The Temperature and Potential Dependence of the Rate Constant for Electron Transfer at the Metal Redox Electrolyte Interface

1995 ◽  
Vol 48 (11) ◽  
pp. 1843 ◽  
Author(s):  
D Matthews
Keyword(s):  
Electron Transfer ◽  
Potential Energy ◽  
Temperature Dependence ◽  
Rate Constant ◽  
Distribution Functions ◽  
State Distribution ◽  
Redox Electrolyte ◽  
High Overpotentials ◽  
Rate Constant Distribution ◽  
Constant Distribution

The Gurney-Gerischer-Marcus (GGM) model is used to investigate the potential and temperature dependence of the rate constant for electron transfer at the interface between a metal and a redox electrolyte. In this model electron transfer is described in terms of nuclear configuration-potential energy diagrams, electronic configuration-potential energy diagrams, state distribution functions and rate constant distribution functions. The model of identical parabolas, which leads to Gaussian electron distribution functions, g(E), for the redox electrolyte, is used for the nuclear configuration diagrams. The rate constant distribution, k(E), is obtained from the overlap between occupied and unoccupied state distribution functions of the metal and redox electrolyte. Integration of k(E) over the vertical transition (Franck-Condon) energies, E, gives the rate constant, k, which is calculated as a function of the electrode potential and temperature for various values of the reorganization energy, λ. Differentiation of k with respect to potential returns g(E) for the redox electrolyte except for a small deviation which is due to the weak dependence on energy of the distribution of states in the metal. For high λ the variation of symmetry factor with potential is small and the Tafel plots do not show a significant decrease in rate at high overpotentials. For small λ the Tafel plots are strongly curved but do not go through a maximum at high overpotential; the Tafel plots tend to a limiting value with only a small decrease in rate constant at high overpotential. This result is reflected in the temperature dependence of the rate constant and in the dependence of the Arrhenius activation energy, Ea, on potential; Ea does not increase at high overpotentials. These results are due to the weak dependence on energy of the distribution function for a metal compared to a redox electrolyte and emphasize the advantages of using distribution functions to describe the kinetics of electron transfer.

Allowance for Force Constant Changes in the Theory of Electron Transfer at the Metal-Redox Electrolyte Interface

1995 ◽  
Vol 48 (11) ◽  
pp. 1853 ◽  
Author(s):  
D Matthews
Keyword(s):  
Electron Transfer ◽  
Force Constant ◽  
Rate Constant ◽  
Small Deviation ◽  
Final States ◽  
Redox Electrolyte ◽  
Symmetry Factor ◽  
Metal Redox ◽  
Rate Constant Distribution ◽  
Constant Distribution

The Gurney-Gerischer-Marcus (GGM) model for electron transfer1 is used to investigate the effects of force constant changes between initial and final states for electron transfer at the interface between a metal and a redox electrolyte. The effects on the symmetry factor, β, and on the determination of the redox electrolyte distribution of states are investigated and compared to the predictions of the GGM model using no change in force constant. Comparisons are also made between the Marcus2,3 and GGM models. The GGM model with non-identical parabolas for the potential energy-nuclear configuration diagrams is used to numerically calculate the distribution of states in the redox electrolyte from which data the rate constant distribution for reduction is obtained from the overlap between occupied states of the metal and the unoccupied states of the redox electrolyte. Numerical integration of the rate constant distribution gives the rate constant which is calculated as a function of the electrode potential. The calculated Tafel plots are found to be non-linear but do not go through a maximum. The Marcus and GGM models predict markedly different dependences of the symmetry factor on potential. Differentiation of the calculated rate constant with respect to potential gives the distribution of states for the redox electrolyte except for a small deviation which is due to the weak dependence on energy of the distribution of states in the metal. Anomalous results reported in the literature are shown to be qualitatively consistent with a difference in force constant between initial and final states for electron transfer.

The Absence of a Marcus Inversion Region for Electron Transfer at the Metal-Redox Electrolyte Interface

1994 ◽  
Vol 47 (12) ◽  
pp. 2171 ◽  
Author(s):  
D Matthews
Keyword(s):  
Electron Transfer ◽  
Potential Energy ◽  
Electron Distribution ◽  
Distribution Functions ◽  
Rate Distribution ◽  
Inversion Region ◽  
Redox Electrolyte ◽  
Electrolyte Interface ◽  
Metal Redox ◽  
Nuclear Configuration

The theory of electron transfer at the metal- redox electrolyte interface is described by starting with the work of Gurney and incorporating that of Gerischer and Marcus. This GGM model brings together diverse approaches to the description of electron transfer at electrodes. The electron transfer is described in terms of nuclear configuration potential energy diagrams, electronic configuration potential energy diagrams, electron distribution functions and rate distribution functions. The distinction between microscopic energies and macroscopic (thermodynamic) energies is made and the concept of the Fermi level of the redox electrolyte is clarified. The model of identical parabolas is used for the nuclear configuration diagrams and this is shown to lead to Gaussian electron distribution functions for the redox electrolyte. The rate distribution is obtained from the overlap between occupied and unoccupied states of the metal and redox electrolyte. Integration of the rate distribution gives the rate which is calculated as a function of the electrode potential for various values of the reorganization energy λ. It is shown that the variation of symmetry factor β is small for high λ and that the Tafel plots do not show significant decrease in rate at high overpotentials in the anomalous or inversion region. The Tafel plots for charge transfer (mass transfer is assumed to be fast at all potentials) tend to a limiting value with only a small decrease at high overpotential. This contrasts with the prediction based on nuclear configuration potential energy curves and is attributed to the fact that the overlap is between a Gaussian and a Fermi function rather than between two Gaussians, the latter being the case for homogeneous reactions.

The Potential Dependence of the Rate Constant for Charge Transfer at the Semiconductor-Redox Electrolyte Interface

1996 ◽  
Vol 49 (7) ◽  
pp. 731
Author(s):  
D Matthews ◽  
A Stanley
Keyword(s):  
Charge Transfer ◽  
Potential Energy ◽  
Rate Constant ◽  
Reorganization Energy ◽  
Distribution Functions ◽  
Doped Semiconductors ◽  
Redox Electrolyte ◽  
Tafel Slopes ◽  
Valence Bands ◽  
Helmholtz Potential

The kinetics of charge transfer at the semiconductor- redox electrolyte interface is described in terms of the Gurney- Gerischer -Marcus (GGM) model by using nuclear configuration potential energy diagrams, electronic configuration potential energy diagrams, density of state distributions and rate constant distributions. The model of identical parabolas for the nuclear configuration diagrams is used; this leads to Gaussian oxidant and reductant distribution functions, g(E), where E is the vertical transition (Franck-Condon) energy. The rate constant distribution, k(E), is obtained from the overlap between occupied and unoccupied state distribution functions of the semiconductor and redox electrolyte. Integration of k(E) gives the rate constant which is calculated as a function of the Helmholtz potential, VH, for various values of the reorganization energy, Ereorg. Three types of semiconductor are considered: intrinsic, doped and highly doped. For intrinsic semiconductors the charge transfer rate constant is relatively small and involves both the conduction and valence bands. For symmetric charge transfer (zero energy change, E0.0, for the reaction) both oxidation and reduction occur between the redox electrolyte and both bands of the semiconductor. For unsymmetrical reactions, charge transfer tends to involve only one of the bands; for net reduction, the valence band is involved, whereas for net oxidation the conduction band is involved. For doped semiconductors the rate constant is larger and only one band is involved; for n-type it is the conduction band, and for p-type it is the valence band. For highly doped semiconductors with the Fermi level in either the conduction or valence bands. the rate constant is even larger and only one band is involved. Changes in Helmholtz potential affect k(E) in a similar way to that for metals. However, unlike for metals, the calculated Tafel plots for highly doped n-type semiconductors are shown to exhibit a Marcus inversion region. This is a consequence of the energy gap between conduction and valence bands of the semiconductor. For doped semiconductors, changes in the Helmholtz potential also produce a maximum in the Tafel plot and because of the relatively low currents involved this maximum should be experimentally observable. For intrinsic semiconductors, variation of Helmholtz potential without inclusion of band bending in the semiconductor produces unexpectedly low Tafel slopes which are related to the ratio of the band gap to the reorganization energy, so that the larger the ratio the smaller the Tafel slope. This unexpected result, which amounts to an assumption of band edge unpinning, is shown to accurately account for the experimentally observed Tafel slopes for reduction at n-WSe2 of the dimethylferrocenium ion in acetonitrile.

ChemInform Abstract: THE √T LAW IN SOLID-PHASE REACTIONS. ANALYSIS OF THE HYPOTHESIS ON RATE CONSTANT DISTRIBUTION

1981 ◽  
Vol 12 (48) ◽  
Author(s):  
V. M. ZASKUL'NIKOV ◽  
V. L. VYAZOVKIN ◽  
B. V. BOL'SHAKOV ◽  
V. A. TOLKATCHEV
Keyword(s):  
Rate Constant ◽  
Solid Phase ◽  
Solid Phase Reactions ◽  
Rate Constant Distribution ◽  
Constant Distribution

An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data

2017 ◽  
Vol 26 (10) ◽  
pp. 1464-1489 ◽  
Author(s):  
Y. Zhang ◽  
P. Forssén ◽  
T. Fornstedt ◽  
M. Gulliksson ◽  
X. Dai
Keyword(s):  
Rate Constant ◽  
Regularization Algorithm ◽  
Adaptive Regularization ◽  
Rate Constant Distribution ◽  
Constant Distribution

Kinetics of recombination of photoseparated charges in Rhodobacter sphaeroides reaction centers analyzed by relaxation rate constant distribution

BIOPHYSICS ◽  
2009 ◽  
Vol 54 (3) ◽  
pp. 296-301 ◽  
Author(s):  
E. P. Lukashev ◽  
P. P. Knox ◽  
A. B. Rubin ◽  
M. V. Olenchuk ◽  
Yu. M. Barabash ◽  
...  
Keyword(s):  
Relaxation Rate ◽  
Rate Constant ◽  
Rhodobacter Sphaeroides ◽  
Reaction Centers ◽  
Kinetics Of ◽  
Rate Constant Distribution ◽  
Constant Distribution ◽  
Relaxation Rate Constant

The Order of Kinetic Models, Rate Constant Distribution, and Maximum Combustible Recovery in Gilsonite Flotation

2019 ◽  
Vol 36 (6) ◽  
pp. 1101-1114
Author(s):  
Ataallah Bahrami ◽  
Fatemeh Kazemi ◽  
Yousef Ghorbani ◽  
Jafar Abdolahi Sharif
Keyword(s):  
Rate Constant ◽  
Kinetic Models ◽  
Rate Constant Distribution ◽  
Constant Distribution

Extended Rate Constant Distribution Model for Sorption in Heterogeneous Systems. 1: Application to Kinetics of Metal Ion Sorption on Polyethyleneimine Cryogels

2019 ◽  
Vol 59 (3) ◽  
pp. 1123-1134 ◽  
Author(s):  
Alexey Golikov ◽  
Irina Malakhova ◽  
Yuliya Azarova ◽  
Marina Eliseikina ◽  
Yuliya Privar ◽  
...  
Keyword(s):  
Rate Constant ◽  
Metal Ion ◽  
Heterogeneous Systems ◽  
Distribution Model ◽  
Ion Sorption ◽  
Kinetics Of ◽  
Rate Constant Distribution ◽  
Constant Distribution

Electron-Transfer Reactions in Non-Aqueous Media. IV. A Temperature-Dependence Study of the Reduction of CoCl(NH3)52+ by Iron(II) in N,N-Dimethylformamide

1979 ◽  
Vol 32 (7) ◽  
pp. 1425 ◽  
Author(s):  
KR Beckham ◽  
DW Watts
Keyword(s):  
Electron Transfer ◽  
Temperature Dependence ◽  
Equilibrium Constant ◽  
Rate Constant ◽  
Iron Atom ◽  
Rate Constants ◽  
Aqueous Media ◽  
Transfer Reactions ◽  
Complex Functions ◽  
Temperature Dependences

A detailed study has been made of the temperature dependence of the rate of reduction of CoCl-(NH3)52+ by iron(II) in N,N-dimethylformamide. The observed rate constants (kobs) for this reaction are complex functions of an equilibrium constant (K) for the formation of a bridged intermediate, the rate constant for electron transfer in this bridged intermediate (k), and the iron(II) concentration. From studies of the dependence of kobs on iron(II) concentration at five temperatures the temperature dependences of both K and k have been resolved, yielding respectively ΔH� -20k�12 kJ mol-1, ΔS� -44�40 J K-1 mol-1 and ΔH* 107�4 kJ mol-1, ΔS* 57�16 J K-1 mol-1. The results are interpreted in terms of a bridged intermediate in which the iron atom is tetrahedrally coordinated.

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