Schmickler charge

The picture of the compact double layer is further complicated by the fact that the assumption that the electrons in the metal are present in a constant concentration which discontinuously decreases to zero at the interface in the direction towards the solution is too gross a simplification. Indeed, Kornyshev, Schmickler, and Vorotyntsev have pointed out that it is necessary to assume that the electron distribution in the metal and its surroundings can be represented by what is called a jellium the positive metal ions represent a fixed layer of positive charges, while the electron plasma spills over the interface into the compact layer, giving rise to a surface dipole. This surface dipole, together with the dipoles of the solvent molecules, produces the total capacity value of the compact double layer. 

For a range of potential in which the interfacial charge is relatively small, the reciprocal of the interfacial electric capacity, C, of metal electrodes has conventionally been represented by a Laurent series with respect to the Debye length L-o of aqueous solution as shown in Eqn. 5-25 [Schmickler, 1993] ... 

Fig. 6-23. Differential capadty Ch of a compact layer observed as a function of interfadal charge oh on a mercury electrode and on a (100) surface of silver electrode in aqueous solution. [From Schmickler, 1993.]...

Fig. 6-26. For the hard sphere model on metal electrodes (a) interfacial dipole induced by adsorbed water molecules and (b) interfadal dipole induced by contact adsorption of partially ionized bromine atoms. - 6 = charge number of adsoihed particle (z ). [From Schmickler, 1993.]...

Fig. 6.70. (a) Parsons-Zobel plots of bare Au(111), covered with decanethiol (DT), co-hydroxydecanethiol (HDT), and 4 -hydroxy-4-mercaptobiphenyl (HBT). (Reprinted with permission from R. P. Janek, W. R. Fawcett, and A. Ulman, J. Rhys. Chem. B 101 8550, Fig. 12, copyright 1997, American Chemical Society.) (b) Helmholtz capacity (CH), as a function of the electrode charge for Ag(111) in contact with an aqueous solution of ions that are not specifically adsorbed. (Reprinted with permission from W. Schmickler, Chem. Rev. 96 3177, Fig. 3, copyright 1996, American Chemical Society.)... 

A thoroughgoing restudy of Tafel s law, involving the use of fast-flow techniques to avoid the introduction of diffusion control at high rates (Iwasita, Schmickler, and Schultze, 1985) shows excellent verification.19 Tafel s law is one of the most tested and verified laws in nature. It Ls also one with the broadest applicability (e.g., in interfacial charge-transfer control, e.g., corrosion metabolism and photosynthesis). In... 

Kornyshev and Schmickler claimed (28) that the most important parameters that determine the charge of the adsorbate are the atom ionization energies, the work function of the metal, and the electronic affinities. This last parameter is taken into account by Barbier et al. (25) to explain the adsorption behavior of sulfur on noble metals. Following this explanation, the smaller the difference of electronic affinities between sulfur and metal, the more covalent the metal-sulfur bond. 

Schmickler [131] proposed a jellium model for the metal where the dielectric film in the solvent was replaced by a planar lattice of dipoles, with each dipole taking up one of three orientations. His calculated capacity-charge curves for different metals all exhibited a pronounced hump with a maximum practically at the pzc. 

A nonprimitive model for the jellium metal-liquid electrolyte interface similar to but more general than that of BRYB was developed by Schmickler and Henderson [132,133]. Their hard sphere ions and solvent molecules had different diameters and the construction of the jellium edge was different. Also their electronic density profile had two adjustable parameters and they assumed that the dependence on metal charge of the nearest distance of approach of solvent molecules to the metal was not important. In one paper [132b] the trial function in Eq. (21) was generalized for x < 0 to read... 

Refs. [i] Erdey-Gruz T (1974) Transport phenomena in aqueous solutions. Adam Hilger, London, p 390 [ii] Inzelt G (1994) Mechanism of charge transport in polymer-modified electrodes. In Bard AJ (ed) Elec-troanalytical chemistry, vol. 18. Marcel Dekker, p 95 [Hi] Lyons MEG (1994) Charge percolation in electroactive polymers. In Lyons MEG (ed) Electroactive polymer electrochemistry, part 1. Plenum, New York, p 1 [iv] FeldbergSW (1986) / Electroanal Chem 198 1 [v] Fritsch-Faules I, Faulkner LR (1989) J Electroanal Chem 263 237 [vi] Leiva E, Mayer P, Schmickler W (1988) J Electrochem Soc 135 1993 [vii] HeegerA] (1989) Faraday Discuss Chem Soc 88 203... 

Near flat-band potential, the space-charge layer becomes considerably more transparent and the tunneling solution correspondingly more complex. By considering a monolayer of water molecules on the surface of the semiconductor that provide a square potential well, analytical solutions were obtained by Schmickler under the assumptions... 

Figure 17. The double layer capacitance measured with two different metals (Ag and Hg) in an aqueous electrolyte solution as a function of the charge density at the surface. The influence of the nature of the metal phase on the total capacitance is clearest around the point of zero charge. The results are taken from W. Schmickler, Chem. Rev. 96, 3177 (1996).

In a polar medium, the partial charge transfer depends on two additional contributions due to the ion-solvent and metal-solvent interactions. Following the theory of electrochemical adsorption by Schmickler [232], the adsorbate energy level in solution, e is given by... 

W. Schmickler and D. Henderson,/. Chem. Phys., 85,1650 (1986). The Interphase Between Jellium and a Hard Sphere Electrolyte Capacity-Charge Characteristics and Dipole Potentials. 

Schmickler, W., Henderson, D., 1986. The interphase between jeUium and a hard sphere electrol3he capacity—charge characteristics and dipole potentials. J. Chem. Phys. 85, 1650-1657. 

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