Computer simulation of electron transfer processes across the electrode|electrolyte interface: a treatment of solvent and electrode polarizability

A polarizable molecular dynamics model for adiabatic electron transfer across the electrode|electrolyte interface is presented. The electronic polarizability of the water and of the metal electrode is accounted for by a dynamical fluctuating charge algorithm, image charges, and the Ewald summation adapted for a conducting interface. The effects of the solvent electronic polarizability are studied by computing the diabatic and adiabatic free energy curves for both polarizable and non-polarizable water models. This represents the first effort to compute the adiabatic free energy curves from simulation for a fully polarizable electrochemical system.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Influence of Nonlocal Effects on Kinetic Parameters of Heterogeneous Charge Transfer Reactions

The influence of the spatial dispersion of the solvent and of the effect of the electrical field penetration into a metal on the free energy of the solvent reorganization and the activation free energy for heterogeneous charge transfer reactions is studied. The calculations are based on the exactly solved model of a sharp metal/electrolyte interface, the model of a Born sphere for the ion, and the three-mode approximation for the dielectric function of the solvent. In the sharp-interface model, in the case of a mirror reflection, a relationship for the dielectric tensor of a heterogeneous system comprising two contacting media with a plane interface is obtained, along with an expression for the potential created by a point charge. This expression formally coincides with the expression derived earlier by Vorotyntsev and Kornyshev, but it contains true bulk dielectric functions of contacting media. In the model of the Born sphere for the ion and the three-mode approximation for the dielectric function of the solvent, an expression for the potential of image forces, which determines the dependence of the solvent reorganization energy on the distance from the reacting ion to the electrode, is obtained. It is shown that both the reorganization energy and the activation free energy decrease with decreasing distance from the ion to the electrode. The calculation results are compared with estimates of the reorganization energy obtained from experimental data for the reaction Fe³⁺/Fe²⁺ and the reaction of the hydronium ion discharge.     

Can marcus theory be applied to redox processes in ionic liquids? A comparative simulation study of dimethylimidazolium liquids and acetonitrile

Simulations of a model system of charged spherical ions in the ionic liquids dimethylimidazolium chloride, [dmim][Cl], dimethylimidazolium hexafluorophosphate, [dmim][PF6], and the polar liquid acetonitrile, MeCN, are used to investigate the applicability of Marcus theory to electrochemical half-cell redox processes in these liquids. The free energy curves for solvent fluctuations are found to be approximately parabolic and the Marcus solvent reorganization free energies and activation free energies are determined for six possible redox processes in each solvent. The similarities between the different types of solvent are striking and are attributed to the essentially long-range nature of the relevant interactions and the effectiveness of the screening of the ion potential. Nevertheless, molecular effects are seen in the variation of solvent screening potential with distances up to 2 nm.     

Electrochemical charge transfer mediated by metal nanoparticles and quantum dots

Electron transfer processes mediated by nanostructured materials assembled at electrode surfaces underpin fundamental processes in novel electrochemical sensors, light energy conversion systems and molecular electronics. Functionalisation of electrode surfaces with hierarchical architectures incorporating self-assembling molecular systems and materials, such as metal nanostructures, quantum dots, carbon nanotubes, graphene or biomolecules have been intensively studied over the last 20 years. Important steps have been made towards the rationalisation of the charge transfer dynamics from redox species in solution across molecular self-assembling systems to electrode surfaces. For instance, a unified picture has emerged describing the factors which determine the rate constant for electron transfer processes across rigid self-assembling molecular barriers. An increasing bulk of evidence has recently shown that the incorporation of nanomaterials into self-assembling monolayers leads to an entirely different electrochemical behaviour. This perspective rationalises some of the key observations associated with nanoparticle mediated charge transfer, such as the apparent distance independent charge transfer resistance observed for redox species in solution. This behaviour only manifests itself clearly in the case where the probability of direct charge transfer from the redox probe to the electrode is strongly attenuated by self-assembling molecular barriers. Here we will highlight specific issues concerning self-assembled monolayers as blocking barriers prior to discussing the effect of nanoparticles on the electrochemical response of the system. Selected examples will provide conclusive evidence that the extent of charge transfer mediation is determined by the overlap between the density of states of the nanostructures and the energy levels of redox species in solution. Only in the case where a strong overlap exists between the energy levels of the two components, the nanostructures behave as "electron launchers", allowing efficient charge transfer across insulating molecular layers.     

应用扫描电化学显微镜研究极化液/液界面上的电子转移反应

将含有氧化还原电对的水溶液滴涂在铂盘电极表面, 然后将该电极插入到1,2-二氯乙烷溶液中, 形成稳定的油/水界面. 液滴中的K3Fe(CN)6和K4Fe(CN)6氧化还原电对既可以作为水相中的参比电对参与控制液/液界面上的电势差, 同时又可以作为水相的电子授受体参与界面上的电子转移反应. 结合扫描电化学显微镜电化学系统的特点, 利用其双恒电位仪分别控制界面电势差和现场扫描的优点, 通过扫描电化学显微镜的渐进曲线得到了不同界面电势差控制的电子转移反应速率常数. 实验结果表明, 应用此方法获得的液/液界面可以被外加电位极化, 在一定的电势差范围内, 反应速率常数与界面电势差的关系遵守Butler-Volmer公式.     

Electrochemical deposition of gold at liquid–liquid interfaces studied by thin organic film-modified electrodes

The unique physico-chemical properties of gold nanoparticles portrayed in their chemical stability, the size-dependent electrochemistry, and the unusual optical properties make them suitable modifiers of various surfaces used in the fields of optical devices, electronics, and biosensors. In this work we present two different methods to obtain metallic gold nanoparticles at a liquid–liquid interface, and to control their growth by adjusting the experimental conditions. Decamethylferrocene (DMFC), used as an oxidizable compound dissolved in an organic solvent that is spread as a thin film on the surface of graphite electrode, serves as a redox partner to exchange electrons across the liquid–liquid interface with the other redox counter-partner [AuCl₄]^? present in the conjoined water phase. The interfacial electron transfer between the DMFC and the [AuCl₄]^? ions leads to deposition of metallic gold nanoparticles at the liquid–liquid interface. The structure and features of the deposited Au nanoparticles were studied by means of microscopic and voltammetric techniques. The morphology of the Au deposit depends on the concentration ratio of redox partners and both electrode and liquid–liquid interfacial potential differences. Depending on whether the Au deposit was obtained by ex situ (at open circuit potential) or by “in situ” (by cycling of the electrode potential) approach, we observed quite different effects to the ion transfer reactions probed by the thin-film electrode set-up. The possible reasons for the different behavior of the Au nanoparticles are discussed in terms of the structure and the properties of the obtained Au deposit. In separate experiments, we have demonstrated catalytic effects of the Au nanoparticles towards enhancing the electron transfer between DMFC and two aqueous redox substrates, hexacyanoferrate and hydrogen peroxide.     

Surface-bound molecular rulers for probing the electrical double layer

Herein, we report the first experimental investigation on the effect of varying the position of redox-active moieties, within the electrical double layer, on the apparent formal potential and on the electron transfer rate constant. This was achieved using a rigid class of molecules, norbornylogous bridges, to place redox species (ferrocene) at a fixed position above the surface of the electrode. Cyclic voltammetry and alternating current voltammetry were used to calculate the apparent formal potential and the electron transfer rate constant for the electron transfer between the ferrocene and the gold electrode. We use the effect of electric field on the apparent formal potential measurement of the surface-bound redox species to calculate the potential drop from the initiation of the electrical double layer to different distances above it. It was found that self-assembled monolayers formed from ω-hydroxyalkanethiol have a potential profile very similar to that described by classical theories for bare metal electrodes. A steep drop in potential in the Stern layer was observed followed by a smaller potential drop in the Gouy-Chapman layer. The electron transfer rate constant was found to decrease as the distance between the ferrocene moiety and the initiation of the double layer is increased. Thus, the electron transfer rate constant appears to be dependent on ion concentration.     

Introducing hydrophilic carbon nanoparticles into hydrophilic sol-gel film electrodes

A hydrophilic carbon nanoparticle–sol-gel electrode with good electrical conductivity within the sol-gel matrix is prepared. Sulfonated carbon nanoparticles with high hydrophilicity and of 10–20 nm diameter (Emperor 2000) are co-deposited onto tin-doped indium oxide substrates employing a sol-gel technique. The resulting carbon nanoparticle-sol-gel composite electrodes are characterized as a function of composition and salt (KCl) additive. Scanning electron microscopy and voltammetry in the absence and in the presence of a solution redox system suggest that the composite electrode films can be made electrically conducting and highly porous to promote electron transport and transfer. The effect of the presence of hydrophilic carbon nanoparticles is explored for the following processes: (1) double layer charging, (2) diffusion and adsorption of the electrochemically reversible solution redox system 1,1′-ferrocenedimethanol, (3) electron transfer to the electrochemically irreversible redox system hydrogen peroxide, and (4) electron transfer to the redox liquid tert-butylferrocene deposited into the porous composite electrode film. The extended electrochemically active hydrophilic surface area is beneficial in particular for surface sensitive processes (1) and (3), and it provides an extended solid|organic liquid|aqueous solution boundary for reaction (4). The carbon nanoparticle–sol-gel composite electrodes are optimized to provide good electrical conductivity and to remain stable during electrochemical investigation.     

A comparison between interfacial electron-transfer rate constants at metallic and graphite electrodes

The Fermi golden rule formalism has been used to derive the rate constant for interfacial electron transfer from a semimetallic electrode, such as highly ordered pyrolytic graphite (HOPG), to a redox couple in solution. A simple expression is presented that semiquantitatively relates the electron-transfer rate constant at a semimetallic electrode to that at a metallic electrode. The approach allows for the estimation of the value of the rate constant for interfacial charge transfer to nonadsorbing outer-sphere redox species at semimetallic electrodes. Rate constants for interfacial electron transfer for a variety of one-electron redox couples at semimetallic electrodes have been calculated relative to the rate constant of the ferrocenium/ferrocene redox couple at a gold electrode. Good agreement is found, in general, between the calculated and observed rate constants.     

Electroreduction of Dy(III) assisted by Zn and its co-deposition with Zn(II) in LiCl–KCl molten salt

To recover dysprosium (Dy) from LiCl–KCl molten salt, the electrochemical mechanism of Dy(III) on liquid Zn electrode and co-deposition of Dy(III) and Zn(II) on W electrode were studied using electrochemical methods. Cyclic voltammetry results demonstrated that the redox process of Dy on liquid Zn electrode is reversible and controlled by diffusion. Reverse chronopotentiograms showed that the transition time ratio of reduction and oxidation is ~3:1, revealing the redox of Dy on liquid Zn electrode is a kind of soluble–soluble system: Dy(III) + 3e⁻ = (Dy–Zn)_solution. The half-wave potential of Dy(III) was almost constant with the increase in scanning rate. The electrochemical separation of metallic Dy from the molten salt was performed using constant potential electrolysis, and the product characterized using X-ray diffraction and scanning electron microscopy–energy-dispersive X-ray spectroscopy was the thermodynamic unstable compound DyZn₅. Also, the co-deposition mechanism of Dy(III) and Zn(II) was explored, indicating that Dy(III) could deposit on pre-deposited Zn and form Dy–Zn compounds: Zn(II) + 2e⁻ = Zn and xDy(III) + yZn + 3xe⁻ = Dy_xZn_y. Moreover, the effect of Dy(III) concentration on the formation of Dy–Zn compounds was investigated. The redox peak currents corresponding to different Dy–Zn compounds changed with the increase in Dy(III) concentration. The co-deposition of Dy(III) and Zn(II) was performed using constant current electrolysis at diverse Dy(III) concentrations. The different Dy–Zn compounds were produced by controlling Dy(III) concentration.     

Colloidal Supercapattery: Redox Ions in Electrode and Electrolyte

Redox chemistry is the cornerstone of various electrochemical energy conversion and storage systems, associated with ion diffusion process. To actualize both high energy and power density in energy storage devices, both multiple electron transfer reaction and fast ion diffusion occurred in one electrode material are prerequisite. The existence forms of redox ions can lead to different electrochemical thermodynamic and kinetic properties. Here, we introduce novel colloid system, which includes multiple varying ion forms, multi‐interaction and abundant redox active sites. Unlike redox cations in solution and crystal materials, colloid system has specific reactivity‐structure relationship. In the colloidal ionic electrode, the occurrence of multiple‐electron redox reactions and fast ion diffusion leaded to ultrahigh specific capacitance and fast charge rate. The colloidal ionic supercapattery coupled with redox electrolyte provides a new potential technique for the comprehensive use of redox ions including cations and anions in electrode and electrolyte and a guiding design for the development of next‐generation high performance energy storage devices.     

Ab initio molecular dynamics simulation of the aqueous Ru2+/Ru3+ redox reaction: the Marcus perspective

A well-behaved (low spin) transition metal aqua ion, Ru(aq)(2+), is used as a model system in an ab initio molecular dynamics study of a redox half reaction to which the Marcus theory of electron transfer is assumed to apply. Using constraint methods, we show that aqueous Ru(2+) can be reversibly transformed to Ru(3+) under the control of the classical solvent electrostatic potential as order parameter. The mean force is found to vary linearly with the order parameter in accordance with the Marcus theory. As can be expected for a half reaction, the slope in the oxidized and reduced states are asymmetric differing by approximately a factor of two. As a further test, we verify that the corresponding quadratic potential of mean force is in excellent agreement with the free energy profile obtained from the Gaussian distribution of potential fluctuations sampled from free (unconstrained) runs of the reduced and oxidized system. Similar to experimental electrochemical methods, our simulation scheme enables us to manipulate the effective thermodynamic driving force and align the free energy minima of product and reactant state. The activation energy and reaction entropy computed under these conditions are discussed and analyzed from the Marcus perspective.     

Theoretically Rational Designs of Transport Organic Semiconductors Based on Heteroacenes

A Marcus electron transfer theory coupled with an incoherent polaron hopping and charge diffusion model in combining with first‐principle quantum chemistry calculation was applied to investigating the effects of heteroatom on the intermolecular charge transfer rate for a series of heteroacene molecules. The influences of intermolecular packing and charge reorganization energy were discussed. It was found that the sulphur and nitrogen substituted heteroacenes were intrinsically hole‐transporting materials due to the reduced hole reorganization energy and the enhanced overlap between HOMOs. For the oxygen‐substituted heteroacene, it was found that both the electronic couplings and the reorganization energies for holes and electrons were comparative, indicating the application potential of ambipolar devices. Most interestingly, for the boron‐substituted heteroacenes, theoretical calculations predicted a promising electron‐transport material, which is rare for organic materials. These findings provide insights into rationally designing organic semiconductors with specific properties.     

Unified interpretation of exciplex formation and marcus electron transfer on the basis of two-dimensional free energy surfaces

The mechanism of exciplex formation proposed in a previous paper has been refined to show how exciplex formation and Marcus electron transfer (ET) in fluorescence quenching are related to each other. This was done by making simple calculations of the free energies of the initial (DA*) and final (D+A-) states of ET. First it was shown that the decrease in D-A distance can induce intermolecular ET even in nonpolar solvents where solvent orientational polarization is absent, and that it leads to exciplex formation. This is consistent with experimental results that exciplex is most often observed in nonpolar solvents. The calculation was then extended to ET in polar solvents where the free energies are functions of both D-A distance and solvent orientational polarization. This enabled us to discuss both exciplex formation and Marcus ET in the same D-A pair and solvent on the basis of 2-dimensional free energy surfaces. The surfaces contain more information about the rates of these reactions, the mechanism of fluorescence quenching by ET, etc., than simple reaction schemes. By changing the parameters such as the free energy change of reaction, solvent dielectric constants, etc., one can construct the free energy surfaces for various systems. The effects of free energy change of reaction and of solvent polarity on the mechanism and relative importance of exciplex formation and Marcus ET in fluorescence quenching can be well explained. The free energy surface will also be useful for discussion of other phenomena related to ET reactions.     

Achievement and assessment of direct electron transfer of glucose oxidase in electrochemical biosensing using carbon nanotubes,graphene, and their nanocomposites

Carbon nanotubes, graphenes, and their hybridized composites with nanoparticles have been attempted to establish a direct electrical communication between the recognition biomolecule and its underlying electrode surface. This review (with 133 refs.) focuses on advances, strategies and technical challenges in the development of reagentless electrochemical biosensors for glucose with enhanced detection sensitivity, selectivity, and simplicity. Specifically, the review commences with a discussion of the relevance of direct electron transfer (DET) in biosensing together with the fundamental of electro-enzymology and kinetics. General aspects of glucose oxidase (GOx), the most popular enzyme with a flavin cofactor, are discussed in view of its historical and important role in the development of electrical biosensors for blood glucose. The next section assesses DET of GOx based on the Marcus theory and the Laviron formalism. The reorganizational energy of the Marcus model and the overpotential play an important role in reaction kinetics and affect the rate of electron transfer significantly. The presence of nanomaterials, particularly for graphene oxide, decreases the electron transfer distance between the enzyme redox center and the underlying electrode surface well beyond 15 Å. The improper Marcus-Hush-Chidsey integral is now simplified to estimate the rate of electron transfer with very good accuracy. Critiques, technical challenges, and future possibilities of glucose electrodes with respect to DET are also presented and discussed.

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Graphical abstract This review (with 133 refs.) focuses on advances, strategies and technical challenges in the development of reagentless electrochemical biosensors for glucose with enhanced detection sensitivity, selectivity, and simplicity.

     

Diabatic free energy curves and coordination fluctuations for the aqueous Ag+Ag2+ redox couple: a biased Born-Oppenheimer molecular dynamics investigation

Biased Born-Oppenheimer molecular dynamics simulations are performed to compute redox potential and free energy curves for the redox half reaction Ag(+)-->Ag(2+)+e(-) in aqueous solution. The potential energy surfaces of reactant and product state are linearly coupled and the system transferred from the reduced state to the oxidized state by variation of the coupling parameter from 0 to 1. The redox potential is obtained by thermodynamic integration of the average ionization energy of Ag(+). Diabatic free energy curves of reduced (R) and oxidized (O) states are obtained to good statistical accuracy by reweighting and combining the set of biased distributions of the ionization energy. The diabatic free energy curves of Ag(+) and Ag(2+) are parabolic over a wide range of the reaction coordinate in agreement with the linear response assumption that underlies Marcus theory. However, we observe deviations from parabolic behavior in the equilibrium region of Ag(+) and find different values for the reorganization free energy of R (1.4 eV) and O (0.9 eV). The computed reorganization free energy of Ag(2+) is in good agreement with the experimental estimate of 0.9-1.2 eV obtained from photoelectron spectroscopy. As suggested by our calculations, the moderate deviation from linear response behavior found for Ag(+) is likely related to the highly fluxional solvation shell of this ion, which exhibits water exchange reactions on the picosecond time scale of the present molecular dynamics simulation.     

Photoinduced electron transfer in hydrogen bonded donor--acceptor systems. Free energy and distance dependence studies and an analysis of the role of diffusion.

The free energy dependence of electron transfer in a few small-molecule donor--acceptor systems having hydrogen-bonding appendages was studied to evaluate the role of diffusion in masking the inverted region in bimolecular PET reactions. A small fraction of the probe molecules associate and this led to the simultaneous observation of unimolecular and diffusion-mediated quenching of the probe fluorescence. Free energy dependence studies showed that the unimolecular electron transfer obeys Marcus behavior and the diffusion-mediated electron transfer obeys Rehm--Weller behavior. The absence of an inverted region in bimolecular PET reactions is thus attributed to diffusion. The results of the free energy dependence studies suggest that distance dependence of electron transfer plays a role in masking the inverted region. To ascertain this aspect we have carried out a study of the distance dependence of electron transfer in the hydrogen-bonded donor--acceptor systems. For a system in the normal region an exponential rate decrease was observed. For a system in the inverted region it was observed that the rate depends very feebly on distance. Thus distance dependence studies did not confirm the prediction of enhanced rates at larger distances in the inverted region.     

Marcus电子转移理论的科学性探讨

利用科学原理对Marcus电子转移理论的科学性进行了考察, 结果表明Marcus电子转移理论违背了能量守恒定律.