Frumkin Effect Research Articles

Double-Layer Inhibition of Peroxydisulfate Reduction at Mercury Ultramicroelectrodes. A Quantitative Analysis of the Frumkin Effect Including Molecular Transport and Long-Range Electron Transfer

The electrical double layer (EDL) can lead to unexpected voltammetric phenomena. A notable example is the Frumkin effect, observed for the reduction of peroxydisulfate (S2O82–). In the absence of excess supporting electrolyte, the rate of S2O82– reduction decreases as the cathodic overpotential is increased, contrary to expectations for faradaic electron-transfer processes. Here, we report a demonstration of the Frumkin effect for S2O82– reduction at Hg ultramicroelectrodes, revealing steady-state voltammetry behavior consistent with prior observations at rotating disk electrodes. A finite element model is used to simulate the effect of the EDL on S2O82– reduction in the presence and absence of excess supporting electrolyte (K2SO4). Semiquantitative agreement between experimental and simulated voltammograms is obtained, including capturing the decrease in current for S2O82– reduction with increasing overpotential. We show that S2O82– migration within the EDL, at electrode potentials negative of the potential of zero charge, is the primary process responsible for the observed decrease in current with increasing driving force. These combined experiments and finite element simulations represent the first quantitative description of the Frumkin effect with rigorous inclusion of the EDL, migrational and diffusional mass-transport, and long-range electron transfer kinetics.

フルムキン効果を表現する数式に関する一考察

Formula to express the Frumkin effect is reconsidered from the viewpoint of easiness of understanding its physical meaning. Although it is usually expressed based on the potential difference, here it is expressed based on the concentration changes. There are two aims of this formula transformation: One is to treat the Red / Ox species equally in the expression. The other is to extend the applicability of the formula to the effects of concentration changes caused by other than pure electrostatic effects.

Tafel Slope Analyses for Homogeneous Catalytic Reactions

Tafel analysis of electrocatalysts is essential in their characterization. This paper analyzes the application of Tafel-like analysis to the four-electron nonelectrochemical oxidation of water by the stoichiometric homogeneous 1-electron oxidant [Ru(bpy)3]3+ to dioxygen catalyzed by homogeneous catalysts, [Ru4O4(OH)2(H2O)4(γ-SiW10O36)2]10− (Ru4POM) and [Co4(H2O)2(PW9O34)2]10– (Co4POM). These complexes have slow electron exchange rates with electrodes due to the Frumkin effect, which precludes the use of known electrochemical methods to obtain Tafel plots at ionic strengths lower than 0.5 M. The application of an electron transfer catalyst, [Ru(bpy)3]3+/2+, increases the rates between the Ru4POM and electrode, but a traditional Tafel analysis of such a complex system is precluded due to a lack of appropriate theoretical models for 4-electron processes. Here, we develop a theoretical framework and experimental procedures for a Tafel-like analysis of Ru4POM and Co4POM, using a stoichiometric molecular oxidant [Ru(bpy)3]3+. The dependence of turnover frequency (TOF) as a function of electrochemical solution potential created by the [Ru(bpy)3]3+/[Ru(bpy)3]2+ redox couple (an analog of the Tafel plot) was obtained from kinetics data and interpreted based on the suggested reaction mechanism.

Dynamic orientation control of bimolecular electron transfer at charged micelle surfaces.

Visible light excitation of the neutral complex [RuII(phen)2(bps)]0 (phen = 1,10-phenanthroline, bps = 4,7-biphenylsulfonate-1,10-phenanthroline) results in the formation of a triplet metal-to-ligand charge transfer excited state with a lifetime, τo, of 4.6 µs, where the promoted electron is localized on the bps ligand, 3*[RuIII(phen)2(bps•-)]0. The complex is dynamically quenched by di-n-heptyl-viologen, C7C7V2+, in solution and when the acceptor is embedded into negatively charged and neutral micelles. Addition of NaCl to solutions containing C7C7V2+ bound to negatively charged dodecyl sulfate sodium dodecyl sulfate micelles results in a monotonic increase in the quenching rate constant from kq = 6.0 × 107 to 1.7 × 109 M-1 s-1. In contrast, kq was independent of [NaCl] and diffusion limited in water and neutral micellar solution. Activated rate constants, kact, revealed that electron transfer was slowed by a factor of 450 when occurring in negatively charged micelle solution relative to neutral octaethylene glycol monododecyl ether (C12E8) micelles. In the 3*[RuIII(phen)2(bps•-)]0 excited state, the bps ligand is oriented away from the anionic micelle surface potential, -141 ≤ ψ ≤ -67 mV, due to a Frumkin effect operative in the deceleration of kact. Frumkin corrected rate constants were within a factor of three of those measured in C12E8 solution. Distance-dependent reorganization energies resulting from the orientation vary from 0.47 eV to 0.35 eV, while electronic coupling decreases by a factor of 10. The collective data show that orientation control over bimolecular rate constants in micellar solution can be achieved by screening micellar surface charges.

Theory for Influence of the Metal Electrolyte Interface on Heterogeneous Electron Transfer Rate Constant: Fractional Electron Transferred Transition State Approach

We develop a theory for outer sphere heterogeneous electron transfer (ET) rate constant (k0) and exchange current density (i0). The model hypothesizes that the transition state is attained by alignment of Fermi and reactant energy levels through exchange of fractional electronic charge (δ≠). This approach accounts the contributions from: (i) work function and Fermi energy of metal, (ii) solvent polarity and size, (iii) electronic nature and size of electroactive species, and (iv) outer Helmholtz plane (OHP) potential-dependent composition. At the outset, we develop a model for the potential ϕ1 at the inner Helmholtz plane accounting the influence of electronic and inner dipolar layer screening on the metal. The equation for ϕ1 is used to obtain the potential ϕ2 at OHP through a modified Gouy–Chapman–Stern approach. The concentration of electroactive species at OHP (ciOHP) under the influence of the Frumkin effect is obtained by substituting ϕ2 in Kornyshev’s packing density restriction model. Our theory o...

PEMFCs multiscale modeling: Determination of overpotential with description of electron transfer in cathodic EDL at different O2 concentrations

The effect of the formation of the electrical double layer (EDL) as a function of O2 concentrations in Pt/H2O interface in a proton-exchange membrane fuel cell (PEMFC) is analyzed in this work. The overpotential associated with the existence of the EDL is calculated at typical fuel cell O2 concentrations by using molecular dynamics (MD). The calculated overpotentials are in the range of −8.865 × 10−6 – 0.0086V for oxygen molar fractions in the cathode between 0 and 0.1273. These overpotential values are included in the ORR kinetic equations of a multiscale model for PEMFCs developed in a previous work to estimate the global electroosmotic drag coefficient and compare it with experimental data from literature. It was found an improvement of the accuracy of the model, at air fed hydration levels of 50% and 70% in the cathode, if the overpotential calculation is carried out considering the electron transfer in the entire interface, not only in the outer Helmholtz plane (OHP) thus, modifying the Frumkin effect calculation.

Analysis of functional genomes from metagenomes: Revealing the accelerated electron transfer in microbial fuel cell with rhamnolipid addition

Extracellular electron transfer is the predominant electricity generation process in microbial fuel cells (MFCs). Our pervious study have proved that the anodic adsorption of rhamnolipid resulted in the Frumkin effect, which enhanced anodic microorganism attachment and accelerated anodic electron transfer. In this study, an in-depth research on the influence of rhamnolipid on functional genes of anodic biofilms metagenomes was carried out to explain its mechanism at the gene level. The result showed that the composition and distribution of functional genes in each dominant genus were different. The category of signal transduction mechanisms was the dominant function category in exoelectrogens, and its relative abundance in the metagenome significantly increased from 4.56 to 5.86% from rhamnolipid addition. Additionally, the metabolic pathway and electron flow analysis revealed that electron flows tend to choose direct electron transfer in the presence of rhamnolipids, and resulting in the increase of Coulombic efficiency from 19.10±0.79% to 27.39±1.07%.

(Invited) Nanogap Voltammetry of Clean Surface of Electron-Beam-Deposited Carbon

Clean surfaces of conducting carbon materials are highly demanded for fundamental and applied electrochemistry to mechanistically understand and practically utilize their intrinsic reactivity. In this presentation, we will discuss about the nanoelectrochemical characterization of clean carbon surfaces to gain novel insights into heterogeneous electron-transfer (ET) mechanism with broad implications beyond carbon electrochemistry. Electron-beam deposited carbon (eC) is formed in high vacuum (<6 µtorr) and protected from adventitious contamination by a washable KCl layer deposited without breaking vacuum. Fast ET kinetics of exceedingly flat, clean eC surfaces is reliably measured in ultrapure water using nanogap voltammetry based on scanning electrochemical microscopy and compared quantitatively with Marcus and Frumkin theories. An outer-sphere ET mechanism, which is typically only presumed, is evidenced experimentally for (ferrocenylmethyl)trimethylammonium and tris(1,10-phenanthroline)cobalt(II) (Co(phen)3 2+) by excluding an inner-sphere mechanism. Indeed, the oxidation of Co(phen)3 2+ agrees unprecedentedly well with Marcus theory of adiabatic outer-sphere kinetics in comparison to any redox couple on carbon or metal electrodes reported previously. The coupled reduction of Co(phen)3 3+ deviates from Marcus theory to reveal a unique double-layer effect caused by the adsorption of a redox molecule itself, i.e. Co(phen)3 2+, which contrasts to the Frumkin effect based on the adsorption of inert electrolytes. Remarkably, the Ru(NH3)6 3+/2+ couple exceeds adiabatic limits not only at eC, but also at other carbons and metals, which we attribute to faster inner-sphere ET of adsorbed forms of this couple. In contrast, an inner-sphere pathway is not mediated by the adsorbed Fe(CN)6 3–/4– couple, which dramatically self-decelerates the outer-sphere pathway through a double-layer effect.

Controlling the Interfacial Environment in the Electrosynthesis of MnOx Nanostructures for High-Performance Oxygen Reduction/Evolution Electrocatalysis.

High-performance, nonprecious metal bifunctional electrocatalysts for the oxygen reduction and evolution reactions (ORR and OER, respectively) are of great importance for rechargeable metal-air batteries and regenerative fuel cells. A comprehensive study based on statistical design of experiments is presented to investigate and optimize the surfactant-assisted structure and the resultant bifunctional ORR/OER activity of anodically deposited manganese oxide (MnOx) catalysts. Three classes of surfactants are studied: anionic (sodium dodecyl sulfate, SDS), non-ionic (t-octylphenoxypolyethoxyethanol, Triton X-100), and cationic (cetyltrimethylammonium bromide, CTAB). The adsorption of surfactants has two main effects: increased deposition current density due to higher Mn2+ and Mn3+ concentrations at the outer Helmholtz plane (Frumkin effect on the electrodeposition kinetics) and templating of the MnOx nanostructure. CTAB produces MnOx with nanoneedle (1D) morphology, whereas nanospherical- and nanopetal-like morphologies are obtained with SDS and Triton, respectively. The bifunctional performance is assessed based on three criteria: OER/ORR onset potential window (defined at 2 and -2 mA cm-2) and separately the ORR and OER mass activities. The best compromise among these three criteria is obtained either with Triton X-100 deposited catalyst composed of MnOOH and Mn3O4 or SDS deposited catalyst containing a combination of α- and β-MnO2, MnOOH, and Mn3O4.The interaction effects among the deposition variables (surfactant type and concentration, anode potential, Mn2+ concentration, and temperature) reveal the optimal strategy for high-activity bifunctional MnOx catalyst synthesis. Mass activities for OER and ORR up to 49 A g-1 (at 1556 mVRHE) and -1.36 A g-1 (at 656 mVRHE) are obtained, respectively.

Accelerating anodic biofilms formation and electron transfer in microbial fuel cells: Role of anionic biosurfactants and mechanism

Anodic electron transfer is the predominant electricity generation process of MFCs. To accelerate anodic biofilms formation and electron transfer, 40mg/L, 80mg/L, and 120mg/L of rhamnolipid biosurfactants were added to the anolyte, resulting in an increased abiotic capacitance from 15.12F/m2 (control) to 16.54F/m2, 18.00F/m2, and 19.39F/m2, respectively. Anodic biofilm formation was facilitated after dosing 40mg/L of rhamnolipids on the 7th day after inoculation, resulting in an increased anodic biofilm coverage from 0.43% to 42.51%, and an increased maximum power density from 6.92±1.18W/m3 to 9.93±0.88W/m3. Furthermore, the adsorption of rhamnolipids on the anode caused the Frumkin effect, leading to a decrease of equilibrium potential from −0.43V to −0.56V, and an increase of exchange current density from 5.09×10−3A/m2 to 8.72×10−3A/m2. However, electron transfer was blocked when the rhamnolipid concentration was further increased to 80mg/L, and 120mg/L. Analysis of the anodic bacterial communities revealed that rhamnolipids facilitated the enrichment of exoelectrogen, increasing the total proportion from 65% to 81%. Additionally, biosurfactants were found to have significant impacts on the composition of exoelectrogens.

Influence of the diffuse double layer on steady-state voltammetry

The influence of the diffuse double layer on the passage of Faradaic current is investigated for steady-state voltammetry. Both mathematical analysis and numerical solution with the Nernst–Planck–Poisson equations are employed. We report a comprehensive study of the effects of reactant charge, electrode charge, electrode size and quantity of supporting electrolyte. Both infinite and finite electrode kinetics are investigated, as well as distance-dependent electron transfer (tunnelling) and activity effects. Certain combinations of reactant and electrode charge are shown to profoundly alter the predicted current by exclusion of the reactant (Levich effect) or deceleration of apparent kinetics (Frumkin effect), although tunnelling can overcome both effects by moving the plane of electron transfer. The structurally altered double layer at nanoelectrodes is shown to either increase or decrease the predicted current depending on the electrode charge, due to an unscreened electric field.

PH-dependent voltammetric responses of microdisc gold electrodes modified with thiotic acid self-assembled monolayers

This paper describes the pH dependence of cyclic voltammograms (CVs) of hexacyanoferrate(III) on microdisc gold electrodes (25 μm in diameter) modified with thioctic acid (TA) monolayers. The use of a microdisc electrode made it possible to directly compare the experimental CV data with theoretical simulation, and thus to discuss the main factors affecting voltammetric responses in ion-channel sensors (ICSs) based on electrostatic repulsion. Whereas unmodified gold microdisc electrodes gave very similar sigmoidal CVs at pH 2.5–7.5, TA-modified microdisc electrodes exhibited gradual decrease in the reduction current of from pH 2.5 to 5.5 due to the deprotonation of the terminal –COOH groups of TA monolayers. The experimental pH dependence was consistent with theoretical quasi-reversible steady-state voltammograms reflecting the Frumkin effect, suggesting that the changes in the electrode reaction kinetics affected by electrode surface charge would be one of the major factors that offer voltammetric response in such ICSs.

Kinetics of Heterogeneous Electron Transfer Reactions at the Externally Polarized Water/o-Nitrophenyl Octyl Ether Interface

The heterogeneous electron transfer (ET) reactions between dimethylferrocenium (DiMFc+) or ferrocenium (Fc+) produced in situ in o-nitrophenyl octyl ether (NPOE) and hexacyanoferrite [Fe(CN)64−] in aqueous phase have been investigated by scanning electrochemical microscopy (SECM). The potential difference across the water/NPOE (W/NPOE) interface was controlled externally to maintain a certain driving force for the ET reactions. The standard kinetic rate constants (k120) for the above bimolecular ET reactions were measured to be 0.075 and 0.050 cm s−1 M−1 when DiMFc and Fc were employed as the respective organic reactants. The transfer coefficients (α) were calculated to be 1.09 and 1.62, respectively. Those abnormal values of α were analyzed and ascribed to the Frumkin effect (or diffuse layer effect) at both sides of the interfaces. Some of the previous reports are summarized and also analyzed based on the Frumkin effect. The possible effect of ion transfer on the ET process is discussed in detail.

The Open-Circuit Potential of a Polarizable and Reactive Electrode

The open-circuit potential (OCP) of a polarizable and reactive electrode is modeled by the combination of the mixed potential theory and the Frumkin effect. The product of surface oxidation reaction alters the electrolyte double layer structures at the interface, which conversely affects the surface reaction rate. Tribo-electrochemical experiments were carried out with a tungsten rotating disc electrode in a series of diluted KIO3 solutions at pH 2.00. The OCP change with time during the passivation of the electrode surface is fitted based on the model. All the fitting results can provide coherent and reasonable physical meanings, and the apparent surface reaction rate of 1.1*10^4 (mol/L)^-1*sec^-1 of the tungsten electrode surface by KIO3 is thus obtained.

Decomposition reactions of bifenox anion radical involving intramolecular electron transfer

The nitropesticide bifenox (methyl 5-(2,4-dichlorophenoxy)-2-nitrobenzoate) is reduced in aprotic media in two reduction steps. The first heterogeneous electron transfer involves the acceptance of one electron leading to the formation of a relatively stable nitro anion radical that was characterized by EPR spectroscopy. The electrochemically generated radical anion eventually decomposes to two stable products. Intramolecular electron transfer coupled with chemical steps leads in the first case to the cleavage of the carboxymethyl group and the formation of the nitropesticide nitrofen ((2,4-dichlorophenyl)(4-nitrophenyl) ether) and in the second case to a trans-esterification process, i.e., an exchange of the methyl group for an alkyl of the supporting electrolyte. Both these final products retain pesticidal activity, which explains the high efficiency of bifenox as a pesticide. The electrochemical characteristics show that the radical anion undergoes a further two-electron reduction at more negative potentials. The second reduction step is strongly influenced by the nature and concentration of the tetraalkylammonium cation of the supporting electrolyte. The influence of the electrolyte concentration was accounted for by the effect of the electrode double-layer structure on the electron transfer kinetics (Frumkin effect) due to repulsion of the radical anion from a negatively charged electrode∣electrolyte interface.

The Voltammetric Response of Nanometer-Sized Carbon Electrodes

in both the presence and absence of supporting electrolyte has been investigated. In the presence of supporting electrolyte, well-defined steady-state voltammograms of sigmoidal shape have been obtained on electrodes with effective radii as small as 1 nm. In the absence of supporting electrolyte, however, the voltammetric behavior varies with the redox system. Deviation from the expected migration-diffusion response is observed when the electrode is smaller than 20 nm for the reduction of the multicharged cationic species hexammineruthenium(III) (Ru(NH3)6 3+ ). Deviation from the ideal behavior of migration-coupled diffusion is exhibited at electrodes even of micrometer size during the reduction of the multicharged hexacyanoferrate(III) anion (Fe(CN)6 3- ), which has a median reduction potential and relatively low k 0 . Such an effect is also observed for the oxidation of the hexacyanoferrate(II) anion (Fe(CN) 6 4- ). In comparison, the hexachloroiridate(IV) anion (IrCl6 2- ), with a higher k 0 and more positive reduction potential, shows deviations similar to those seen for hexaammineruthenium(III); i.e., no deviation from expected behavior is seen until the electrode size is less than ca. 20 nm. It is argued that the dynamic diffuse double-layer effect rather than the Frumkin effect is the major source of the observed nonideal behavior. The results indicate that the dynamic diffuse doublelayer effect can function even when the electrode reaction is reversible or quasi-reversible and becomes more pronounced at very small electrodes. The nature of size effects on the voltammetric response at nanometer size electrodes are discussed.

Application of the Unequal Distances of Closest Approach Theory to the Analysis of Double-Layer Effects on Zn(II) Reduction at a Mercury Electrode

The orthogonal collocation technique has been applied to the development of a numerical solution of the unequal distances of closest approach (UDCA) theory for any number of electrolytes and planes of closest approach to the electrode surface. On the basis of theoretical analysis of the reaction coordinate of Zn2+ reduction by Schmickler et al. (Chem. Phys. 2000, 252, 349), a UDCA analysis of the Frumkin effect on the observed charge-transfer rate constants has been performed. The supporting electrolytes LiClO4, Mg(ClO4)2, and Al(ClO4)3 were chosen to vary systematically the distance of closest approach of the electrolyte cation with respect to that of the electroactive species. UDCA distances of closest approach derived from electrocapillary data are shown to provide a reasonable account of the Frumkin effect. However, more consistent results are obtained when variations of the Zn2+ activity coefficient, computed from the MSA theory, are also considered.

Extended electron transfer and the Frumkin correction

Abstract It is now well established that the rate constant for electron transfer between a metal electrode and a given redox moiety (at distance x from the electrode) decays according to exp[−βx]; values of β are of the order of 108 cm−1 and depend primarily upon the nature of the intervening medium. The present work demonstrates how this ‘extended’ electron transfer can modify the Frumkin correction for diffuse layer effects in the measurement of heterogeneous rate constants. We quantify the effect of this ‘extended’ electron transfer by comparing the electron transfer rate constants deduced with (k′eff) and without (keff) extended electron transfer. Butler–Volmer kinetics and a single electron transfer are assumed. The ratio k′eff/keff is deduced as a function of β/κ, where κ is the reciprocal Debye length; (F/RT)φPCA where φPCA is the diffuse layer potential at the plane of closest approach; and zox−α, where zox is the charge of the oxidized redox species and α is the Butler–Volmer transfer coefficient. The deviation of k′eff/keff from unity is greatest when the diffuse layer potential, φx, decays over distances of a few angstroms from the plane of closest approach, as is the case with higher concentrations of supporting electrolyte and/or large values of the diffuse layer potential. When |zox|≤|zse| and |zred|≤|zse| the classical Frumkin expression is applicable as long as − ln 1+ β κ ≤ F RT φ PCA z ox −α ≤ ln 1+ β κ When |zox|>|zse| or |zred|>|zse| and (F/RT)φPCA(zox−α) 0 ≤ (F/RT)φ PCA (z ox − α) ≤ln [1+β/κ] thus ensuring that the redox species is not disproportionately accumulated in the diffuse layer. We also show that when β/κ≤0.5, φPCAzox≥0 and φPCAzred≥0 then virtually all ET occurs outside the diffuse layer and there is no Frumkin effect. However, this condition is not easily achieved experimentally.

Mechanism of the oscillatory reduction of peroxodisulfate on gold(110) at electrode potentials positive to the point of zero charge

The oscillatory reduction of S 2O 2− 8 ions on the Au(110) electrode in dilute solutions of NaF at potentials positive to the known value of the potential of zero charge (PZC) has been studied. Experimental results based on cyclic voltammetry with rotating disk electrodes and potentiostatic current transients indicate that in the course of S 2O 2− 8 reduction the surface state of the electrode is modified. It is proposed that the point of zero charge shifts to a more positive potential, and that the oscillatory S 2O 2− 8 reduction is governed by the Frumkin effect.

The catalysis of the electrochemical reduction of cadmium ions by chloride ions: A mechanistic study in mixed 1 M KF + KCl aqueous solutions at the dropping mercury electrode

From the rate data obtained with impedance and demodulation voltammetry at varied concentrations of chloride ion acting as the catalyst, it is concluded that the cadmium ion reduction proceeds according to a CECEC mechanism. The second and third “chemical” steps show up because the catalyst accelerates specifically the first chemical and the first electrochemical step and because it does not affect the other steps to a significant extent. It is argued that the addition of a catalyst may serve as a general tool to unraveling the mechanism of an electrode reaction in a way that has some resemblance to variation of the electrode potential. The rate data, after correction for the Frumkin effect and complex formation, are treated as a function of the concentration, the surface excess and the surface activity of the catalyst, leading to a preference for the latter quantity. The way in which the catalyst exerts its activity is found to be greatly different from the results obtained earlier in this laboratory with thiourea catalyzing the Cd(II) reduction and with iodide ions catalyzing the Zn(II) reduction.