Electrochemical reaction adiabatic

FIGURE 34.6 Scheme of multiple electron transitions in adiabatic electrochemical reactions. 

Marcus stressed that only harmonic modes U = were involved in the ion-solvent interactions and went further than Weiss in formulating a simple equation for the rate of adiabatic electron transfer, taking the case of an isotopic reaction so that the AG° term was eliminated. Under this condition and using Eq. (9.32), the current density (or electrochemical reaction rate) at a given overpotential t], in the cathodic direction (T] is negative) is... 

Relatively little attention has been given in the literature to the electronic transmission coefficient for electrochemical reactions. On the basis of the conventional collisional treatment of the pre-exponential factor for outer-sphere reactions, Kel has commonly been assumed to equal unity, i.e. adiabatic reaction pathways are followed. Nevertheless, as noted above, the dependence of xei upon the spatial position of the transition state is of key significance in the "encounter pre-equilibrium treatment embodied in eqns. (13) and (14). Thus, the manner in which Kel varies with the reactant-electrode separation for outer-sphere reactions will influence the integral of reaction sites that effectively contribute to the overall measured rate constant and hence the effective electron-tunneling distance, Srx, in eqn. (14). 

The present consensus is that most reactions of the outer-sphere type between simple metal complexes in solution are either weakly adiabatic or weakly nonadiabatic with in the range of perhaps 10 to 1 but that inner-sphere reactions are probably more adiabatic, and reactions such as equation (3) (above) are strongly adiabatic. Also, many electrochemical reactions proceeding via a direct contact between the reactant and the electrode are adiabatic. ... 

An additional test of the theory is given by the comparison of the data for different electrode materials. Experimentally the reduction of the same anion at different metals leads to quite different patterns for the polarization curve, in particular, a drastic variation of the interval in which the diffuse-layer minimum is observed. According to the theory (24), if the reacting species do not enter the compact layer and the possible change of the electron-tunneling factor does not influence the reaction rate (e.g. for adiabatic electrochemical reactions [58]) the corrected Tafel plots must be independent of the electrode material. This prediction has also been confirmed experimentally for the persulfate reduction at Hg (amalgams), Bi, Sn,... 

In concluding this section, we note that nonadiabatic electrochemical reactions were considered above. Calculations on adiabatic electrode processes at metals and semiconductors is more complex. In the model of independent electrons, calculations on such a process were performed in Ref. 48, using the semiclassical method. The physical mechanism of the process consists in the manyfold electron transitions from the electrode to the reactant, and backwards, in the course of variation of the solvent polarization. 

Nevertheless, the electronic coupling can still influence the rate of such adiabatic pathways by diminishing the barrier height. A general expression for the observed rate constant of bimolecular homogeneous-phase or electrochemical reactions is [2,4,5] ... 

Even if such an idea (sort of an adiabatic reduction cell) is realized, the Hall-Heroult reduction process will likely require a sufficiently greater surface of electrochemical reaction (to be discussed in Sect. 2.5). 

FIGURE 35.2 Scheme of diabatic (solid line) and adiabatic (dashed line) free-energy curves for a simple electrochemical redox reaction Ox —> Red. 

Both the initial- and the final-state wavefunctions are stationary solutions of their respective Hamiltonians. A transition between these states must be effected by a perturbation, an interaction that is not accounted for in these Hamiltonians. In our case this is the electronic interaction between the reactant and the electrode. We assume that this interaction is so small that the transition probability can be calculated from first-order perturbation theory. This limits our treatment to nonadiabatic reactions, which is a severe restriction. At present there is no satisfactory, fully quantum-mechanical theory for adiabatic electrochemical electron-transfer reactions. 

Relationships having the same form as eq 14 can also be written for the enthalpic and entropic contributions to the intrinsic free energy barriers (10). Provided that the reactions are adiabatic and the conventional collision model applies, eq 14 can be written in the familiar form relating the rate constants of electrochemical exchange and homogeneous self-exchange reactions (13) ... 

Substrate and intermediate species adsorb on an electrode surface and orient themselves so that their least hindered sides face the electrode, unless there is another effect such as a polar one. An electrode interface has a layered structure in which a nonuniform electric field (some slope of potential) is generated by polarization of the electrode. An extremely strong electric field of approximately 10 V cm i in the innermost layer might cause a variety of polar effects. For instance, electrochemical one-electron oxidation of o-aminophenol derivatives proceeds adiabatically. On the contrary, the homogeneous reaction is nonadiabatic. This difference in behavior is related to... 

The terms adiabatic and nonadiabatic are confusing. Thus, students who approach kinetics at an electrochemical interface via studies of chemistiy will be used to the term adiabatic. In thermodynamics, adiabatic indicates a process in which no heat enters or escapes from the system, e.g., from the vessel in which the reaction... 

Medvedev, LG. (2006) The effect of the electron-electron interaction on the pre-exponential factor of the rate constant of the adiabatic electrochemical electron transfer reaction. Journal of Eiectroanaiytical Chemistry, 598,1-14. 

In the non-adiabatic limit, the total ET rate can be expressed as the sum of ET rates to all possible accepting states in the semiconductor (Marcus, 1965 Gao et al, 2000 Gao and Marcus, 2000 Gosavi and Marcus, 2000). For electron injection from an adsorbate excited state with electrochemical redox potential of U°(S /S ) to a semiconductor k state at e = E- Ecb) above the band edge (with flatband potential of U°cb), the reaction can be written as... 

Robie et al. have carried out excellent measurements of the heat capacity of Ni2Si04 olivine between 5 and 387 K by cryogenic adiabatic-shield calorimetry and between 360 and 1000 K by differential scanning calorimetry. At 298.15 K the molar heat capacity and entropy of Ni2Si04 olivine were determined. This molar heat capacity and entropy were accepted by this review. The thermal heat capacity function proposed by Robie et al. for the temperature range between 300 and 1300 K was, however, not adopted by this review, because it is based on measurements which were made only at temperatures up to 1000 K. Combining the heat capacity measurements with results of molten salt calorimetry, thermal decomposition of Ni2Si04 olivine into its constituent oxides, and equilibrium studies, both by CO reduction and solid state electrochemical cell measurements for the reaction ... 

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