Double layer, definition

Clavilier eta/.196,794-796have studied CO adsorption on electrochemi-cally faceted Pt(lll) and Pt(110) electrodes and from the charge transients, with the provision that the CO dipole has a negligible contribution to the electrical double-layer potential these authors have provided a definite determination of ( =o- However, electrochemically faceted Pt(lll) electrodes have a polycrystalline surface structure, and thus the value of Eq-q for such electrodes lies between fiULO for terraces and forst s.197 786 787... 

Thus far, Ft has never found a definite position in Ea vs. correlations, more for the uncertainty in the reliability of its pzc than for its work function. On the other hand, Pt is a highly heterogeneous metal and the fact that only polycrystalline surfaces have been used in double-layer studies has not helped remove suspicions. According to Frumkin s data,10,14 the pzc ofpc-Pt is around 0.2 V(SHE) (in acidic solution). If this value is introduced into Fig. 14 (the 0 of pc-Pt is around 5.5 eV),22,65 343,856 865,866 the point of Pt would fall far distant from the line of mercurylike metals and near the line of d-metals. 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

Effective core potential, 269 Effective double layer characterization of, 189 isotherm, 306, 315 kinetic expressions, 316 observations of with STM, 259 stability of, 225, 351, 503 Effectiveness factor of promotion computation of, 505 definition of, 505 Electrocatalysis... 

The concept of surface concentration Cg j requires closer definition. At the surface itself the ionic concentrations will change not only as a result of the reaction but also because of the electric double layer present at the surface. Surface concentration is understood to be the concentration at a distance from the surface small compared to diffusion-layer thickness, yet so large that the effects of the EDL are no fonger felt. This condition usually is met at points about 1 nm from the surface. 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

A classic definition of electrochemical ultracapacitors or supercapacitors summarizes them as devices, which store electrical energy via charge in the electrical double layer, mainly by electrostatic forces, without phase transformation in the electrode materials. Most commercially available capacitors consist of two high surface area carbon electrodes with graphitic or soot-like material as electrical conductivity enhancement additives. Chapter 1 of this volume contains seven papers with overview presentations, and development reports, as related to new carbon materials for this emerging segment of the energy market. 

As was discussed above, it is essential to determine the effect, if any, that the emersion process has on the double layer. To do this, Wilhelm and colleagues have performed the definitive type of blank experiment. CO was adsorbed onto the Pt working electrode from sulphuric acid electrolyte. After adsorption, the CO-saturated solution was replaced with pure electrolyte. The potential of the electrode was then ramped in order to oxidise off the adsorbate, as C02, and the voltammogram so obtained is shown in Figure 2.118(a). The experiment was then repeated CO was adsorbed as before, but the electrode was emersed and transferred into the UHV chamber, before being re-immersed and the potential ramp applied. The voltammogram so... 

The definition of the electrosorption valence involves the total surface excess, not only the amount that is specifically adsorbed. It is common to correct the surface excess F, for any amount that may be in the diffuse double layer in order to obtain the amount that is specifically adsorbed. This can be done by calculating the excess in the... 

At the electrocapillary maximum, the charge density, a, is zero (point of zero charge) (Fig. A.4.5c). By definition, the differential capacity of the double layer, Cd, is equal (Second Lippmann Equation). 

For the electron transfer of hydrated redox particles (the outer-sphere electron transfer), the electrode acts merely as a source or sink of electrons transferring across the compact double layer so that the nature of the electrode hardly affects the reaction kinetics this lack of influence by the electrode has been observed for the ferric-ferrous redox reaction. On the other hand, the electron transfer of adsorbed redox particles (the inner-sphere electron transfer) is affected by the state of adsorption so that the nature of the electrode exerts a definite influence on the reaction kinetics, as has been observed with the hydrogen electrode reaction where the reaction rate depends on the property of electrode. 

The double-layer charging current i may be calculated from the definitions of capacitance. 

An ion adsorbed on the surface of a suspension will draw near to it an ion of opposite sign in the solution these ions in the double layer are thus hound and can only escape if their kinetic energy exceeds a definite critical value W. If the chemically adsorbed ions have a valency % and n is the valency of the opposite charged ions in the liquid of dielectric constant K in contact with the solid and separated from the former by a distance x, we obtain... 

The probability of an ion remaining fixed is given by 1 — e where h is the Boltzmann gas constant == 1 372 x 10 erg/degree, T the absolute temperature. There will thus be at any definite temperature a number of free ions and ions bound to the double layer, the free ions will, as it were, form a second sheet in the double layer. 

For the definition of the outer potential, the appropriate amounts of charge were then conferred on the two separated phases. Here, a layer of solvent dipoles will be fixed on the electrolyte so that the net orientation and the number per unit area of dipoles corresponds to that obtaining on the solution side of the double layer. 

Going a step further, what does the parallel-plate model of the double layer have to say regarding the capacity of the interface Rearranging Eq. (6.119) in the form of the definition of differential capacity [Eq. (6.97)],... 

The term tertiary electroviscous effect is applied to the changes in the conformation of poly electrolytes that are caused by //t/ramolecular double-layer interactions. It is customary to extend this definition to include all effects in which the geometry of the system is altered as a result of double-layer interactions. 

Since the electro-osinotic flow is induced by the interaction of the externally applied electric field with the space charge of the diffuse electric double layers at the channel walls, we shall concentrate in our further analysis on one of these 0 1 2) thick boundary layers, say, for definiteness, at... 

Molecules in adsorbed layers have also a definite orientation. If a complete layer is formed over a surface, with those groups possessing the greatest attraction for the surface turned inward, we have virtually a new surface with properties determined by the nature of the groups which are directed outwards. There seems to be no very good reason why this, in certain cases, should not adsorb a second layer of molecules. Indeed, the assumption that this double-layer adsorption occurs has occasionally been found helpful. But there is a large difference between this extension of the single-layer theory and the atmospheric. theory. 

In contrast to the chronocoulometric technique, the information obtained from the impedance technique concerns the derivatives with respect to potential of To, In /30 and d(ln (30)/dE. It is therefore needed to postulate an explicit isotherm in order to fit experimental data to the theoretical equations. However, the results, e.g. for (dT0/dE, can be integrated to give T0 as a function of potential within the faradaic region. As chronocoulometry is, by definition, applicable to potentials outside the faradaic region, the two methods may be considered as complementary tools to study adsorption phenomena that are hard to detect in the classical way, i.e. from double-layer data (e.g. the capacity Cd) that are influenced by the presence of electro-inactive absorbates. 

The above definition of the symmetric surface excess and the classical Guoy-Chapman model of the diffuse double layer are combined to show that the surface excess cannot be considered a surface concentration in the presence of an ionized monolayer on an impenetrable solid/liquid interface. 

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