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 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.

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

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.

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

Extended Rate Constant Distribution Model for Sorption in Heterogeneous Systems: 3. From Batch to Fixed-Bed Application and Predictive Modeling

2020 ◽  
Vol 59 (43) ◽  
pp. 19415-19425
Author(s):  
Alexey Golikov ◽  
Irina Malakhova ◽  
Yuliya Privar ◽  
Yuliya Parotkina ◽  
Svetlana Bratskaya
Keyword(s):  
Rate Constant ◽  
Predictive Modeling ◽  
Fixed Bed ◽  
Heterogeneous Systems ◽  
Distribution Model ◽  
Rate Constant Distribution ◽  
Constant Distribution

The ?t law in solid-phase reactions. Analysis of the hypothesis on rate constant distribution

1981 ◽  
Vol 13 (8) ◽  
pp. 707-728 ◽  
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
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