Butler-Volmer equation oxidation

As tire reaction leading to tire complex involves electron transfer it is clear that tire activation energy AG" for complex fonnation can be lowered or raised by an applied potential (A). Of course, botlr tire forward (oxidation) and well as tire reverse (reduction) reaction are influenced by A4>. If one expresses tire reaction rate as a current flow (/ ), tire above equation C2.8.11 can be expressed in tenns of tire Butler-Volmer equation (for a more detailed... 

This is the relaxation time of the polymer oxidation under electro-chemically stimulated conformational relaxation control. So features concerning both electrochemistry and polymer science are integrated in a single equation defining a temporal magnitude for electrochemical oxidation as a function of the energetic terms acting on this oxidation. A theoretical development similar to the one performed for the Butler-Volmer equation yields... 

The two-step charge transfer [cf. Eqs. (7) and (8)] with formation of a significant amount of monovalent aluminum ion is indicated by experimental evidence. As early as 1857, Wholer and Buff discovered that aluminum dissolves with a current efficiency larger than 100% if calculated on the basis of three electrons per atom.22 The anomalous overall valency (between 1 and 3) is likely to result from some monovalent ions going away from the M/O interface, before they are further oxidized electrochemically, and reacting chemically with water further away in the oxide or at the O/S interface.23,24 If such a mechanism was operative with activation-controlled kinetics,25 the current-potential relationship should be given by the Butler-Volmer equation... 

Butene, catalytic oxidation, 35 168-169 n-Butene dimerization, 31 36-37 composition change, 31 25-26 But-2-en-l-ol oxidation, 41 307 Butler-Volmer equation, 40 89 Butterfly cluster compounds, 38 294-295 Butyl alcohols... 

The first exponential term in both equations is independent of the applied potential and is designated as k and A(L for the forward and backward processes, respectively. These represent the rate constants for the reaction at equilibrium, e.g. for a monolayer containing equal concentrations of both oxidized and reduced forms. However, the system is at equilibrium at E0/ and the products of the rate constant and the bulk concentration are equal for the forward and backward reactions, i.e. k must equal Therefore, the standard heterogeneous electron transfer rate constant is designated simply as k°. Substitution into Equations (2.19) and (2.20) then yields the Butler-Volmer equations as follows ... 

This is one of the few electrode reactions that does not follow the Butler-Volmer equation. The reason is that the dual-site dissociatidn of the H2 molecule is the rate-controlling step. But although this is a non-electrochemical step, the reaction rate is still a function of the potential, because the hydrogen oxidation is self-... 

In this equation, and represent the surface concentrations of the oxidized and reduced forms of the electroactive species, respectively k° is the standard rate constant for the heterogeneous electron transfer process at the standard potential (cm/sec) and oc is the symmetry factor, a parameter characterizing the symmetry of the energy barrier that has to be surpassed during charge transfer. In Equation (1.2), E represents the applied potential and E° is the formal electrode potential, usually close to the standard electrode potential. The difference E-E° represents the overvoltage, a measure of the extra energy imparted to the electrode beyond the equilibrium potential for the reaction. Note that the Butler-Volmer equation reduces to the Nernst equation when the current is equal to zero (i.e., under equilibrium conditions) and when the reaction is very fast (i.e., when k° tends to approach oo). The latter is the condition of reversibility (Oldham and Myland, 1994 Rolison, 1995). 

The usual procedure for extracting the exchange current Iq is then to measure q as a function of I and to plot Inl vs q (Tafel plot). Such plots are shown in Figures 3 and 4 for Pt and Ag catalyst electrodes deposited on YSZ and acting as catalyst for C2H4 oxidation. Throughout the rest of this discussion, we omit the subscript "W" from q and simply write q, since the only overpotential of interest is that of the catalyst film. When Iql >100 mV, then the Butler-Volmer equation (16) reduces to its "high field approximation" form, i.e.. 

ITR take place at the oxide/electrolyte interface. They can be described by the Butler-Volmer equation using the potential drop at the interface A oh or the overvoltage r]u... 

In the electrochemical mechanism of corrosion, the metal dissolution—which involves the loss of electrons vis- -vis oxidation—must be accompanied by a cathodic reaction that consumes electrons, which is typically oxygen or proton or water reduction. According to the Butler-Volmer equation, the current density for the anodic reaction varies according to... 

The hydrogen oxidation reaction can be considered as sufficiently rapid and in this case jo °° and j7c 0. The Butler-Volmer equation can be linearised ... 

According to (6.24), the ionic current density in the film varies exponentially with the electric field. Even though this relation has been derived here from a rather simple model, it holds true quite generally. We therefore can also look at equation (6.24) as an empirical equation that describes the relation between the ionic current, the potential and the thickness of solid oxide films, in a similar way as the Butler-Volmer equation describes the relation between current and potential for a metal-electrolyte interface. 

The activation overpotential is a function of current and determined by the Butler-Volmer equation. For a generic oxidation reaction of... 

In equilibrium, the standard reduction and oxidation processes occur at equal rates and the exchange currents produced by the two reactions balance each other. The current density, i A/cm2, is given by Butler-Volmer equation [3] ... 

When the system is no longer at equihbrium, the reaction is favored in the direction of oxidation at the anode (production of electrons) and in the direction of reduction at the cathode (consumption of electrons). We can write a Butler-Volmer equation at each electrode ... 

Regarding catalyst aging. Darling and Meyers have proposed a mechanistic model, based on empirical parameters, of the Pt oxidation/dissolution in a PEMFC cathode, largely cited by experimentalists in subsequent papers. By using classical Butler-Volmer equations written in terms of the CL electrode potential and empirical parameters (e.g. symmetry factors, zero-exchange current and... 

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