Effect of the debye screening on the tunnel current through simple electrochemical bridged contact

General equations for tunnel current through electrochemical contact containing a redox-center in molecular bridge group are observed with allowing for potential distribution in the tunnel gap. Simple approximate expressions appropriate for the analysis of experimental data are also derived. The dependences of the position of the current maximum and its width on the bias voltage, the position of the bridge group in the tunnel gap, and the system’s physical parameters (like the electrolyte ionic strength) are calculated. It is shown that the Debye screening in solution affects these dependences significantly.     

Theoretical analysis of the telegraph-like fluctuations in bridged electrochemical contacts

Steady-state current-voltage characteristic of an electrochemical bridged contact and the telegraph noise power are calculated in terms of the model of two redox states. It is shown that the overvoltage dependence of the tunnel current at a constant bias voltage is S-shaped, which was observed in works on the electron tunneling in similar systems. The overvoltage dependence of the contact conductance has a maximum near the equilibrium potential of the bridge-molecule redox group. The overvoltage dependence of the noise power at zero frequency has a maximum whose position is determined by the bias voltage.     

Electrochemical transistor based on bridge tunneling contact containing two redox groups

The method of kinetic equations was used to show that a bridge tunneling contact containing two redox groups in the sequential configuration immersed into a solution of electrolyte at the room temperature features pronounced transistor properties at a given set of physical system parameters. Valence electrons of redox groups interact strongly with the classical phonon subsystem of the liquid medium. Debye screening of the electric field in the tunneling gap and Coulomb repulsion between electrons in different redox groups are taken into account. The case of nonadiabatic electron transfer both between redox groups and between electrodes and redox groups is considered in the limit of infinitely high Coulomb repulsion between electrons in a redox group. For sufficiently high absolute values of difference δ between unperturbed energy levels of redox groups, the system features voltammetric characteristics typical for a transistor. The amplification effect appears due to a strong dependence of tunneling current on overpotential. The emphasis is upon the peculiaritiespeculiarities of voltammetric characteristics in the case of asymmetric tunneling contacts.     

A theory of single-electron non-adiabatic tunneling through a small metal nanoparticle with due account of the strong interaction of valence electrons with phonons of the condensed matter environment

A theory of electrochemical behavior of small metal nanoparticles (NPs) which is governed both by the charging effect and the effect of the solvent reorganization on the dynamic of the electron transfer (ET) is considered under ambient conditions. The exact expression for the rate constant of ET from an electrode to NP which is valid for all values of the reorganization free energy E(r), bias voltage, and overpotential is obtained in the non-adiabatic limit. The tunnel current/overpotential relations are studied and calculated for different values of the bias voltage and E(r). The effect of E(r) on the full width at half maximum of the charging peaks is investigated at different values of the bias voltage. The differential conductance/bias voltage and the tunnel current/bias voltage dependencies are also studied and calculated. It is shown that, at room temperature, the pronounced Coulomb blockade oscillations in the differential conductance/bias voltage curves and the noticeable Coulomb staircase in the tunnel current/bias voltage relations are observed only at rather small values of E(r) in the case of the strongly asymmetric tunneling contacts.     

Theory of the shot noise in electrochemical bridge contacts

Correlation functions of the current and the noise power for a redox-group-containing electrochemical tunnel contact are calculated under the assumption on a shot character of the electron tunneling. Weak and strong interaction between the redox group and electrodes is considered. Overvoltage dependence of the Fano factor at different bias-potentials is found. The conditions of passing of the calculated dependences into the Schottky law are formulated.     

Effect of Coulomb interaction between the electrons on two-electron redox-mediated tunneling

Two-electron non-adiabatic redox-mediated tunneling through a symmetric electrochemical contact with a bridge molecule having one electron energy level participating in tunneling is considered under ambient conditions. It is shown that the current/overpotential dependence in this system can disclose two distinct or overlapping clear-cut maxima depending on the value of the effective Coulomb repulsion energy. This new effect is due to the opening of the channel for tunneling of second electron with the variation of the electrode potential. The system manifests also a rectification effect in the current/bias voltage curve which depends on the value of the effective Coulomb repulsion energy.     

Electrochemical proton relay at the single-molecule level

A scheme for the experimental study of single-proton transfer events, based on proton-coupled two-electron transfer between a proton donor and a proton acceptor molecule confined in the tunneling gap between two metal leads in electrolyte solution is suggested. Expressions for the electric current are derived and compared with formalism for electron tunneling through redox molecules. The scheme allows studying the kinetics of proton and hydrogen atom transfer as well as kinetic isotope effects at the single-molecule level under electrochemical potential control.     

Electrochemical gating of single osmium molecules tethered to Au surfaces

The electrochemical study of electron transport between Au electrodes and the redox molecule Os[(bpy)₂(PyCH₂ NH₂CO-]ClO₄ tethered to molecular linkers of different length (1.3 to 2.9 nm) to Au surfaces has shown an exponential decay of the rate constant k _ET ⁰ with a slope β = 0.53 consistent with through bond tunneling to the redox center. Electrochemical gating of single osmium molecules in an asymmetric tunneling nano-gap between a Au(111) substrate electrode modified with the redox molecules and a Pt-Ir tip of a scanning tunneling microscope was achieved by independent control of the reference electrode potential in the electrolyte, E _ref ? E _s, and the tip-substrate bias potential, E _bias. Enhanced tunneling current at the osmium complex redox potential was observed as compared to the off resonance set point tunneling current with a linear dependence of the overpotential at maximum current vs. the E _bias. This corresponds to a sequential two-step electron transfer with partial vibration relaxation from the substrate Au(111) to the redox molecule in the nano-gap and from this redox state to the Pt-Ir tip according to the model of Kuznetsov and Ulstrup (J Phys Chem A 104: 11531, 2000). Comparison of short and long linkers of the osmium complex has shown the same two-step ET (electron transfer) behavior due to the long time scale in the complete reduction-oxidation cycle in the electrochemical tunneling spectroscopy (EC-STS) experiment as compared to the time constants for electron transfer for all linker distances, k _ET ⁰.     

Does the electron spin affect the rates of electron tunneling in electrochemical systems?

An effect of spin degeneracy of electron energy levels in the metal electrode on the observable characteristics of electrochemical systems in the absence of magnetic field is discussed. Single-electrode outer-sphere electron transfer reactions are considered as well as redox-mediated electron tunneling in electrochemical contacts. Particular attention is paid to the difference between the spin-less model and the limit of infinitely large Coulomb repulsion of the electrons occupying the same valence orbital in the redox group. Adiabatic and non-adiabatic regimes of the transitions are studied and the expressions for the tunnel current are obtained.     

Electrochemistry in nanometer-wide electrochemical cells

The electrochemical properties of an electrochemical cell defined by two concentric spherical electrodes, separated by a 1 to 20-nm-wide gap, and a freely diffusing electrochemically active molecule (e.g., ferrocene) have been investigated by coupling of Brownian dynamics simulations with long-range electron-transfer probability values. The simulation creates a trajectory of a single molecule and calculates the likelihood that the molecule undergoes a redox reaction during each time interval based on a probability-distance function derived from literature first-order kinetic data for a surface-bound ferrocene. Steady-state voltammograms for the single-molecule concentric spherical electrochemical cell are computed and are used to extract a heterogeneous electron-transfer rate for the freely diffusing molecule redox reaction. The Brownian dynamics simulations also indicate that long-range electron transfer, between the redox molecule and electrode, leads to nonsigmoidal-shaped i-E characteristics when the distance between electrodes approaches the characteristic redox tunneling decay length. The long-range electron transfer generates a "tunneling depletion layer" that results in a potential-dependent diffusion-limited current.     

Enhancement of the transverse conductance in DNA nucleotides

We theoretically study the electron transport properties of DNA nucleotides placed in the gap between two single-wall carbon nanotubes capped or terminated with H or N. We show that in the case of C-cap and H-termination the current at low electric bias is dominated by nonresonant tunneling, similarly to the cases of gold electrodes. In nitrogen-terminated nanotube electrodes, the nature of current is primarily quasiresonant tunneling and is increased by several orders of magnitude. We discuss the consequence of our result on the possibility of recognition at the level of single molecule.     

Changes in zeta potential caused by a dc electric current for thin double layers

An asymptotic solution was obtained to describe one-dimensional, steady-state transport of a symmetric binary electrolyte normal to two large parallel electrodes, in the limit in which the Debye length is infinitesimal compared to the distance separating the two electrodes. Despite the nonzero ion flux, Boltzmann's equation continues to describe the relationship between either ion concentration and the electrostatic potential inside the diffuse part of the double layer, while local electroneutrality applies outside, even for current densities approaching the limiting value. In the absence of ion adsorption or dissociation reactions at the electrodes, the magnitude of any charge or zeta potential arising on the electrodes at zero current is determined by the equilibrium constant for the redox reactions which would exchange ionic charge carriers for electric charge carriers at the electrode surface. Nonzero current causes the ionic strength of the bulk to vary with position. This perturbs the Debye length of the diffuse cloud on either electrode: it is the local ionic strength just outside the cloud which determines the Debye length for that cloud. Nonzero current also changes the zeta potential. The dimensionless rate of change dζ/dJ was as large as 30.     

Thermoelectric transport properties in atomic scale conductors

The thermoelectric transport properties in atomic scale conductors consisting of a Si atom connected by two electrodes are investigated. It is found that both the electrical current and the heat current have two contributions, one from the voltage and the other from the temperature gradient. The quantities such as the Seebeck thermopower and the thermal conductance that characterize the thermoelectric transport properties of the tunnel atomic junction are studied quantitatively with a first-principles technique within the framework of Landauer-Buttiker formalism in the linear response regime. A finite thermopower only exists in a very narrow range where the energy derivative of the transmission function is nonzero. The thermopower anomaly is observed in the tunneling regime in this device but this does not violate the thermodynamic law with respect to the heat current.     

Electrolyte gating in redox-active tunneling junctions--an electrochemical STM approach

We report on the construction of an asymmetric tunneling junction between a Au STM tip and a Au(111)-(1 x 1) substrate electrode modified with the redox-active molecule N-hexyl-N'-(6-thiohexyl)-4,4'-bipyridinium bromide (HS6V6) in an electrochemical environment. The experiments focused on the reversible one-electron transfer reaction between the viologen dication V(2+) and the radical cation V(+*). Employing the concept of "electrolyte gating" we demonstrate transistor- and diodelike behavior based on in situ scanning tunneling spectroscopy at constant or variable bias voltages. We derived criteria and verified that the experimental data could be represented quantitatively by a model assuming a two-step electron transfer with partial vibrational relaxation. The analysis illustrates that the magnitude of the tunneling enhancement depends on the initial redox state of HS6V6 (V(2+) or V(+*)). Characteristic parameters, such as reorganization energy, potential drop, and overpotential across the tunneling gap were estimated and discussed. We present a clear discrimination between the redox-mediated enhanced and the off-resonance tunneling currents I(enh) respective I(T) and distinguish between electron transfer in symmetric and asymmetric Au | redox-molecule | Au configurations.     

Electrochemical reactivity at redox-molecule-based nanoelectrode ensembles

A model describing electrochemical reactivity at nanoelectrode ensembles consisting of redox-molecule-based active sites immobilized on otherwise passivated electrode surfaces is presented. A mathematical treatment in terms of hemispherical diffusion of redox-active solutes to a layer of independent molecule-based nanoelectrode sites is shown to be equivalent to one in terms of a bimolecular diffusion-limited reaction between a layer of immobilized redox molecules and a reservoir of redox-active solutes. This equivalence derives from the fact that in both cases the mass-transfer problem is essentially that of hemispherical diffusion. The model is further developed to consider rate limitation by both the bimolecular redox reaction between the active-site molecule and redox molecules in solution and the heterogeneous redox reaction between the electrode and the active-site molecule. Analytical expressions are derived for the current–voltage relation corresponding to catalyzed electron transfer at an ensemble of redox-molecule-based nanoelectrode sites, and the expressions are used to interpret preliminary data for ultrasensitive electrochemical detection in flow streams via an electrochemical amplification process that is thought to involve redox mediation by individual analyte molecules adsorbed onto monolayer-coated electrodes.     

Electrochemical origin of voltage-controlled molecular conductance switching

We have studied electron transport in bipyridyl-dinitro oligophenylene-ethynelene dithiol (BPDN) molecules both in an inert environment and in aqueous electrolyte under potential control, using scanning tunneling microscopy. Current-voltage (IV) data obtained in an inert environment were similar to previously reported results showing conductance switching near 1.6 V. Similar measurements taken in electrolyte under potential control showed a linear dependence of the bias for switching on the electrochemical potential. Extrapolation of the potentials to zero switching bias coincided with the potentials of redox processes on these molecules. Thus switching is caused by a change in the oxidation state of the molecules.     

Thermally activated electron transport in single redox molecules

We have studied electron transport through single redox molecules, perylene tetracarboxylic diimides, covalently bound to two gold electrodes via different linker groups, as a function of electrochemical gate voltage and temperature in different solvents. The conductance of these molecules is sensitive to the linker groups because of different electronic coupling strengths between the molecules and electrodes. The current through each of the molecules can be controlled reversibly over 2-3 orders of magnitude with the gate and reaches a peak near the redox potential of the molecules. The similarity in the gate effect of these molecules indicates that they share the same transport mechanism. The temperature dependence measurement indicates that the electron transport is a thermally activated process. Both the gate effect and temperature dependence can be qualitatively described by a two-step sequential electron-transfer process.     

Cyclic voltammetry at microstructured electrodes

We present the theoretical treatment of cyclic voltammograms at microstructured electrodes. Calculations of voltammograms permit the determination of electrochemical parameters of redox systems in a single cell in parallel with the determinations of the spectroscopic parameters. The structural parameters of the electrode can be determined using the theoretical treatment presented if the electrochemical parameters of the redox system are known. Furthermore, lithographic-galvanic (LIGA) structures can be used as a model for microporous electrodes. Regression analysis was used to compare experimental and calculated cyclic voltammograms as well as to determine the electrochemical and spectroscopic parameters. A modified Randles-Sevčik equation has been derived to described the peak current dependence of cyclic voltammograms at micro-structured electrodes for both reversible and quasi-reversible charge transfer.     

Reformulated space-charge-limited current model and its application to disordered organic systems

We have reformulated a traditional model used to describe the current-voltage dependence of low mobility materials sandwiched between planar electrodes by using the quasi-electrochemical potential as the fundamental variable instead of the local electric field or the local charge carrier density. This allows the material density-of-states to enter explicitly in the equations and dispenses with the need to assume a particular type of contact. The diffusion current is included and as a consequence the current-voltage dependence obtained covers, with increasing bias, the diffusion limited current, the space-charge limited current, and the injection limited current regimes. The generalized Einstein relation and the field and density dependent mobility are naturally incorporated into the formalism; these two points being of particular relevance for disordered organic semiconductors. The reformulated model can be applied to any material where the carrier density and the mobility may be written as a function of the quasi-electrochemical potential. We applied it to the textbook example of a nondegenerate, constant mobility material and showed how a single dimensionless parameter determines the form of the I(V) curve. We obtained integral expressions for the carrier density and for the mobility as a function of the quasi-electrochemical potential for a Gaussianly disordered organic material and found the general form of the I(V) curve for such materials over the full range of bias, showing how the energetic disorder alone can give rise, in the space-charge limited current regime, to an I∝V(n) dependence with an exponent n larger than 2.