Reversible Charge Transfer Research Articles

Computer simulation of a square scheme with reversible and irreversible charge transfer by the network method

Digital simulation of the square scheme in cyclic voltammetry has been carried out by the network method. A network model for this mechanism, with or without cross-reaction and with reversible or irreversible charge transfer, is proposed. Results obtained using uniform or quasi-uniform grids are compared with those obtained by other methods using exponential grids. It is shown that the network method is accurate and efficient over all kinetic domains of interest, without increases in CPU time, and it is not necessary to consider either numerical- or programming aspects. The influence of the second-order cross-reaction on the cyclic voltammograms has also been examined for reversible and irreversible charge transfers.

Mass transport to tubular electrodes

The mathematical treatment of mass transport in tubular electrodes has been examined for the EC process when a reversible electrode charge transfer is followed by a reversible chemical reaction. The transition from fast chemical reaction to slow chemical reaction is investigated. The system of convective-diffusion equations, representing the physical phenomena, are solved using properties of the integral transform and numerical computation of the integral equation. The effects of the chemical equilibrium parameter, the axial velocity of the flow and the potential scan rate on theoretical current-potential curves are elucidated and a simple procedure to determine the chemical reaction rate constant is presented.

Electron beam lithography of two-component radical ion salt films: Reversible charge transfer in copper- and silver-TCNQ

The electron beam induced lithography process of radical ion salts of copper and silver tetracyanoquinodimethane ( Cu(TCNQ) x and Ag(TCNQ) 1 with x=1 and 2), gives direct access to microstructures of these organic conductors. The films are prepared in a vacuum chamber attached directly to a modified scanning electron microscope. They are obtained by a solid state reaction of subsequently deposited TCNQ and metal layers. Electrical measurements of wire structures have been performed in situ, showing a deviation from the expected resistance versus width relation when approaching the micron scale. Absorption spectroscopy of large irradiated areas is used to identify the process being a back-transformation of the salt into neutral TCNQ and suspended metal. The application of these microstructures in the field of molecular electronics is discussed with respect to electrical and optical switching properties of these films.

General analytical solution for a reversible i/t response to a double potential step at spherical electrodes in the absence/presence of amalgamation effects

The general rigorous theory corresponding to double potential step chronoamperometry for a reversible charge transfer reaction in a spherical electrode whose area increases with tz, where z ≥ 0, is presented. The static mercury drop electrode (z = 0) and the dropping mercury electrode (z = 2/3) are addressed specifically. The explicit equations for the current versus time response assuming unequal diffusion coefficients for the oxidized and reduced species are valid when the product is soluble in both the electrolytic solution and the electrode. Comparisons with previous general treatments in the literature are made. The theory is applied to the detection of amalgamation in RP and DNP techniques.Moreover, in this work we show the origin of errors appearing in some general treatments in the literature, these errors lead to physically meaningless results when amalgamation takes place.

Reversible charge transfer complexes between molecular oxygen and poly(3‐alkylthiophene)s

The interaction of poly(3‐hexylthiophene), P3HT, with oxygen has been investigated. Evidencein the form of UV–vis absorption, electron paramagnetic resonance data, and a field effect conductivity analysis of a polymer‐based field effect transistor–is presented for the existence of a reversible charge transfer complex between P3HT and oxygen. Oxygen‐sensor applications can be foreseen for thin film transistors incorporating P3HT.

Reversible charge transfer in dielectric restricted and fractal solids: Low concentration of acceptors

We study the influence of dielectric properties of medium with dielectric constant ε in the charge transfer processes in the restricted and fractal solid spaces. It is shown that this influence is determined by the space restriction and its regularity. The increasing of ε promotes charge separation in restricted and fractal systems. The fractal properties grow weakly with increasing of ε; its increasing transfers the irregular fractal space into the regular one with respect to the charge transfer at ε≫α. The corresponding dependencies of the charge transfer efficiency on the value of ε are presented. The space restriction and breach of its homogeneous with alteration of ε give qualitatively identical results. The obtained results are good for low concentration of acceptors.

The electrochemistry of dibutyltin at mercury electrodes in aqueous media

AbstractThe electrochemical reduction of dibutyltin (Bu2Sn2+) at mercury electrodes has been investigated in aqueous media containing nitrate and chloride electrolytes using the techniques of direct current (DC) polarography, differential pulse (DP) polarography, DP voltammetry, and cyclic voltammetry. In 0.10 M nitrate media, the initial charge transfer process occurs at approximately –0.7 V (vs. Ag/AgCl) and is described by the equation in which a reversible charge transfer occurs with completely surface‐confined dibutyltin. However, when longer time domains at a hanging mercury drop electrode (HMDE) are used, the complexity of the electrochemistry increases, which is attributed to the occurrence of butyl exchange processes with the electrode mercury and consequent disruption of the film of adsorbed dibutyltin. In 0.50 M chloride media, the extent of adsorption is considerably less, and the processes, but not necessarily the postulated mechanism, correspond more closely to that described by previous workers for the reduction of dibutyltin compounds in ethanol‐water mixtures.

Reverse pulse polarography of labile metal + macromolecule systems with induced reactant adsorption: theoretical analysis and determination of complexation and adsorption parameters

A model for the interpretation of reverse pulse polarography (RPP) in metal macromolecular ligand systems is developed, including both adsorption of the macromolecule and the induced adsorption of the metal ion. The following basic assumptions are made: reversible charge transfer at a stationary planar electrode (static mercury drop electrode), labile complex, large excess of ligand compared with the total metal concentration, formation of a 1:1 complex and diffusion coefficients for ligand and complex species different from that of the free metal ion. Equations for the limiting current I lim and for the RPP full wave are deduced for both linear and Langmuirian adsorption. It is found that adsorption does not modify the expressions for I lim valid for the case without adsorption. Thus the stability constant K can be determined. In contrast, adsorption influences the shape and position of the RPP full wave. In the case of linear adsorption, an analytical expression has been deduced which relates the adsorption parameter K ML 1 to Δ E 1 2 values, thus allowing the calculation of K ML 1 from RPP waves. This method has been applied to experimental results obtained for the Cd(II) polymethacrylate system.

Reversible charge transfer with unknown mass transfer. Characterization and modelling by using a mass-transfer operator determined from experimental data

When a charge transfer is reversible and when the two associated mass-transfer steps are of the same nature, the electrical current is formulated very simply as a result of the application of a single mass-transfer operator on a potential-dependent equilibrium constant. The charge-transfer equilibrium constant is then obtained from the current by inversion of this equation. With such a “reverse modelling” approach, the characteristics of this operator can be experimentally measured and the charge-transfer equilibrium constant can be determined for any kind of thermodynamic equilibrium, nernstian or not. Consequently, the response of an electrochemical mechanism to any perturbation function can be modelled without mathematical description of the mass transfer. It is sufficient to measure experimentally, and correct adequately for instrument limitations and double-layer charging, the response of the electrochemical system to a series of steps, and then to use the convolution tool, to obtain “Theoretical” working curves. Conversely, analysis of an experimental response to any kind of perturbation can also be performed by convolution with experimentally determined operator characteristics. The main advantage of this new methodology is the ability to model or to analyse complex mechanisms for which a good mathematical description of the mass transfer is not available, or when the mass transfer mode is unknown. This powerful theory is extremely simple. Apart from the convolution product, the mathematics is easy and reduced to a minimum. The experimental verification of the proposed approach is performed without sophisticated instrumentation on the N-methylphenothiazine redox couple in acetonitrile with a mathematically poorly defined mass transport such as transient convection.

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.

Effect of a steric spacer on chromophoric interactions of ruthenium complexes containing covalently bound anthracene

Abstract To study interchromophore interactions in a ruthenium complex linked covalently to an anthryl group, we have synthesized 4-(9-anthrylethyl),4′-methyl-2,2′-bipyridine (dmb-an) and complexed it with ruthenium in two asymmetric complexes, [Ru(L) 2 (dmb-an)] 2+ , where L4,4′-dimethyl, 2,2′-bipyridine (dmb) or 4,4′-di- tert -butyl, 2,2′-bipyridine (dtb). In both complexes, the two independent chromophores rapidly undergo singlet—singlet and triplet—triplet energy transfer which nearly quantitatively quenches luminescence: Φ F =3.5 × 10 −4 from the anthryl group and Φ −5 from the metal—ligand charge transfer state of the complex. Both complexes also readily undergo photoinduced oxygenation of the anthryl group. The anthryl group is charge transfer quenched by methyl viologen, with a cage escape yield that differs substantially for the two complexes. When Ldmb, the cage escape yield is 0.26, in common with other ruthenium tris-imines and much less than free anthracene. However, when Ldtb, the cage escape yield rises to 0.55±0.05. We interpret the improved yield as arising from the bulky tert -butyl substituents, which prevent the anthryl moiety from close approach to the metal center and reduce metal-mediated enhancement of reverse charge transfer.

Computer elimination of voltammogram deformations by catalytic reaction to improve their signal for quantitative analysis. Determination of catalytic rate constant

AbstractChemical reactions coupled with the electrode process lead to the change of shape and/or height of the measured voltammogram, thus complicating its application in quantitative analysis. This article describes a fractional differintegration procedure which corrects voltammograms for interference by catalytic reactions while simultaneously providing a value for the catalytic rate constants. A peocedure is proposed which utilizes the change of the shape of a reversible charge transfer voltammogram caused by slow and moderately fast catalytic reaction to the elimination of its influence on the analytical signal. It is based upon computer symmetrization of the voltammogram by fractional differentiation of the optimized order and the following correction of the signal. The procedure also enables an advantageous determination of the catalytic reaction rate constant. Since the height of the symmetrized signal is more sensitive to the catalytic process than the height of the original voltammogram, it is of special importance for lower rate constant values. Both elimination of catalytic influence and the determination of rate constant were tested with the Ti(III) NH2OH catalytic system.

Photoinduced absorption of polymer solutions.

We present a study of the photoexcitation mechanism of poly-3-alkylthienylene and poly-3-alkylthienylenevinylene polymer solutions. We study the photoinduced absorption under steady-state and far from steady-state conditions. By calculating the analytical dependence of the photoinduced signal on the pump intensity and on the chop frequency we distinguish a bimolecular recombination mechanism for both single chain and aggregated chain solutions. The results are discussed assuming that a weak reversible charge transfer between the photoexcited polymer and the solvent takes place.

Voltammetry of labile metal—complex systems with induced reactant adsorption. Theoretical analysis for any ligand-to-metal ratio

The validity of the hypothesis of ligand excess is discussed for the voltammetric reduction of a metal ion (M) in the presence of a ligand (L). The following basic assumptions are made: (i) formation of the electroinactive ML complex, (ii) equal mobility of species M, ML and L, (iii) reversible charge transfer, (iv) labile complex and (v) Langmuirian adsorption of the ligand and the complex. The model proposed is solved rigorously for normal pulse polarography (NPP) in the four possible cases assuming either ligand excess or ligand deficiency or either adsorption or non-adsorption. For the case without adsorption, the assumption of ligand excess affects only the increasing part of the NPP wave independent of the total ligand-to-metal ratio. Then ( I NNP) lim has the same value for both ligand excess and ligand deficiency while E 1 2 differs, thus preventing the use of the DeFord—Hume method to obtain the stability constant. An analytical expression for E 1 2 is performed, which allows the evaluation of the stability constant at any total ligand-to-metal ratio and provides a quantitative estimation of the error made by applying the classical procedure assuming ligand excess. In the presence of adsorption, the assumption of ligand excess modifies the whole wave. The discrepancy between the currents obtained from the hypothesis of ligand excess with respect to that with ligand deficiency is even higher for the case with adsorption than for the case without adsorption.

An explicit finite difference simulation for chronoamperometry at a disk microelectrode in a channel flow solution

An explicit finite difference simulation is used to describe chronoamperometry at a disk microelectrode in a channel flow solution. All known phenomenologically important processes are represented in the simulation, including the electrode “edge effect” in all three spatial dimensions and the parabolic flow profile of a viscous liquid in a channel. The simulation was achieved with the use of an exponentially expanding spatial grid and a variable time increment to minimise the computational requirements. The simulation was used to study the effects of electrode radius, solution velocity and channel thickness on both the near steady-state limiting current ( I lim nss) and the time taken to achieve the near steady-state condition ( t nss) for a reversible one-electron charge transfer process. It was found that the solution velocity had a dramatic effect on both I lim nss and t nss, with an increase in I lim nss and decrease in t nss being observed with increased solution velocity. The relationships between I lim nss or t nss and solution velocity were found to be non-linear. The results of the simulation compared favourably with experimental data obtained from the limiting current region of near steady-state voltammograms for the reversible oxidation of ferrocene at platinum disk microelectrodes of radii over the range 5–50 μm.

Vacancy-related centers in diamond.

It is established that vacancies in diamond migrate, during annealing, primarily in their neutral charge state, with an activation energy of 2.3\ifmmode\pm\else\textpm\fi{}0.3 eV. Negative vacancies are destroyed by first converting to neutral centers in a reversible charge transfer process. In relatively pure diamonds (type IIa) and in diamonds (type I) containing large concentrations of nitrogen, effectively all the vacancies in the samples after irradiation can be accounted for in their neutral (${\mathit{V}}^{0}$) and negative (${\mathit{V}}^{\mathrm{\ensuremath{-}}}$) charge states. In nitrogen-rich diamonds, the vacancies are predominantly trapped during annealing at the nitrogen. From the annealing data we derive the relative oscillator strengths of the main absorption bands of ${\mathit{V}}^{0}$, ${\mathit{V}}^{\mathrm{\ensuremath{-}}}$, and of one vacancy combined either with a single N atom, a pair of N atoms, or the larger ``B'' aggregate of nitrogen. In the absence of the intrinsic nonradiative decay channels of luminescence from ${\mathit{V}}^{0}$, we show that the radiative decay time would be 35\ifmmode\pm\else\textpm\fi{}7 ns. In common natural (``type IaA'') diamonds, variations of absorption linewidths during annealing imply that about 40% of the vacancies are created within a few atomic sites of the nitrogen impurity, and direct observation confirms that vacancy production is enhanced in these diamonds. About half the vacancies, including those created near the nitrogen, anneal at each temperature about 12 times faster than those vacancies whose creation is not correlated with the nitrogen.

Induced reactant adsorption in metal—polyelectrolyte systems: pulse polarographic study

A theoretical model is developed for describing the reduction, by normal-pulse polarography, of a metal ion in the presence of a macromolecular ligand, including both the ligand adsorption and the induced adsorption of the metal ion. The following basic assumptions are made: reversible charge transfer at a stationary planar electrode (static mecury drop electrode); labile complex; large excess of ligand compared with the total metal concentration; Langmuirian adsorption for both the ligand and complex species; and diffusion coefficients for ligand and complex species very different from that of the free metal. The mathematical approach is based on transforming the system of differential equations with their boundary conditions into an integral equation which has been solved numerically. A simple procedure to obtain stability constants and adsorption parameters simultaneously from the experimental data is described. This model has been used to reproduce some experimental data from the Cd(II)—polymethacrylate system.

Induced reactant adsorption in normal pulse polarography of labile metal polyelectrolyte systems part 1. Study of current-potential relationship assuming potential-independent adsorption parameters

A model for the interpretation of the normal pulse polarographic reduction of a metal ion in a metal polyelectrolyte system, including both the polyelectrolyte adsorption and the induced adsorption of the metal ion, is developed. The influence of the physical parameters included in the model on the maximum and limiting currents has received special attention. This knowledge is of great importance for the development of a physical picture of the behaviour of the system. The following restrictions have been assumed: (i) large excess of the macromolecular ligand; (ii) labile complex; (iii) reversible charge transfer; (iv) Langmuirian adsorption of both the complex and the ligand species; and (v) the adsorption coefficients of the ligand and the complex are potential-independent.

Study by cyclic voltammetry of a reversible surface charge transfer reaction when the reactant diffuses to the electrode

A general theoretical equation for the I - E curve of cyclic voltammetry for a reversible surface charge transfer reaction has been established at low scan rates. It is considered that the substrate diffuses to the hanging mercury drop electrode and is adsorbed during the potential sweep. The molecules of both oxidized and reduced species are assumed to be strongly adsorbed on the electrode surface, following a Langmuir isotherm, and to form a non-compact monolayer. From this equation, the theoretical expressions for cathodic and anodic peak currents have been obtained. The equations for the I - E curve, the peak potentials and the peak currents when the film of adsorbed molecules is compact before reduction or oxidation in the negative or positive scan have also been deduced. The validity of the equations obtained has been confirmed by means of an experimental study of the benzo( c)cinnoline—dihydrobenzo( c)cinnoline system in a basic aqueous organic medium at low scan rates and substrate concentrations.

Analysis of cyclic voltammetric responses by Fourier transform-based deconvolution and convolution procedures

Numerical procedures for processing linear sweep and cyclic voltammetric responses are suggested in order to (1) deconvolve a sequence accounting for diffusion from the original signals; (2) convolve these with the same sequence. Deconvolution and convolution operations are performed via the Fourier transform method. Responses obtained by simulation of uncomplicated reversible, quasi-reversible and irreversible charge transfers are considered. The values of the parameters characterizing deconvolution and convolution responses are computed and discussed; a comparison is made with the corresponding parameters of the original current/potential curves, as well as with data reported in the literature for nernstian and totally irreversible charge transfers, obtained by following different mathematical procedures.