Partial reaction mixed-potential theory

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. 

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. 

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. 

Interaction between Partial Reactions. The original mixed-potential theory assumes that the two partial reactions are independent of each other (1). In some cases this is a valid assumption, as was shown earlier in this chapter. However, it was shown later that the partial reactions are not always independent of each other. For example, Schoenberg (13) has shown that the methylene glycol anion (the formaldehyde in an alkaline solution), the reducing agent in electroless copper deposition, enters the first coordination sphere of the copper tartrate complex and thus influences the rate of the cathodic partial reaction. Ohno and Haruyama (37) showed the presence of interference in partial reactions for electroless deposition of Cu, Co, and Ni in terms of current-potential curves. 

The two partial reactions (2) and (3) determine the potential of electroless deposition, called mixed potential. The concept presented above is called the mixed potential theory , a term derived from a concept proposed for interpreting corrosion... 

According to the mixed potential theory, the overall reaction should be interpretable simply by superimposing the respective electrochemical behavior of the two partial reactions, determined independently. More recent studies, however, show that electroless deposition processes are much more complicated than represented by the simple mixed potential theory described above. Interdependence of partial reactions and participation of a third reaction are among the complications which limit the significance of simple combination of independently studied partial reactions. Examples of such complications Eire discussed in the subsequent sections. 

The isotopic labeling of the source molecules should lead to the ratio H/D = 1 (D2 mol% = 50) in the evolved gas under open-circuit conditions at equal rates of reactions (19.11) and (19.12) (equal partial currents in and /12). Furthermore, as it follows from the mixed potential theory, the isotopic composition of the evolving gas could be varied by changing the electrode potential due to the change in the partial reaction rates. 

Online mass spectrometry data presented and discussed in the previous sections suggest that catalytic hypophosphite oxidation on nickel in D2O solutions proceeds via the coupling of anodic (19.11) and cathodic (19.12) half-reactions at the catalyst surface. The classical mixed-potential theory for simultaneously occurring electrochemical partial reactions [14] presupposes the catalyst surface to be equally accessible for both anodic (19.11) and cathodic (19.12) half-reactions. Equilibrium mixtures of H2, HD, and D2 should be formed in this case due to the statistical recombination of Hahalf-reactions (19.11) and (19.12) for example, the catalytic oxidation of hypophosphite on nickel in D20 solution under open-circuit conditions should result in the formation of gas containing equal amounts of hydrogen and deuterium (H/D=l) with the distribution H2 HD D2= 1 2 1 (the probability of HD molecule formation is twice as high as for either H2 or D2 formation [75]). Therefore, to get further mechanistic insight, the distribution of H2, HD, and D2 species in the evolved gas was compared to the equilibrium values at the respective deuterium content [54]. 

However, according to the mixed potential theory, the value of the open-circuit potential varies when changing the rate of reaction (19.18) or reaction (19.19) due to H/D substitution in formaldehyde or water (for corresponding Em values see Figure 19.8A(b) and B(b)). Therefore, the effect of H/D substitution on the rates of individual partial reactions must be studied under electrode potential control. 

According to mixed potential theory, any electrochemical reaction consists of partial reduction and oxidation reactions. In any redox reaction, such as the corrosion of a metal, there is no net accumulation of electric chaise and the rate of the oxidation must equal the rate of reduction. At the intersection of the cathodic and anodic kinetic lines (see Fig. 3.8), the rates of oxidation and reductions are equal. This point represents the corrosion potential, Eco .> and the corrosion current, At the... 

Polarisation methods involve changing the potential of the WE and monitoring the current which is produced as a function of time or potential. One of the most relevant physical quantities measured by DC polarisation methods is linear polarisation resistance (LPR). Its definition is based on the mixed potential theory proposed by Wagner and Traud [4], that explains the corrosion reactions by assuming that cathodic and anodic partial reactions occur at the metal-electrolyte interface at a certain corrosion (or mixed ) potential,... 

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. 

Clearly, in the subsystem resolution one could also consider all intermediate specifications of the molecular (constrained) equilibria, when only a part of the subsystems remains externally open (characterized by the fixed chemical potentials of a common reservoir) with the remaining, complementary set of subsystems being closed (characterized by the fixed subsystem numbers of electrons) [4,5]. Such mixed representations can be also naturally defined in the CSA approach. We would like to observe, that in the theory of chemical reactivity these partially opened situations do indeed arise, e.g., in the surface reactions, when one adsorbate is opened (chemisorbed) while the other reactant remains externally closed (physisorbed) on the catalyst surface, which acts as the electron reservoir for the reaction. 

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