14 Faraday Film formation

As shown in Table 1, slightly more than two electrons per equivalent of monomer are required for film formation, i.e., = 2.1 to about 2.7 faradays per mole. Each monomer unit consumes two electrons, while the excess charge oxidizes the resulting polymer. Note that the total reaction at the electrode surface is considered when determining n values. Therefore, the n values may contain some contribution from charge consumed in a secondary reaction, for example, in the generation of soluble products. Cyclic voltammetry data are typically used to obtain n values using a method described by Nicholson and Shain [16] for a totally irreversible reaction. 

Assume a defect-free single crystal and a mechanism of oxide film growth by vacancy migration. Thus, the rate of film formation for a single crystal, related to Faraday s law, can be approximated as [13]... 

The kinetics of passivation is normally characterized through Faraday s law for determining the rate of film formation in terms of growth of film thickness according to eq. (6.1). As a cmde approximation, the rate of film formation dxjdt) is related to vacancy diffusion and it is assumed to obey the Arrhenius equation (6.2). In fact, dx/dt increases provided that there exists a net anodic current density i and an overpotential r/, at a distance x from the electrode surface. 

Here is a solvated ion, e is an electrom, and n represents the ion state of charge. The electrons, liberated by the oxidation, must flow through the material M to be consumed in an appropriate cathodic reaction. Beyond a solubility limit, precipitates of hydroxide or hydrated oxide are formed, and this surface film can provide a barrier to further dissolution. In fact, there are two film formation mechanisms the dissolution-precipitation mechattism addressed before and also the solid-state oxidation proeess M + H2O MO + 2H+ + 2e. Some films are termed passive, for stainless steels or aluminum alloys, for instance. These films can play an important role in environment-sensitive erack mitiation and fracture. Under thermodynamic equilibrium conditions, the film stability may be inferred from E =y(pH) diagrams, where E is the electrical potential related to the chemical free energy G by G = -nEF, and F is Faraday s ntrmber. At eqirilibrium, one can define the electrode potential (related to AG) and the eurrent density 1(1 ... 

The capacitance determined from the initial slopes of the charging curve is about 10/a F/cm2. Taking the dielectric permittivity as 9.0, one could calculate that initially (at the OCP) an oxide layer of the barrier type existed, which was about 0.6 nm thick. A Tafelian dependence of the extrapolated initial potential on current density, with slopes of the order of 700-1000 mV/decade, indicates transport control in the oxide film. The subsequent rise of potential resembles that of barrier-layer formation. Indeed, the inverse field, calculated as the ratio between the change of oxide film thickness (calculated from Faraday s law) and the change of potential, was found to be about 1.3 nm/V, which is in the usual range. The maximum and the subsequent decay to a steady state resemble the behavior associated with pore nucleation and growth. Hence, one could conclude that the same inhomogeneity which leads to pore formation results in the localized attack in halide solutions. 

Gutmann, J.S., Muller-Buschbaum, P., Stamm, M. Complex pattern formation by phase separation of polymer blends in thin films. Faraday Discuss. 112, 285-297 (1999)... 

The electrochemical reactions which produce polyaromatic compounds from the monomer have stoichiometries in the range of 2-2.5 Faraday/mole of monomer. The stoichiometry for the formation of the polymer chain is 2 for large chain lengths, plus the charge associated with reversible oxidation of the polymer (0 to 0.5). The latter quantity varies with the individual monomer system, with the anion which is inserted upon oxidation of the polymer, and with the solvent and other components of the electrolyte medium. Anion content and degree of oxidation of various polymer films is presented in Table 2.2. 

A typical example of the application of EIS is the investigation of passive films on Zn, Zn-Co, and Zn-Ni (Fig. 7-18), which were carried out to explain the difference in the corrosion behavior of pure and low-alloyed zinc by the possible formation of electron traps through the incorporation of cobalt or nickel into the oxide film (Vilche et al., 1989). Passive films of zinc in alkaline solutions are known to be n-type semiconductors with a band gap Eg = 3.2 eV (Vilche et al., 1989). The n-type character arises from an excess of zinc atoms in the nonstoichiometric oxide. The impedance measurements in 1 N NaOH solution were carried out at potentials at which Faraday reactions like transpassive dissolution and oxygen evolution do not interfere. The passive layer was formed for 2 h at positive potential before the potential was swept in the negative direction for the impedance meas-... 

Mott N.E., Theory of the formation of protective oxides films on metals. Transactions of the Faraday Society, vol. 35, 1939, p. 1175-1177. 

Passivity of metals was initially stated by Faraday and Schoenbein over 150 years ago. The origin of the passivity was argued and at the present the passivity is thought to be the formation of three dimensional oxide films. It is stably formed in aqueous solution. The passive oxides are extremely thin (usually a few nm), so it is very ( icult to detect them analytical techniques. For the quantitative description, electrochemistry is a key technology, because the oxidation state of the metal surface can be precisely controlled by electrochemical apparatus. Since the electrochemical control is restricted into solution phase, the passivated surface should be characterized in the same phase. To overcome the difficulty for characterization, several optical techniques have been applied. 

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