The potential-dependence and the upper limits of electrochemical rate constants

Hale, J.M.

doi:10.1016/s0022-0728(68)80131-7

Cited by 34 publications

(6 citation statements)

References 5 publications

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“…Our formula improves upon classical asymptotic approximations [11,22,24] and recent series expansions [18,19,23] and provides the first uniformly valid approximation for all reasonable choices of the reorganization energy and overpotential with less than 5% error at small overpotentials and vanishing error at large overpotentials. This result could be conveniently used in classi- cal battery models [21] or new models based on non-equilibrium thermodynamics [4] for electrode phase transformations limited by Faradaic reactions [2].…”

Section: Discussionmentioning

confidence: 70%

“…This corresponds to the zero temperature limit of the FermiDirac distribution, which enables an accurate approximation to the original integral [11],…”

Section: B Large Reorganization Energies λmentioning

confidence: 99%

“…2. When a positive free-energy barrier is formed in the inverted region in response to the large overpotential, electrons below the Fermi level (µ e ) with roughly unity Fermi factor follow a lower-energy parabola that enables a barrierless transfer, which dominates the overall reduction rate and leads to a constant, non-zero limiting current [11,22,24]. More detailed comparisons between BV and MHC kinetics can be found in Appleby and Zagal [1], Chen and Liu [7], and the enlightening review of Henstridge et al [12].…”

Section: Introductionmentioning

confidence: 99%

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Simple formula for Marcus–Hush–Chidsey kinetics

Zeng

Smith

Bai

et al. 2014

Journal of Electroanalytical Chemistry

100

153

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The Marcus-Hush-Chidsey (MHC) model is well known in electro-analytical chemistry as a successful microscopic theory of outer-sphere electron transfer at metal electrodes, but it is unfamiliar and rarely used in electrochemical engineering. One reason may be the difficulty of evaluating the MHC reaction rate, which is defined as an improper integral of the Marcus rate over the Fermi distribution of electron energies. Here, we report a simple analytical approximation of the MHC integral that interpolates between exact asymptotic limits for large overpotentials, as well as for large or small reorganization energies, and exhibits less than 5% relative error for all reasonable parameter values. This result enables the MHC model to be considered as a practical alternative to the ubiquitous Butler-Volmer equation for improved understanding and engineering of electrochemical systems.

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Section: Discussionmentioning

confidence: 70%

“…This corresponds to the zero temperature limit of the FermiDirac distribution, which enables an accurate approximation to the original integral [11],…”

Section: B Large Reorganization Energies λmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simple formula for Marcus–Hush–Chidsey kinetics

Zeng

Smith

Bai

et al. 2014

Journal of Electroanalytical Chemistry

100

153

View full text Add to dashboard Cite

show abstract

“…Taking into account these observations points to the necessity of applying to the kinetics of the electrochemical reaction the full Marcus-HushLevich (MHL) quadratic model (31)(32)(33)(34)(35) rather than a linearized version, amounting to the old Butler-Volmer empirical law, in which the transfer would be constant and close to 0.5 as often done with standard cyclic voltammetric responses (31).…”

Section: Kinetics and Mechanisms Of The Electrochemistry Of The Cu IImentioning

confidence: 99%

Electrochemical and homogeneous electron transfers to the Alzheimer amyloid-β copper complex follow a preorganization mechanism

Balland

Hureau

Savéant

2010

Proc. Natl. Acad. Sci. U.S.A.

116

177

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Deciphering the electron transfer reactivity characteristics of amyloid β-peptide copper complexes is an important task in connection with the role they are assumed to play in Alzheimer’s disease. A systematic analysis of this question with the example of the amyloid β-peptide copper complex by means of its electrochemical current–potential responses and of its homogenous reactions with electrogenerated fast electron exchanging osmium complexes revealed a quite peculiar mechanism: The reaction proceeds through a small fraction of the complex molecules in which the peptide complex is “preorganized” so as the distances and angles in the coordination sphere to vary minimally upon electron transfer, thus involving a remarkably small reorganization energy (0.3 eV). This preorganization mechanism and its consequences on the reactivity should be taken into account for reactions involving dioxygen and hydrogen peroxide that are considered to be important in Alzheimer’s disease through the production of harmful reactive oxygen species.

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“…For large values of Λ, the function f varies more slowly than g, which varies from ≈ 1 for η < 0 to ≈ 0 for η > 0. Therefore, a first approximation is simply to replace g by a step function, which gives [16]:…”

Section: 3mentioning

confidence: 99%

Numerical computations of Marcus–Hush–Chidsey electron transfer rate constants

Fourmond

Léger

2020

Journal of Electroanalytical Chemistry

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Two theories are available to predict the values of the rate constants of electron transfer between a redox species and an electrode as a function of electrode potential: the Butler-Volmer theory, and the Marcus "Density of States" (MDoS) theory. While the Butler-Volmer is purely empirical, it is widely used, in part because of its ability to represent experimental data, but also because of its simplicity: the rates are just exponential functions of the potential. By contrast, in the case of the MDoS theory, whose justification comes from the well-established theory of electron transfer proposed by Marcus, the rates are expressed in the form of indefinite integrals, which are harder to compute. A number of algorithms have been presented in the literature, with various merits in terms of accuracy and computation time; however, these algorithms have never been compared under the same conditions, which prevent making informed choices. We systematically compared the algorithms, both in terms of accuracy and computation time, and also propose a new algorithm which is very fast and reasonably accurate.

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The potential-dependence and the upper limits of electrochemical rate constants

Cited by 34 publications

References 5 publications

Simple formula for Marcus–Hush–Chidsey kinetics

Simple formula for Marcus–Hush–Chidsey kinetics

Electrochemical and homogeneous electron transfers to the Alzheimer amyloid-β copper complex follow a preorganization mechanism

Numerical computations of Marcus–Hush–Chidsey electron transfer rate constants

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