Mixed-potential theory

The electrochemical potential is a measure of the driving force (or free energy change) of the oxidation/reduction reactions that occur during metal dissolution. As mentioned, copper dissolution and redeposition may occur by the reduction-oxidation reaction  

Where e for reaction (4.23) is 337 mVsHE and (Cu ) indicates copper ion activity. As is common, we assume all ion activities are 

In order to understand the origin of the mixed corrosion potential, we must utilize mixed potential theory and the Cu/Cu system as an example. A Cu/Cu system is removed from the equilibrium given by Equation. (4.34) by the application of a driving force or an overpotential, t]. The application of an overpotential results in the system attempting to return to equilibrium by driving reaction (4.23) either in the reverse direction, for a positive overpotential, or in the forward direction, for a negative overpotential. Because electrochemical reactions involve the flow of electrons, the reaction rate may be considered as a reaction current or current density. The reaction current is the rate at which electrons flow from the site of the anodic reaction to the site of the cathodic reaction. The rate at which the reaction proceeds is determined by kinetics, and the magnitude of the overpotential which is related to the reaction current density by  

Because the mixed potential involves many unknown variables, it is difficult to calculate the concentration of metal ions in the slurry directly from a measurement of the mixed potential. However, relative changes in ion concentration may be inferred from changes in the mixed potential. When the Cu ion concentration increases, the reversible potential increases, shifting the entire Cu/Cu oxidation curve in the noble direction. As a result, the equilibrium with the reduction reaction shifts in the noble direction (higher potential). Thus, an increase in potential is indicative of an 

Equilibrium betwera Cu/Cu reaction and hypothetical reduction reaction. The mixed corrosion potential, and the 

This chapter is coniined to analyze the complex aqueous corrosion phenomaion using the principles of mixed-potential, which in turn is related to the mixed electrode electrochemical corrosion process. This theory has been introduced in Chapter 3 and 4 as oxidation and reduction electrochemical reactions. Basically, this Chapter is an extension of the principles of electrochemistry, in which partial reactions were introduced as half-cell reactions, and their related kinetics were related to activation and concentration polarization processes. The principles and concepts introduced in this chapter represent a unique and yet, simplified approach for understanding the electrochemical behavior of corrosion (oxidation) and reduction reactions in simple electrochemical systems. 

Both Evans and Stem diagrams are included in order to compare and analyze simple and uncomplicated electrochemical systems. The concept of anodic control and cathodic control polarization is also introduced. In addition, the predetermined corrosion circuit is included in order to analyze corrosion using an electrochemical device containing an external circuit. 

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Mital et al. [40] studied the electroless deposition of Ni from DMAB and hypophosphite electrolytes, employing a variety of electrochemical techniques. They concluded that an electrochemical mechanism predominated in the case of the DMAB reductant, whereas reduction by hypophosphite was chemically controlled. The conclusion was based on mixed-potential theory the electrochemical oxidation rate of hypophosphite was found, in the absence of Ni2 + ions, to be significantly less than its oxidation rate at an equivalent potential during the electroless process. These authors do not take into account the possible implication of Ni2+ (or Co2+) ions to the mechanism of electrochemical reactions of hypophosphite. 

In the mixed potential theory (MPT) model, both partial reactions occur randomly on the surface, both with respect to time and space. However, given the catalytic nature of the reductant oxidation reaction, it may be contended that such a reaction would tend to favor active sites on the surface, especially at the onset of deposition, and especially on an insulator surface catalyzed with Pd nuclei. Since each reaction strives to reach its own equilibrium potential and impose this on the surface, a situation is achieved in which a compromise potential, known as the mixed potential (.Emp), is assumed by the surface. Spiro [27] has argued the mixed potential should more correctly be termed the mixture potential , since it is the potential adopted by the complete electroless solution which comprises a mixture of reducing agent and metal ions, along with other constituents. However, the term mixed potential is deeply entrenched in the literature relating to several systems, not just electroless deposition. 

The incorporation of a third element, e.g. Cu, in electroless Ni-P coatings has been shown to improve thermal stability and other properties of these coatings [99]. Chassaing et al. [100] carried out an electrochemical study of electroless deposition of Ni-Cu-P alloys (55-65 wt% Ni, 25-35 wt% Cu, 7-10 wt% P). As mentioned earlier, pure Cu surfaces do not catalyze the oxidation of hypophosphite. They observed interactions between the anodic and cathodic processes both reactions exhibited faster kinetics in the full electroless solutions than their respective half cell environments (mixed potential theory model is apparently inapplicable). The mechanism responsible for this enhancement has not been established, however. It is possible that an adsorbed species related to hypophosphite mediates electron transfer between the surface and Ni2+ and Cu2+, rather in the manner that halide ions facilitate electron transfer in other systems, e.g., as has been recently demonstrated in the case of In electrodeposition from solutions containing Cl [101]. 

The mixed potential theory (MPT) model has stimulated much research in electroless deposition from an electrochemical standpoint. In this sense, the MPT model has been of considerable value in promoting our understanding of the electroless deposition process. 

Marmatite has a narrower band gap than (Zn, Cu)S, thus it should be more easily oxidized than (Zn, Cu)S. But in fact, the sphalerite after Cu activation has the most excellent flotation response using xanthate. These phenomena can be explained by the mixed potential theory. 

According to the mixed potential theory, an anodic reaction can occur only if there is a cathodic reaction proceeding at finite rate at that potential (Rand and Woods, 1984). For the flotation systems, the cathodic reaction is usually given by the reduction of oxygen. The corresponding anodic reaction involves interaction of xanthate on the sulphide minerals in various ways, including the reaction of xanthate with the sulphide mineral (MS) to form metal xanthate and the oxidation of xanthate to dixanthogen (X2) at the mineral surface. 

A series of nucleation and growth models was developed by, for example, Bewick et al. (11), Armstrong and Harrison (16), and Scharifker and Hills (17). Amblart et al. (18) have shown that nickel epitaxial growth starts with the formation of three-dimensional epitaxial crystallites. An electrochemical model for the process of electroless metal depositions (mixed-potential theory) was suggested by Paunovic (14) and Saito (14b). 

An electrochemical model for the process of electroless metal deposition was suggested by Paunovic (10) and Saito (8) on the basis of the Wagner-Traud (1) mixed-potential theory of corrosion processes. According to the mixed-potential theory of electroless deposition, the overall reaction given by Eq. (8.2) can be decomposed into one reduction reaction, the cathodic partial reaction. 

Wagner-Traud Diagram, According to the mixed-potential theory, the overall reaction of the electroless deposition, [Eq. (8.2)] can be described electrochemically in terms of three current-potential i-E) curves, as shown schematically in Eigure 8.2. First, there are two current-potential curves for the partial reactions (solid curves) (1) ic =f(E), the current-potential curve for the reduction of ions, recorded from the rest potential E eq M the absence of the reducing agent Red (when the activity of is equal to 1, eq,M E m) and (2) = f(E), the current-potential... 

Electroless Deposition of Copper. The basic ideas of the mixed-potential theory were tested by Paunovic (10) for the case of electroless copper deposition from a cupric sulfate solution containing ethylenediaminetetraacetic acid (EDTA) as a complexing agent and formaldehyde (HCHO) as the reducing agent (Red). The test involved a comparison between direct experimental values for and the rate of deposition with those derived theoretically from the current-potential curves for partial reactions on the basis of the mixed-potential theory. 

Thus, one concludes that the mixed-potential theory is essentially verified for the case of electroless copper deposition. These conclusions were later confirmed by Donahue (15), Molenaar et al. (25), and El-Raghy and Abo-Salama (33). The mixed-potential theory has been verified for electroless copper deposition as well using hypophosphite as the reducing agent (72). 

Comparison between the values of the mixed potential and the rate of deposition via direct determination with those derived from the mixed-potential theory is very good. Thus, the mixed-potential theory was verified for this case of electroless Ni deposition. 

Electroless Deposition of Gold. Okinaka (21) verified the mixed-potential theory for the case of electroless gold deposition. Eigure 8.6 shows that the partial cathodic... 

Electroless Deposition in the Presence of Interfering Reactions. According to the mixed-potential theory, the total current density, is a result of simple addition of current densities of the two partial reactions, 4 and However, in the presence of interfering (or side) reactions, 4 and/or may be composed of two or more components themselves, and verification of the mixed-potential theory in this case would involve superposition of current-potential curves for the electroless process investigated with those of the interfering reactions in order to correctly interpret the total i-E curve. Two important examples are discussed here. 

Conclusions. The discussion in this section shows the validity of the mixed-potential theory for electroless deposition of Cu, Ni, and An. The discussions in the sections Electroless Deposition in the Presence of Interfering Reactions and Interaction Between Partial Reactions illustrate the complexities of electroless processes and the presence of a variety of factors that should be taken into account when applying the mixed-potential theory to the electroless processes. 

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