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Impedance of cation-coupled electron transfer reaction: Theoretical description of one pathway process
... The AIC gives us a strategy to avoid under-and over-fitting. [42,43] Underfitting occurs when the fitted expression fails to identify effects that were supported by the data, i. e., high bias -low variance. In contrast, overfitting occurs when the fitted expression contains spurious variables and is characterised by low bias-high variance. ...
Different strategies can be used to acquire dynamic impedance spectra during a cyclic voltammetry experiment. The spectra are then analyzed by fitting them with a model using a weighted non‐linear least‐squares minimization algorithm. The choice of the weighting factors is not trivial and influences the value of the extracted parameters. At variance with the classic EIS, dynamic impedance measurements are performed under non‐stationary conditions, making them typically more affected by the noise of the voltage and current amplifiers. Under the assumption that the noise in the voltage and current signals have a constant variance and that it is uncorrelated among the samples, we calculate an expression for the expected variance of the error of the resulting immittances, which considers the specific procedure used to extract the spectra under the time‐varying nature of the measurements. The calculated variance of the error is then used as a rigorous way to evaluate the weighting factors of the least‐squares minimization, assuming that the fitted model is ideally exact and that there are no systematic errors. By exploring two classical electrochemical systems and fitting the measured spectra with a transfer function measurement model, namely with the Padé approximants, we show that the variance evaluated with our method captures the frequency dependence of the resulting residuals and can be used for reliably performing the complex non‐linear least‐squares fitting procedure.
... Particularly, the results obtained when the cell was discharged under various conditions of the electrode indicated that the impedance of both the positive and the negative electrodes could not be overlooked. In another relevant theoretical analysis of impedance under potentiostatic conditions, the Slepski group aimed to describe the impedance of a cation electron-coupled transfer reaction (66). They found that in the potentiodynamic mode, the polarization depended on the resistance of the potential scan rate and adsorption capacity. ...
Finding suitable measurement methods for the effective management of electrochemical problems is of paramount importance, particularly for improving efficiency in corrosion protection. The need for accurate measurement techniques specific to nonstationary conditions has long been recognized, and promising approaches have emerged. This chapter introduces dynamic electrochemical impedance spectroscopy as a novel advancement in electrochemistry that can be used efficiently in galvanostatic and potentiostatic modes. The review focuses first on an explanation of the method and second on presenting a comprehensive corpus covering available studies that have applied dynamic electrochemical impedance spectroscopy for the purpose of preventing corrosion phenomena. This chapter defines the merits of this novel approach compared with the conventional electrochemical impedance spectroscopy method.
Functionalizing molecules through the selective cleavage of carbon-carbon bonds is an attractive approach in synthetic chemistry. Despite recent advances in both transition-metal catalysis and radical chemistry, the selective cleavage of inert Csp3-Csp3 bonds in hydrocarbon feedstocks remains challenging. Examples reported in the literature typically involve substrates containing redox functional groups or highly strained molecules. In this article, we present a straightforward protocol for the cleavage and functionalization of Csp3-Csp3 bonds in alkylbenzenes using photoredox catalysis. Our method employs two distinct bond scission pathways. For substrates with tertiary benzylic substituents, a carbocation-coupled electron transfer mechanism is prevalent. For substrates with primary or secondary benzylic substituents, a triple single-electron oxidation cascade is applicable. Our strategy offers a practical means of cleaving inert Csp3-Csp3 bonds in molecules without any heteroatoms, resulting in primary, secondary, tertiary, and benzylic radical species.
The dimeric bridging carbonyl complexes [(μ-CO)2[CpCo]2]ⁿ (n = 0, 1−) have occupied a central position in the understanding of metal–metal bonding interactions when bridging ligands are present. Based on simple electron-counting formalisms, these dimers have been proposed to possess formal Co–Co bond orders of 2 and 1.5, respectively. However, this simple bonding scheme has been contrasted by molecular orbital theory considerations, as well as spectroscopic data that probes M–M bonding interactions generally. While this system has received considerable attention, there has been a long-standing synthetic limitation in that the doubly reduced dianionic dimer, [(μ-CO)2[CpCo]2]2–, has not been amenable to isolation, thereby precluding an analysis of ostensible full-integer reduction in a homologous series. Accordingly, herein is presented the synthesis of a homologous, three-membered series of bridging-isocyanide [(μ-CNAr)2[CpCo]2]ⁿ dimers, including the dianionic member. Structural and spectroscopic analyses of these [(μ-CNAr)2[CpCo]2]ⁿ dimers, which feature the m-terphenyl isocyanide CNArMes2 (ArMes2 = 2,6-(2,4,6-Me3C6H2)2C6H3), reveal that this series possesses similar overall properties to the bridging carbonyl counterparts. However, high-resolution X-ray crystallographic studies have revealed important structural differences that were not discernible in older studies of the carbonyl complexes. Also presented is the synthesis of the bridging-isocyanide/η⁶-arene dimers [Co2((η⁶-Mes)(μ-CNArMes))2]ⁿ (n = 0, 1+), which are valence isoelectronic to the mono- and dianionic [(μ-CNAr)2[CpCo]2]ⁿ derivatives. Structural and spectroscopic studies of these η⁶-arene complexes, as well as the related neutral nickel dimer (μ-CNArMes)2[CpNi]2 provide evidence for an electronic structure environment dominated by M→(CN)π* back-bonding interactions, rather than direct M–M bonding. This conclusion is supported by DFT-derived molecular orbital analysis on the bridging-isocyanide [(μ-CNArMes2)2[CpCo]2]ⁿ dimers.
A bio-mimetic system on reversible bond coupled electron transfer (BCET) has been proposed and investigated in a switchable Rh-N molecule with redox active subunits. We discover that energy barrier of C-N bond breaking is reduced dramatically to less than 1/7 (from 40.4 kcal/mol to 5.5 kcal/mol), and 1/3 of the oxidation potential has been simultaneously lowered (from 0.67 V to 0.43 V) with the oxidation of Rh-N. The concept, cation coupled electron transfer (CCET), is highly recommended by analyzing existing proton coupled electron transfer (PCET) and metal coupled electron transfer (MCET) along with aforementioned BCET, which have same characteristic of transferring positive charges, such as proton, metal ion, and organic cation. Molecular switch can be controlled directly by electricity through BCET process. Solid electrochromic device was fabricated with extremely high color efficiency (720 cm2/C), great reversibility (no degradation for 600 cycles) and quick respond time (30 ms).
Enzymes of the mitochondrial respiratory chain serve as proton pumps, using the energy made available from electron transfer reactions to transport protons across the inner mitochondrial membrane and create an electrochemical gradient used for the production of ATP. The ATP synthase enzyme is reversible and can also serve as a proton pump by coupling ATP hydrolysis to proton translocation. Each of the respiratory enzymes uses a different strategy for performing proton pumping. In this work, the strategies are described and the structural bases for the action of these proteins are discussed in light of recent crystal structures of several respiratory enzymes. The mechanisms and efficiency of proton translocation are also analyzed in terms of the thermodynamics of the substrate transformations catalyzed by these enzymes.
Cytochrome c oxidase (CcO) is the terminal enzyme of the cell respiratory chain in mitochondria and aerobic bacteria. It catalyzes the reduction of oxygen to water and utilizes the free energy of the reduction reaction for proton pumping across the inner-mitochondrial membrane, a process that results in a membrane electrochemical proton gradient. Although the structure of the enzyme has been solved for several organisms, the molecular mechanism of proton pumping remains unknown. In the present paper, continuum electrostatic calculations were employed to evaluate the electrostatic potential, energies, and protonation state of bovine heart cytochrome c oxidase for different redox states of the enzyme along its catalytic cycle. Three different computational models of the enzyme were employed to test the stability of the results. The energetics and pH dependence of the P-->F, F-->O, and O-->E steps of the cycle have been investigated. On the basis of electrostatic calculations, two possible schemes of redox-linked proton pumping are discussed. The first scheme involves His291 as a pump element, whereas the second scheme involves a group linked to propionate D of heme a(3). In both schemes, loading of the pump site is coupled to ET between the two hemes of the enzyme, while transfer of a chemical proton is accompanied by ejection of the pumped H(+). The two models, as well as the energetics results are compared with recent experimental kinetic data. The proton pumping across the membrane is an endergonic process, which requires a sufficient amount of energy to be provided by the chemical reaction in the active site. In our calculations, the conversion of OH(-) to H(2)O provides 520 meV of energy to displace pump protons from a loading site and overall about 635 meV for each electron passing through the system. Assuming that the two charges are translocated per electron against the membrane potential of 200 meV, the model predicts an overall efficiency of 63%.
A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.
A theoretical study of coupled electron-proton transfer is presented for heterogeneous electron transfer to redox centers attached to electrodes. Proton transfer steps are assumed to be at equilibrium and the transfer coefficients are assumed to exhibit the potential dependence predicted by Marcus Density-of-States theory. Five cases are considered: 1e1H, 1e2H, 2e, 2e1H, and 2e2H. Procedures are given for calculating the apparent standard rate constant, the apparent transfer coefficient, and the path of electron transfer as a function of overpotential and pH. The behavior of these parameters are compared with a previous theoretical treatment in which the transfer coefficient for each electron transfer step was assumed to be 0.5 independent of overpotential. The predictions of the two treatments are qualitatively similar but quantitatively different. In particular, when the transfer coefficient depends on the electrode potential, apparent standard rate constants are smaller, asymmetrical Tafel plots appear in the 1e1H and 1e2H cases, and the path of electron transfer depends on potential as well as pH. Experimental evidence for the validity of the model is described.
A theoretical study of the direct apparent 2 e−, 2 H+ homogeneous isotopic electron exchange is presented (large overlap of the two stages), when the protonations are assumed to be at equilibrium. Under these conditions, the system behaves as a simple e−e− reaction with strong overlap of the two stages, the theory of which was presented earlier (E. Laviron, J. Electroanal. Chem., 148 (1983) 1). The apparent rate constant kapp for the electron exchange is a complex function of the individual isotopic rate constants, of the disproportionation rate constants, of the equilibrium constants in the nine-member square scheme, and of the pH. The behaviour of the benzoquinone—hydroquinone system is studied as an example. The reaction sequence is discussed. The curves log kapp = f(pH) have a slope of ±1 or 2, and the rate constant is considerably decreased relative to the individual isotopic or disproportionation rate constants. The theory explains why the exchange rate is slow in solution or in redox polymer-modified electrodes with 2 e−, 2 H+ systems with a strong overlap, and predicts the same effect for the exchange between a couple attached on an electrode (monolayer) and the same couple in solution.
A nonlinear description of a first order reaction proceeding in activation control conditions is presented. The effect of the amplitude of perturbation signal on the values of the effective potential and the direct current has been determined. A dependence between the effective potential, the direct current and the frequency of the generated sine perturbation signal is stated. Based on the derived dependencies current, potential and practical criteria referring to impedance measurements have been formulated.
In artificial photosynthesis, the goal is to mimic the ability of green plants and other photosynthetic organisms in their use of sunlight to make high-energy chemicals. This is a difficult problem chemically, which accounts for much of the complexity of the natural photosynthetic apparatus. Nonetheless, a number of promising approaches have appeared in recent years based on semiconductors, membranes, vesicles, and molecular systems. In this Account the author will describe some of the approaches that my own group has taken to the design of chemical systems for artificial photosynthesis.
Electrochemical properties of a 1-hydroxy-anthraquinone derivative (1-hydroxyAQ) self-assembled monolayer (SAM) were studied using reflectance infrared, cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS). The results of the electrochemical investigation into the proton-coupled electron transfer (PCET) reaction at various pHs and temperatures demonstrate a strong pH-charge transfer rate dependence. The charge transfer rates are faster in both acidic and basic solutions than near physiological pH. Interestingly, the activation enthalpy for the charge transfer reactions at physiological pH is low at 23kJmol−1 compared to 67kJmol−1 at pH 1.5. Variable temperature studies showed the entropic cost associated with the charge transfer reaction at pH 7.5 causes the slow charge transfer rate and suggests that pre-organizing proton donor solvents could lead to very fast charge transfer reactions at the hydrophobic|hydrophilic interface.
The a.c. impedance for a reaction involving an intermediate species is discussed and compared with other work in this area.
For Abstract see ChemInform Abstract in Full Text.
The effect of dielectric confinement on proton-coupled electron-transfer behavior and spectroscopic properties of cyanoferrate ions in a polymer electrolyte membrane (Nafion) has been investigated in an "all-solid-state" electrochemical cell, using techniques such as cyclic voltammetry, zero current chronopotentiometry, electrochemical impedance, diffuse reflectance infrared Fourier transform spectroscopy (DRIFT), UV-visible spectroscopy, X-ray photoelectron spectroscopy (XPS), and electron spin resonance spectroscopy (ESR). From the above investigations, we found that cyanoferrate(III) ions undergo autoreduction in the ionomer matrix, for which a sulfonate-coupled mechanism has been proposed. This report demonstrates the effectiveness of the micellar interface in tuning the redox potential of the confined ions. A systematic analysis of the cyclic voltammetry and impedance data for the [Fe(CN)(6)](4)(-)- containing Nafion membrane enables the estimation of a standard rate constant for [Fe(CN) 6](4-) oxidation, k(o), as 5.44 x 10(-6) cm/s and a diffusion coefficient, D-o, as 1.3 x 10(-12) cm(2)/s. A similar calculation yields a value of 4.8 x 10(-12) cm(2)/s for the diffusion coefficient of protons and 9.1 x 10(-6) cm/s for the standard rate constant for hydrogen oxidation. The similarity in mass-transfer coefficients calculated for protons and [Fe(CN)(6)](4-) ions suggests a proton-coupled electron-transfer mechanism for the [Fe(CN)(6)](4-)/[Fe(CN)(6)](3-) couple. The results of the above investigations could have direct technological relevance for deciding catalyst materials having redox compatibility with the polymer electrolyte, especially in the preparation of catalyst-coated membranes (wherein the fuel-cell catalyst is directly coated onto the polymer membrane instead of on the carbon support).
This document provides an inventory of the parameters that are in use to describe impedances of electrochemical cells. The definitions of these parameters are given, as well as recommendations for their terminology and nomenclature. Where relevant, experimental determination of a parameter and limitations to its validity are briefly discussed.
The objective of this work was to deactivate poly(o-aminophenol) (POAP) films and then study how their permeation and electron-transport processes are modified by the degree of deactivation. POAP films were deactivated by soaking in a ferric cation solution. The degree of deactivation (θc) was assessed by employing Cyclic Voltammetry within the potential region where POAP exhibits its maximal electroactivity (−0.2V
This paper demonstrates the effectiveness of using the IrCl62-/3- redox couple to investigate DNA monolayers, and compares the potential advantages of this system to the standard Fe(CN)63-/4- redox couple. B-DNA monolayers were converted to M-DNA by incubation in buffer containing 0.4mM Zn2+ at pH 8.6 and studied by cyclic voltammetry (CV), impedance spectroscopy (IS) and chronoamperometry (CA) with IrCl62-/3-. Compared to B-DNA, M-DNA showed significant changes in CV, IS and CA spectra. However, only small changes were observed when the monolayers were incubated in Mg2+ at pH 8.6 or in Zn2+ at pH 6.0. The heterorgeneous electron-transfer rate (kET) between the redox probe and the surface of a bare gold electrode was determined to be 5.7×10−3cm/s. For a B-DNA modified electrode, the kET through the monolayer was too slow to be measured. However, under M-DNA conditions, a kET of 1.5×10−3cm/s was reached. As well, the percent change in resistance to charge transfer, measured by IS, was used to illustrate the dependence of M-DNA formation on pH. This result is consistent with Zn2+ ions replacing the imino protons on thymine and guanine residues. The IrCl62-/3- redox couple was also effective in differentiating between single-stranded and double-stranded DNA during de-hybridization and rehybridization experiments.
The charge-transfer resistance, the redox capacitance and the diffusion coefficient of charge carriers at poly(o-phenylenediamine)-modified electrodes were determined by electrochemical impedance spectroscopy. Impedance results are interpreted in terms of the diffusion–migration transport of both electrons and protons through the film. Their coupled diffusion coefficients obtained at different potentials show a maximum near the formal potential of the polymer. This relationship between the oxidation level and the coupled diffusion coefficient indicates that the rate of charge transport within the film may be controlled by interchain electron-hopping. An exponential decrease in the coupled diffusion coefficient with increasing solution pH implies that the electron-hopping process is coupled with intermolecular proton exchange. Deprotonation of the polymer can result in a decrease in the homogeneous electron-transfer rate constant.
General expressions for the kinetics of a 1e, 1H+ surface electrochemical reaction (“square scheme”: two protonation and two electrochemical reactions) are established under the following conditions: all the participants are strongly adsorbed; in every case a Langmuir isotherm is obeyed; the protonation reactions are at equilibrium. When the symmetry coefficients of the electrochemical reactions are both equal to 0.5, the reaction behaves as a single monoelectronic process; an apparent electrochemical rate constant can be defined, whose pH-dependent value can become smaller than the actual rate constants by several orders of magnitude.
The impedance for an electrochemical reaction with an adsorbed intermediate is derived.
The behaviour of the impedance as displayed in the complex impedance plane is considered. No assumptions as to the order of the reaction or the surface concentration isotherm are necessary to predict the general behaviour.
The treatment is extended to cases where diffusion effects in the solution are important.
The kinetics of the p-benzoquinone/hydroquinone Q/QH2 couple on a platinum electrode are analysed on the basis of the theory presented earlier (E. Laviron, J. Electroanal. Chem., 146 (1983) 15) for the nine-member square scheme when the protonations are assumed to be at equilibrium, using experimental data from the literature. The square scheme is of the NN type. The Tafel plots and the variations of the experimental apparent rate constants between pH 0 and 7 are in good agreement with the theoretical predictions. The heterogeneous rate constants found for the elemental electrochemical steps are as follow: Q Q−, kh3=1/6×10−3 cm s−1; QH.QH−, kh5=0.11 cm s−1; QH+QH., kh2⋍160 cm s−1; kh4 for the reaction QH2+.QH2 is in the range 0.5–4 cm s−1. Between pH 0 and 7, the reaction sequence during the reduction is, for the most part, successively H+e−H+e−, e−H+H+e−, and e−H+e−H+ (reverse sequence during the oxidation).
Hemoglobin was successfully immobilized in cetylpyridinium bromide (CPB) film on a polyacrylamide (PAM) modified glassy carbon electrode (GC). Cyclic voltammetry showed a pair of well-defined and nearly reversible CV peaks at about −0.2165V vs SCE (pH=4.22), indicating the character of Hb heme Fe(II)/heme Fe(III) redox couple. The apparent standard potentials of hemoglobin in the CPB were linearly varied with pH in the range from 4.22 to 9.18 with a slope of −48.85mVpH−1, implying that one proton was accompanied with one electron transferred in the electrochemical reaction. The adsorption of Hb on the surface of PAM/GC electrode have been investigated by electrochemical impedance spectroscopy. The apparent standard potentials of hemoglobin were also studied through direct electrochemistry method as a function of temperature and the thermodynamic parameters (ΔSrc and ΔHrc) for the protein redox were calculated. Hemoglobin in the CPB exhibited catalytic activity for electrochemical reduction of NO.
Cyclic Voltammetry was employed to prepare fresh poly(o-aminophenol) (POAP) films and also to degrade them quantitatively. Then, the different behaviour of freshly prepared and degraded POAP films was studied by Steady-State Rotating Disc Electrode Voltammetry and Electrochemical Impedance Spectroscopy, when a mediated redox reaction is taking place at the polymer-solution interface. With regard to the last technique, the resulting experimental impedance diagrams of these POAP films, contacting the p-benzoquinone/hydroquinone redox couple, were interpreted on the basis of the homogeneous impedance model described in M.A. Vorotyntsev, C. Deslouis, M.M. Musiani, B. Tribollet, K. Aoki, Electrochimica Acta, 44 (1999) 2105-2115. The different dependencies of the charge transfer and charge transport parameters on the degree of degradation of the polymer (θRed,Max), were obtained. The different features of some of these dependencies (for instance, bulk electronic and ionic transport on θRed,Max) were explained in terms of the different mechanisms of electron and proton transport in this polymer. Also, similar behaviours of the transversal charge transfer resistance at the metal-polymer interface R m| f (obtained by impedance spectroscopy) and the lateral resistance ΔR/R along the electrode (obtained by Surface Resistance measurements), as functions of θRed,Max, were explained in terms of two different aspects of the electron motion at metal surfaces contacting a polymeric material. The results of this work allows one to demonstrate that after to subject POAP films to rough conditions, as in some of practical applications of POAP, ion and electron diffusion inside the film and rates of interfacial charge transfer processes, are strongly reduced. It should be expected that this deterioration process reduces drastically the efficiency of the material to act in practical applications.
A metastable pitting corrosion impedance investigation has been performed. The shape of the de current is connected with the shape of the impedance diagram. The corrosion rate inside an active pit is charge transfer controlled. The active surface area expansion is proportional to the double layer capacity changes. Changes of the electrolyte resistance inside the pit have been detected.
The synthesis, coordination and electrochemical properties of a novel 4,4′-bipyridinium bis benzo-15-crown-5 ligand are described whose group 1, 2 metal and ammonium cation redox-responsive behaviour is dependent upon cation induced conformational switching effects.
It is shown that the Warburg (diffusion) impedance is coupled to the charge transfer resistance, even to the extent that the sign of the Warburg impedance is determined by that of the charge transfer resistance. Experimental data obtained with the polarographic reduction of In (III) in aqueous NaSCN solution illustrate the existence of a negative Warburg impedance. The coupling between the diffusional and interfacial impedances (that is, between homogeneous mass transport and heterogeneous mass consumption or production) appears to be quite a general one, present with both redox and desad phenomena.Several graphical representations of the frequency-dependence of the electrode admittance or impedance are discussed, and the advantages of the complex capacitance plane are illustrated.
Electrochemical properties of self-assembled monolayers (SAMs) of a 1-aminoanthraquinone derivative (1-aminoAQ) were studied using electrochemical impedance spectroscopy (EIS) and cyclic voltammetry. The results of EIS studies at different temperatures and applied potentials established that SAMs of 1-ammoniumAQ undergo proton-coupled electron transfer (PCET) in 0.1 M H2SO4 with a rate constant of 7.4 s−1. Variable-temperature studies of the charge-transfer reaction gave a high activation barrier of 69 kJ·mol−1 for the 1-ammoniumAQ redox reaction, which is attributed to cleavage of a strong intramolecular hydrogen bond; this conclusion is supported by NMR and FTIR spectroscopic analyses, as well as DFT calculations. The 1-ammoniumAQ redox reactions were found to have a reorganizational energy term of 2.7 eV, consistent with large solvent reorganization and substantial nuclear rearrangement upon reduction.
A one-electron, one-proton (1e1H) redox couple based in an osmium aquo complex is attached to a self-assembled monolayer of alkanethiol on a gold electrode. The formal potential behavior of the Os aquo complex exhibits the expected pH dependence for a 1e1H system. The thermodynamic parameters are a formal potential of +0.30 V vs SCE for [Os(II/III)(H2O)], a formal potential of −0.11 V vs SCE for [Os(II/III)(OH)], a pKa of 2.4 for [Os(III)(H2O/OH)], and a pKa of 9.3 for [Os(II)(H2O/OH)]. A stepwise electron−proton transfer model, widely used in the electrochemical literature, predicts the effects of pH and overpotential on the kinetics of charge transfer for the 1e1H system. The kinetic behavior of the Os aquo complex deviates substantially from the predictions of the stepwise model. In particular, the standard rate constant and the transfer coefficient at zero overpotential are nearly independent of pH over the pH range at which proton-coupled electron transfer occurs, and Tafel plots are asymmetrical (steeper anodic branch) over most of the pH range examined (1−12). Possible double-layer effects caused by the presence of ionizable carboxylate moieties in the monolayer are ruled out by the absence of any pH effects on the formal potential and kinetics of an analogous Os chloride complex. A concerted electron−proton transfer mechanism is hypothesized to explain the observed kinetic behavior.
A theoretical study of coupled electron−proton transfer is presented for heterogeneous electron transfer to redox centers attached to electrodes. Proton transfer steps are assumed to be at equilibrium and the transfer coefficients are assumed to exhibit the potential dependence predicted by Marcus Density-of-States theory. Five cases are considered: 1e1H, 1e2H, 2e, 2e1H, and 2e2H. Procedures are given for calculating the apparent standard rate constant, the apparent transfer coefficient, and the path of electron transfer as a function of overpotential and pH. The behavior of these parameters are compared with a previous theoretical treatment in which the transfer coefficient for each electron transfer step was assumed to be 0.5 independent of overpotential. The predictions of the two treatments are qualitatively similar but quantitatively different. In particular, when the transfer coefficient depends on the electrode potential, apparent standard rate constants are smaller, asymmetrical Tafel plots appear in the 1e1H and 1e2H cases, and the path of electron transfer depends on potential as well as pH. Experimental evidence for the validity of the model is described.
Stable thin films made from amphiphilic polymer polyacrylamide (PAM) on pyrolytic graphite (PG) electrodes demonstrated direct electrochemistry for the incorporated redox protein hemoglobin (Hb). Cyclic voltammetry of Hb-PAM films showed a pair of well-defined and nearly reversible peaks for Hb Fe(III)/Fe(II) redox couple at about –0.27 V (vs. SCE) in pH 5.5 buffers. Compared to bare PG in Hb solutions, the electron transfer between Hb and PG electrodes was greatly facilitated in the microenvironment of PAM hydrogel films. Positions of Soret absorption band suggest that Hb keeps its secondary structure similar to its native state in the films at medium pH. The formal potential of the Hb Fe(III)/Fe(II) couple in PAM films shifted linearly between pH 4.5 and 11 with a slope of –47 mV pH–1, suggesting that one proton transfer is coupled to each electron transfer in the electrochemical reaction. Hb can act as an enzyme-like catalyst in PAM films as demonstrated by catalytic reduction of trichloroacetic acid (TCA) with significant decreases in the electrode potential required, showing the possible future application of the films for biosensors and biocatalysis.
A theoretical study of a two-step reversible electrochemical reaction OPR is made in thin layer linear potential sweep voltammetry when O, P and R can undergo one or several of the following irreversible chemical reactions: P→Z, R→Z, 2P→Z, 2R→Z, O+P→Z, P+R→Z and O+R→Z. The equations of the reduction and oxidation peaks are calculated. Criteria permitting the determination of the reaction involved are given. Values of the disproportionation constant K larger than 0.05 can be calculated from the experimental curves, and values of the rate constant of the chemical reaction k when 10−3<k (s−1)<1 for a first order reaction and 1<k (mol l−1 s−1)<104 for a second order reaction.
We report an extraction-reconstruction strategy for obtaining a novel voltammogram for a specific electrochemical process. While a conventional voltammogram is obtained from potentiodynamic currents, our voltammogram is obtained from a large body of potentiodynamic electrochemical impedance spectra by taking advantage of their highly resolvable power. As a proof of concept, construction of a mass transfer admittance voltammogram (MTAV) is demonstrated, which is made up of purely mass transfer admittances plotted vs. potential, excluding effects from other interfering electrochemical components. We also compare the MTAV with the AC voltammogram to show its enhanced accuracy and apply the novel voltammetry to clearly determine the number of electrons transferred and diffusion coefficients, which may vary depending on experimental conditions, for a complex electrochemical reaction.
Theoretical principles for determination of instantaneous impedance spectra were formulated. Coupling of the pseudo-white noise and short-time Fourier transformation methods allows determination of impedance spectra changes as the function of time. The theoretical principles of the new measurement method indicate the possibility of conducting impedance investigations of non-stationary processes. The frequency resolution and time selection of the total time–frequency analysis of impedance spectra depend on the choice of the size of the Gaussian window.
Continuous STFT transforms of a sinusoidal perturbation signal and current have been found for the first order electrode reaction. Electrode impedance has been determined in the joint time–frequency domain. Measurements of the Cd(II) reduction reaction have been performed on a dropping mercury electrode as a function of time. A possibility of instantaneous impedance spectra generation has been presented. Time characteristics of charge transfer resistance, Warburg coefficient and double layer capacitance has been described.
This short review highlights the mechanisms involved in electrochemically sensing cationic, anionic and neutral guest species by redox-active receptors and is an update to a previously published review article (P.D. Beer, P.A. Gale, Z. Chen, Adv. Phys. Org. Chem. 31 (1998) 1). Mechanisms of redox–complexation coupling are discussed together with recent examples of redox-responsive molecular receptors from the literature that illustrate them.
Continuous short time Fourier transformation transforms of the sinusoidal perturbation signal and current have been found for the first order electrode reaction. The electrode impedance has been determined in the joint time–frequency domain. Measurements of the Cd(II) reduction reaction have been performed on a hanging mercury electrode (HDME) as a function of potential. The possibility of instantaneous impedance spectra generation has been presented. The dependence of the charge transfer resistance, Warburg coefficient and double layer capacitance on potential has been described.
Iron(III) protoporphyrin IX (Fe(III)PP) and iron(III) hematoporphyrin (Fe(III)HP) were selectively and covalently attached to dimercaptoalkane-modified gold electrodes. Reaction of their vinyl or hydroxyethyl groups with the surface-immobilized thiols produced thioether linkages, reminiscent of the heme macrocycle attachment in c-type cytochromes. Cyclic voltammetry revealed reversible electrochemistry of self-assembled monolayers (SAMs) of FePPs and FeHPs on the thiol-modified gold substrates. The surface coverage estimated from the charges transferred corresponds to 30% of a monolayer. The heterogeneous rate constant of electron transfer between the Fe(III)PPs and the gold substrate decreases exponentially with the length of the spacer, demonstrating a value of 1.0 A-1 for the tunneling length coefficient, beta. At pH 8, a linear increase of the formal redox potential (Eo`) with the length of the linker was also observed. This suggests that in the film, there is a close contact between the porphyrins and the alkane SAM: the Eo` is affected by the drop of the electrostatic potential from the electrode to the surface of the alkane SAM, and also that there is a strong ion pairing of the Fe(III)PPs in the film with the anions of the solution. The Eo` of Fe(III)PPs in the SAM shows a strong and complex dependency on the pH of the solution, explained by variations in the coordination of the iron, involving hydroxyl ions, water, and eventually dioxygen molecules. Interactions of the iron with either functional groups present at the surface of the substrate or with the propionate groups attached to the porphyrin ring, do not appear to be involved in the electronproton transfer coupling mechanisms.
Room temperature ionic liquid N-butylpyridinium hexafluorophosphate (BPPF6) was used as a binder to construct a new carbon ionic liquid electrode (CILE), which exhibited enhanced electrochemical behavior as compared with the traditional carbon paste electrode with paraffin. By using the CILE as the basal electrode, hemoglobin (Hb) was immobilized on the surface of the CILE with nano-CaCO3 and Nafion film step by step. The Hb molecule in the film kept its native structure and showed good electrochemical behavior. In pH 7.0 Britton-Robinson (B-R) buffer solution, a pair of well-defined, quasi-reversible cyclic voltammetric peaks appeared with cathodic and anodic peak potentials located at -0.444 and -0.285 V (vs SCE), respectively, and the formal potential (E degrees') was at -0.365 V, which was the characteristic of Hb Fe(III)/Fe(II) redox couples. The formal potential of Hb shifted linearly to the increase of buffer pH with a slope of -50.6 mV pH-1, indicating that one electron transferred was accompanied with one proton transportation. Ultraviolet-visible (UV-vis) and Fourier transform infrared (FT-IR) spectroscopy studies showed that Hb immobilized in the Nafion/nano-CaCO3 film still remained its native arrangement. The Hb modified electrode showed an excellent electrocatalytic behavior to the reduction of H2O2, trichloroacetic acid (TCA), and NaNO2.
Proton-coupled electron transfers (PCETs) are omnipresent in natural and artificial chemical processes. Given the contemporary challenges associated with energy conversion, pollution abatement, and the development of high-performance sensors, a greater understanding of the mechanisms that underlie the practical efficiency of PCETs is a timely research topic. In contrast to hydrogen-atom transfers, proton and electron transfers involve different centers in PCET reactions. The reaction may go through an electron- or proton-transfer intermediate, giving rise to the electron-proton transfer (EPT) and the proton-electron transfer (PET) pathways. When the proton and electron transfers are concerted (the CPET pathway), the high-energy intermediates of the stepwise pathways are bypassed, although this thermodynamic benefit may have a kinetic cost. The primary task of kinetics-based mechanism analysis is therefore to distinguish the three pathways, quantifying the factors that govern the competition between them, which requires modeling of CPET reactivity. CPET models of varying sophistication have appeared, but the large number of parameters involved and the uncertainty of the quantum chemical calculations they may have to resort to make experimental confrontation and inspiration a necessary component of model testing and refinement. Electrochemical PCETs are worthy of particular attention, if only because most applications in which PCET mechanisms are operative involve collection or injection of electricity through electrodes. More fundamentally, changing the electrode potential is an easy and continuous means of varying the driving force of the reaction, whereas the current flowing through the electrode is a straightforward measure of its rate. Consequently, the current-potential response in nondestructive techniques (such as cyclic voltammetry) can be read as an activation-driving force relationship, provided the contribution of diffusion has been taken into account. Intrinsic properties (properties at zero driving force) are consequently a natural outcome of the electrochemical approach. In this Account, we begin by examining the modeling of CPET reactions and then describe illustrating experimental examples inspired by two biological systems, photosystem II and superoxide dismutase. One series of studies examined the oxidation of phenols with, as proton acceptor, either an attached nitrogen base or water (in water as solvent). Another addressed interconversion of aquo-hydroxo-oxo couples of transition metal complexes, using osmium complexes as prototypes. Finally, the reduction of superoxide ion, which is closely related to its dismutation, allowed the observation and rationalization of the remarkable properties of water as a proton donor. Water is also an exceptional proton acceptor in the oxidation of phenols, requiring very small reorganization energies, both in the electrochemical and homogeneous cases. These varied examples reveal general features of PCET reactions that may serve as guidelines for future studies, suggesting that research emphasis might be profitably directed toward new biological systems on the one hand and on the role of hydrogen bonding and hydrogen-bonded environments (such as water or proteins) on the other.
We describe a novel technique for measuring electrochemical impedance, in which the electrode potential is ramped to a desired bias potential and a small potential step is applied to the working electrode after a short time delay. Fourier transform of the first derivative of the current signal thus obtained provides ac currents in the frequency domain, which allows the computation of impedances of the electrode/electrolyte interface in the whole frequency range. A home-built data acquisition system for these measurements and the results obtained therefrom were used for the measurements. The advantage of the technique includes an extremely short time of less than 1 ms for impedance measurements in the whole frequency region while equilibrium conditions of the electrochemical system are being maintained before and after the measurements, among many others. This technique is expected to revolutionize electrochemical measurements and to find important applications such as in situ measurements during battery cycling, corrosion testing, and other electrochemical experiments.
According to current estimates, the photosynthetic water oxidase functions with a quite restricted driving force. This emphasizes the importance of the catalytic mechanisms in this enzyme. The general problem of coupling electron and proton transfer is discussed from this viewpoint and it is argued that 'weak coupling' is preferable to 'strong coupling'. Weak coupling can be achieved by facilitating deprotonation either before (proton-first path) or after (electron-first path) the oxidation step. The proton-first path is probably relevant to the oxidation of tyrosine Y(Z) by P-680. Histidine D1-190 is believed to play a key role as a proton acceptor facilitating Y(Z) deprotonation. The pK(a) of an efficient proton acceptor is submitted to conflicting requirements, since a high pK(a) favors proton transfer from the donor, but also from the medium. H-bonding between Y(Z) and His, together with the Coulombic interaction between negative tyrosinate and positive imidazolium, are suggested to play a decisive role in alleviating these constraints. Current data and concepts on the coupling of electron and proton transfer in the water oxidase are discussed.
This Account presents a theoretical formulation for proton-coupled electron transfer reactions. The active electrons and transferring protons are treated quantum mechanically, and the free energy surfaces are obtained as functions of collective solvent coordinates corresponding to the proton and electron transfer reactions. Rate expressions have been derived in the relevant limits, and methodology for including the dynamical effects of the solvent and protein has been developed. This theoretical framework allows predictions of rates, mechanisms, and kinetic isotope effects for proton-coupled electron transfer reactions.
The reaction center Photosystem II is a key component of the most successful solar energy converting machinery on earth: the oxygenic photosynthesis. Photosystem II uses light to drive the reduction of plastoquinone and the oxidation of water. Water-oxidation is catalyzed by a manganese cluster and gives the organism an abundant source of electrons. The principles of photosynthesis have inspired chemists to mimic these reactions in artificial molecular assemblies. Synthetic light-harvesting antennae and light-induced charge separation systems have been demonstrated by several groups. More recently, there has been an increasing effort to mimic Photosystem II by coupling light-driven charge separation to water oxidation, catalyzed by synthetic manganese complexes.
This minireview addresses questions on the mechanism of oxidative water cleavage with special emphasis on the coupling of electron (ET) and proton transfer (PT) of each individual redox step of the reaction sequence and on the mode of O-O bond formation. The following topics are discussed: (1) the multiphasic kinetics of Y(Z)(ox) formation by P680(+*) originate from three different types of rate limitations: (i) nonadiabatic electron transfer for the "fast" ns reaction, (ii) local "dielectric" relaxation for the "slow" ns reaction, and (iii) "large-scale" proton shift for the micros kinetics; (2) the ET/PT-coupling mode of the individual redox transitions within the water oxidizing complex (WOC) driven by Y(Z)(ox) is assumed to depend on the redox state S(i): the oxidation steps of S(0) and S(1) comprise separate ET and PT pathways while those of S(2) and S(3) take place via proton-coupled electron transfer (PCET) analogous to Jerry Babcock's hydrogen atom abstractor model [Biochim. Biophys. Acta, 1458 (2000) 199]; (3) S(3) is postulated to be a multistate redox level of the WOC with fast dynamic equilibria of both redox isomerism and proton tautomerism. The primary event in the essential O-O bond formation is the population of a state S(3)(P) characterized by an electronic configuration and nuclear geometry that corresponds with a complexed hydrogen peroxide; (4) the peroxidic type S(3)(P) is the entatic state for formation of complexed molecular oxygen through S(3) oxidation by Y(Z)(ox); and (5) the protein matrix itself is proposed to exert catalytic activity by functioning as "PCET director". The WOC is envisaged as a supermolecule that is especially tailored for oxidative water cleavage and acts as a molecular machine.
Proton-coupled electron transfer (PCET) reactions involve the concerted transfer of an electron and a proton. Such reactions play an important role in many areas of chemistry and biology. Concerted PCET is thermochemically more favorable than the first step in competing consecutive processes involving stepwise electron transfer (ET) and proton transfer (PT), often by >=1 eV. PCET reactions of the form X-H + Y X + H-Y can be termed hydrogen atom transfer (HAT). Another PCET class involves outersphere electron transfer concerted with deprotonation by another reagent, Y+ + XH-B Y + X-HB+. Many PCET/HAT rate constants are predicted well by the Marcus cross relation. The cross-relation calculation uses rate constants for self-exchange reactions to provide information on intrinsic barriers. Intrinsic barriers for PCET can be comparable to or larger than those for ET. These properties are discussed in light of recent theoretical treatments of PCET.
In aerobic organisms, cellular respiration involves electron transfer to oxygen through a series of membrane-bound protein complexes. The process maintains a transmembrane electrochemical proton gradient that is used, for example, in the synthesis of ATP. In mitochondria and many bacteria, the last enzyme complex in the electron transfer chain is cytochrome c oxidase (CytcO), which catalyses the four-electron reduction of O2 to H2O using electrons delivered by a water-soluble donor, cytochrome c. The electron transfer through CytcO, accompanied by proton uptake to form H2O drives the physical movement (pumping) of four protons across the membrane per reduced O2. So far, the molecular mechanism of such proton pumping driven by electron transfer has not been determined in any biological system. Here we show that proton pumping in CytcO is mechanistically coupled to proton transfer to O2 at the catalytic site, rather than to internal electron transfer. This scenario suggests a principle by which redox-driven proton pumps might operate and puts considerable constraints on possible molecular mechanisms by which CytcO translocates protons.
The goal of artificial photosynthesis is to use the energy of the sun to make high-energy chemicals for energy production. One approach, described here, is to use light absorption and excited-state electron transfer to create oxidative and reductive equivalents for driving relevant fuel-forming half-reactions such as the oxidation of water to O2 and its reduction to H2. In this "integrated modular assembly" approach, separate components for light absorption, energy transfer, and long-range electron transfer by use of free-energy gradients are integrated with oxidative and reductive catalysts into single molecular assemblies or on separate electrodes in photelectrochemical cells. Derivatized porphyrins and metalloporphyrins and metal polypyridyl complexes have been most commonly used in these assemblies, with the latter the focus of the current account. The underlying physical principles--light absorption, energy transfer, radiative and nonradiative excited-state decay, electron transfer, proton-coupled electron transfer, and catalysis--are outlined with an eye toward their roles in molecular assemblies for energy conversion. Synthetic approaches based on sequential covalent bond formation, derivatization of preformed polymers, and stepwise polypeptide synthesis have been used to prepare molecular assemblies. A higher level hierarchial "assembly of assemblies" strategy is required for a working device, and progress has been made for metal polypyridyl complex assemblies based on sol-gels, electropolymerized thin films, and chemical adsorption to thin films of metal oxide nanoparticles.
A new attempt to obtain electron transfer kinetic parameters at an electrified electrode/electrolyte interface using Fourier transform electrochemical impedance spectroscopic (FTEIS) analyses of small potential step chronoamperometric currents is presented. The kinetic parameters thus obtained allowed mass transport free voltammograms to be constructed in an overpotential region, where the diffusion limits the electron transfer reaction, using the Butler-Volmer (B-V) relation. The B-V voltammograms clearly distinguish electrode reactions that are not much different in their electron transfer kinetic parameters, thus showing very similar normal linear sweep voltammetric (SCV) behaviors. Electrochemical reduction of p-benzoquinone, which displays nearly the same SCV responses at a gold electrode regardless whether the electrode is covered by a thiolated beta-cyclodextrin self-assembled monolayer, was taken as an example for the demonstration. The results show that the two voltametrically similar systems display very different electron transfer characteristics.
Proton-coupled electron-transfer reactions are central to enzymatic mechanism in many proteins. In several enzymes, essential electron-transfer reactions involve oxidation and reduction of tyrosine side chains. For these redox-active tyrosines, proton transfer couples with electron transfer, because the phenolic pKA of the tyrosine is altered by changes in the tyrosine redox state. To develop an experimentally tractable peptide system in which the effect of proton and electron coupling can be investigated, we have designed a novel amino acid sequence that contains one tyrosine residue. The tyrosine can be oxidized by ultraviolet photolysis or electrochemical methods and has a potential cross-strand interaction with a histidine residue. NMR spectroscopy shows that the peptide forms a beta-hairpin with several interstrand dipolar contacts between the histidine and tyrosine side chains. The effect of the cross-strand interaction was probed by electron paramagnetic resonance and electrochemistry. The data are consistent with an increase in histidine pKA when the tyrosine is oxidized; the effect of this thermodynamic coupling is to increase tyrosyl radical yield at low pH. The coupling mechanism is attributed to an interstrand pi-cation interaction, which stabilizes the tyrosyl radical. A similar interaction between histidine and tyrosine in enzymes provides a regulatory mechanism for enzymatic electron-transfer reactions.
The molecular mechanism of the monooxygenase (phenolase) activity of type 3 copper proteins has been examined in detail both in the model systems and in the enzymatic systems. The reaction of a side-on peroxo dicopper(II) model compound ( A) and neutral phenols proceeds via a proton-coupled electron-transfer (PCET) mechanism to generate phenoxyl radical species, which collapse each other to give the corresponding C-C coupling dimer products. In this reaction, a bis(mu-oxo)dicopper(III) complex ( B) generated by O-O bond homolysis of A is suggested to be a real active species. On the other hand, the reaction of lithium phenolates (deprotonated form of phenols) with the same side-on peroxo dicopper(II) complex proceeds via an electrophilic aromatic substitution mechanism to give the oxygenated products (catechols). The mechanistic difference between these two systems has been discussed on the basis of the Marcus theory of electron transfer and Hammett analysis. Mechanistic details of the monooxygenase activity of tyrosinase have also been examined using a simplified enzymatic reaction system to demonstrate that the enzymatic reaction mechanism is virtually the same as that of the model reaction, that is, an electrophilic aromatic substitution mechanism. In addition, the monooxygenase activity of the oxygen carrier protein hemocyanin has been explored for the first time by employing urea as an additive in the reaction system. In this case as well, the ortho-hydroxylation of phenols to catechols has been demonstrated to involve the same ionic mechanism.
All higher life forms use oxygen and respiration as their primary energy source. The oxygen comes from water by solar-energy conversion in photosynthetic membranes. In green plants, light absorption in photosystem II (PSII) drives electron-transfer activation of the oxygen-evolving complex (OEC). The mechanism of water oxidation by the OEC has long been a subject of great interest to biologists and chemists. With the availability of new molecular-level protein structures from X-ray crystallography and EXAFS, as well as the accumulated results from numerous experiments and theoretical studies, it is possible to suggest how water may be oxidized at the OEC. An integrated sequence of light-driven reactions that exploit coupled electron-proton transfer (EPT) could be the key to water oxidation. When these reactions are combined with long-range proton transfer (by sequential local proton transfers), it may be possible to view the OEC as an intricate structure that is "wired for protons".
Some of the important conclusions reached in this analysis of PCET are summarized below. The sections in which they are discussed are also cited. (1) PCET describes reactions in which there is a change in both electron and proton content between reactants and products. It originates from the influence of changes in electron content on acid-base properties and provides a molecular-level basis for energy transduction between proton transfer and electron transfer (section 1). (2) Coupled electron-proton transfer or EPT is defined as an elementary step in which electrons and protons transfer from different orbitals on the donor to different orbitals on the acceptor. There is (usually) a clear distinction between EPT and H-atom transfer (HAT) or hydride transfer, in which the transferring electrons and proton come from the same bond. Hybrid mechanisms exist in which the elementary steps are different for the reaction partners (sections 5.1 and 5.2). (3) EPT pathways such as PhO*/PhOH exchange have much in common with HAT pathways in that electronic coupling is significant, comparable to the reorganization energy with HDA ∼ λ. (4) Multiple-Site Electron-Proton Transfer (MS-EPT) is an elementary step in which an electron-proton donor transfers electrons and protons to different acceptors, or an electron-proton acceptor accepts electrons and protons from different donors. It exploits the long-range nature of electron transfer while providing for the short-range nature of proton transfer (section 5.1). (5) A variety of EPT pathways exist, creating a taxonomy based on what is transferred, e.g., le-12H+ WEPT (section 5.1). (6) PCET achieves "redox potential leveling" between sequential couples and the buildup of multiple redox equivalents, which is of importance in multielectron catalysis (section 2. 1). (7) There are many examples of PCET and pH-dependent redox behavior in metal complexes, in organic and biological molecules, in excited states, and on surfaces (section 2). (8) Changes in pH can be used to induce electron transfer through films and over long distances in molecules. Changes in pH, induced by local electron transfer, create pH gradients and a driving force for long-range proton transfer in Photosysem 11 and through other biological membranes (sections 3 and 7.2). (9) In EPT, simultaneous transfer of electrons and protons occurs on time scales short compared to the periods of coupled vibrations and solvent modes. A theory for EPT has been developed which rationalizes rate constants and activation barriers, includes temperature- and driving force (ΔG)-dependences implicitly, and explains kinetic isotope effects. The distance-dependence of EPT is dominated by the short range nature of proton transfer, with electron transfer being far less demanding (sections 4.2 and 5). (10) Changes in external pH do not affect an EPT elementary step. Solvent molecules or buffer components can act as proton donor acceptors, but individual H2O molecules are neither good bases (pKa(H3)O+) = - 1.74) nor good acids (pK(H2O) = 15.7) (section 5.5.3). (11) There are many examples of mechanisms in chemistry, in biology, on surfaces, and in the gas phase which utilize EPT (sections 6 and 7). (12) PCET and EPT play critical roles in the oxygen evolving complex (OEC) of Photosystem Il and other biological reactions by decreasing driving force and avoiding high-energy intermediates (section 7.2).