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Butler, energy profiles

FIGURE 1.13. Free-energy profiles in outer-sphere electron transfer according to the Butler-Volmer approximation (a) and to the Marcus-Hush model (b). [Pg.31]

Figure 6.6. Gibbs energy profiles of the outer-sphere one-electron transfer process (4) in the Butler -Volmer formalism at electrode potential Ej (a) and electrode potential E2 (b). Figure 6.6. Gibbs energy profiles of the outer-sphere one-electron transfer process (4) in the Butler -Volmer formalism at electrode potential Ej (a) and electrode potential E2 (b).
As already mentioned above, the derivation of the Butler-Volmer equation, especially the introduction of the transfer factor a, is mostly based on an empirical approach. On the other hand, the model of a transition state (Figs. 7.1 and 7.2) looks similar to the free energy profile derived for adiabatic reactions, i.e. for processes where a strong interaction between electrode and redox species exists (compare with Section 6.3.3). However, it should also be possible to apply the basic Marcus theory (Section 6.1) or the quantum mechanical theory for weak interactions (see Section 6.3.2) to the derivation of a current-potential. According to these models the activation energy is given by (see Eq. 6.10)... [Pg.156]

Figure 1. Potential energy profile diagrams for a charge transfer process as in ion discharge with coupled atom transfer (based on representations by Gurney and Butler L In (b), curve / represents the H /H20 proton interaction potential and m that for discharged H with the metal M. R is the repulsive interaction of H with H2O and A the resultant interaction curve for H with M. Figure 1. Potential energy profile diagrams for a charge transfer process as in ion discharge with coupled atom transfer (based on representations by Gurney and Butler L In (b), curve / represents the H /H20 proton interaction potential and m that for discharged H with the metal M. R is the repulsive interaction of H with H2O and A the resultant interaction curve for H with M.
In the original treatment of Gurney/ the current was expressed as the integral of the product of electrolyte and electron energy distribution functions but with the electronic one written as a Boltzmann factor, exp( A /fcT). The symmetry factor was introduced intuitively in terms of the shift of intersection point of energy profiles in relation to change of electrode potential, i.e., of the Fermi-level energy (cf. Butler ). [Pg.136]

So far presented is a basic mechanistic picture of the ORR. It comprises discussions of potential-controlled formation of surface-adsorbed oxygen intermediates, alternative reaction pathways, and free energy profiles of typical stepwise reaction sequences. The overarching questions are How can these ingredients be cast into a consistent picture of the ORR at Pt-based catalystsl What controls the net rate of the reaction How are phenomenological parameters, which are employed in the Butler-Volmer equation, related to fundamental mechanisms and parameters ... [Pg.207]

Overall, the kinetic model and the statistical analysis of Equation 3.59 represent a way to reconcile kinetic modeling of surface reactions with ab initio studies of reaction pathways and free energy profiles, experimental studies of the abundance of reaction intermediates, and macroscopic effective parameters used in surface reactivity models based on the phenomenological Butler-Volmer equation. A specific sequence of elementary reaction steps has been focused on, corresponding to the widely accepted associative mechanism. The same formalism could be used for different reaction sequences. [Pg.211]

Figure 7.3 Schematics of the energy profiles along the reaction coordinate for C-CI and C-Br bond fission. The upper panel is the adiabatic point of view. The excitation is to the upper electronic state that correlates to the same products as the ground state. The lower panel shows the avoided crossings at the two barriers to dissociation on the upper electronic state (the coupling is to a bound higher excited state). The hindrance of the dissociation of the C—Br bond is shown schematically as a trajectory that makes a transition to a higher electronic state and is thereby reflected. The gap between the two adiabatic states, whose magnitude is the coupling between the diabetic states, is higher for the C—Cl bond fission [adapted from M. D. Person, P. W. Kash, and L. J. Butler, J. Chem. Phys. 97, 355 (1992) see also Waschewsky etal. (1994), Butler and Neumark (1996), Butler (1998), Conroy etal. (2001)1. Figure 7.3 Schematics of the energy profiles along the reaction coordinate for C-CI and C-Br bond fission. The upper panel is the adiabatic point of view. The excitation is to the upper electronic state that correlates to the same products as the ground state. The lower panel shows the avoided crossings at the two barriers to dissociation on the upper electronic state (the coupling is to a bound higher excited state). The hindrance of the dissociation of the C—Br bond is shown schematically as a trajectory that makes a transition to a higher electronic state and is thereby reflected. The gap between the two adiabatic states, whose magnitude is the coupling between the diabetic states, is higher for the C—Cl bond fission [adapted from M. D. Person, P. W. Kash, and L. J. Butler, J. Chem. Phys. 97, 355 (1992) see also Waschewsky etal. (1994), Butler and Neumark (1996), Butler (1998), Conroy etal. (2001)1.
Petch D, Butler M (1994), Profile of energy metabolism in a murine hybridoma glucose and glutamine utilization,). Cell. Physiol. 161 71-76. [Pg.109]

Once the local concentration overpotential is known, the activation overpotential, ria, is obtained by subtracting Tjc from total Tj. The local activation overpotential is the actual driving force of the electrochemical reaction. It is related to the local current density at any point of the reaction zone by an electrochemical rate equation such as the Butler-Volmer equation (Eq. (10a)). Therefore, the rate equation, the Nernst equation (Eq. (37)), and the potential balance in combination couple the electric field with the species diffusion field. In addition, the energy balance applies also at the electrode level. Although this introduces another complication, a model including a temperature profile in the electrode is very useful because heat generation occurs mainly by electrochemical reaction and is localised at the reaction zone, while the... [Pg.320]


See other pages where Butler, energy profiles is mentioned: [Pg.15]    [Pg.109]    [Pg.363]    [Pg.81]    [Pg.209]    [Pg.75]    [Pg.91]    [Pg.85]    [Pg.108]   
See also in sourсe #XX -- [ Pg.109 ]




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