmholtz plane" (OHP), and specifically adsorbed species reside closer to the electrode in the "inner Helmholtz plane" (IHP). The double-layer structure is completed by a "diffuse" layer, composed of electrostatically attracted species at some distance from the electrode surface. The fuU thickness of the double layer can be defined as the external boundary of the diffuse layer separating it from the bulk solution, where the measured potential becomes equal to that of the bulk solution and no local potential gradient driven by the difference between the electrode potential ( )j and the solution potential can be determined (Figure 5-4). 

There is a similar quantity called the inner Helmholtz plane, where the potential is ( )j. This is determined by the radius of the anions in solution, which tend to be specifically adsorbed on the metal surface. A discussion of this phenomenon and its effect on the double-layer capacitance is outside the scope of this book. 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

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