Mikhail A. Vorotyntsev

Electron and proton conducting polymers: recent developments and prospects

Abstract The most important topics of the rapidly developing field of conducting polymers are surveyed. Particular emphasis is laid on the problems of synthesis, structure, thermodynamics and kinetic behaviour of these systems. The relevant experiences, existing models and theories are outlined. Abundant examples of the growing applications are also discussed.

Modelling the impedance properties of electrodes coated with electroactive polymer films

The response of a metal/electroactive polymer film/solution system to a low-amplitude variation of electrode polarization is analysed, taking account of both the electrodiffusion transport of electronic and ionic species in the bulk film and non-equilibrium heterogeneous charge transfer, namely electrons at the metal-film boundary and ions at the film-solution boundary. Exact analytical solutions are obtained for concentration and electric field profiles inside the film, interfacial potential drops, and complex impedance. Their dependence on frequency and the ratio of diffusion coefficients, De and Di, are analysed. For unequal values, De ≠ Di, the electric field inside the film is shown to be non-uniform and the instantaneous concentration profile is non-symmetrical with respect to the middle-plane of the film. The impedance of the system contains (in addition to the interfacial charging and solution contributions) a frequency-independent resistivity due to ohmic potential drops in the bulk film and at both interfaces as well as distributed capacitive and resistive elements.

Electrochemical impedance spectroscopy of thin films with two mobile charge carriers: effects of the interfacial charging

In the electrochemical systems containing an excess of the background electrolyte, the faradaic process and the interfacial (‘double-layer’) charging are coupled to the fluxes of different charge carriers, the former being related to the diffusional transport of electroactive entities while the latter being realized mostly by ions of the supporting electrolyte. As a result, the interfacial capacitance Cdl may simply be added in parallel to the faradaic impedance specific for each particular system (Randles & Ershler). This simple treatment is not justified in the absence of an indifferent electrolyte, if the same charged species take part in both the electrode reaction and the double layer charging. This is the case where at least one of the ions of a binary electrolyte participates in the electron transfer process or cross the interface. A similar situation arises in the case of an electrochemically active polymer film in that mixed electronic–ionic conductivity prevails, i.e. the charging of the polymer (electron transport) is accompanied by the motion of the charge-compensating counterions (or co-ions). In such systems both interfacial processes are coupled with the same flux of the ‘electroactive’ component. Moreover, the distributions of both charged species inside the film are interrelated due to the electroneutrality condition and the self-consistent electric field so that their transport cannot be considered as pure diffusion. This paper presents an analysis of the alternating current passage across a thin film containing mobile charge carriers of two types, which for the sake of specificity are referred to as ‘electrons’ and ‘counterions’ (although the results are also valid for other systems with two charge carriers). The contributions at the interfaces related to the faradaic processes (or the ion exchange) and to the double-layer charging have been taken into consideration ‘ab initio’. Analytical expressions for the complex impedance have been obtained for three principal arrangements of the system, m ∣ f ∣ m′ (film between two electronic conductors), s′ ∣ f ∣ s (‘membrane’, film between two solutions) and m ∣ f ∣ s (modified electrode). Besides the parameters characterizing the transport processes of the charged species in the bulk film, these formulae contain four characteristics of each interface α (α=m ∣ f or f ∣ s), Rα (charge transfer resistance), Cα (interfacial capacitance), teα=1−tiα (‘double-layer numbers’) and Cμα (‘asymmetry factor’). The predicted complex-impedance plots demonstrate a greater variety of shapes compared to those predicted by traditional approaches.

Comparison of the AC Impedance of Conducting Polymer Films Studied as Electrode‐Supported and Freestanding Membranes

The ac impedance response of a symmetrically bathed membrane consisting of a conducting polymer is modeled. The model is an extension of a recent one proposed for a conducting polymer film contacting an electronic and an ionic conductor on its two faces (modified electrode geometry) and takes into account both diffusion-migration of ionic and electronic charge carriers inside the film and charge-transfer across metal/polymer and polymer/electrolyte interfaces. The membrane impedance is calculated for various combinations of parameters in order to stress the effect of diffusion coefficients, charge-transfer resistance, and double layer capacitance at the interfaces. The impedance responses in the modified electrode and membrane geometries are compared. It is thus shown how some ambiguities in the attribution of certain features of the impedance of modified electrodes to either the polymer/electrode or polymer/electrolyte interfaces may be eliminated by this comparison

Short-range electron-ion interaction effects in charging the electroactive polymer films

Abstract This paper has analyzed the effects of the polymer/solution interfacial potential as a function of electrode polarization as well as of various short-range interactions between the charged components of the polymer phase, electronic and ionic species. Charging/discharging processes depend crucially on whether the value of interaction parameter is greater (repulsion or weak attraction between the species) or less (sufficiently strong attraction) than its critical value. In the former case it can be realized as a “continuous” transition between the insulative and conductive states of the film at sweeping polarization, the difference between the film charging and discharging (“hysteresis”) being solely due to conventional relaxation processes (diffusion, slow interfacial transfer etc ). Anodic and cathodic current peaks are generally non-symmetrical, due to the film/solution potential variation. In the latter case, two quasi-equilibrium states, low- and high-density ones, coexist within a polarization range separated by a free-energy barrier so that the charging/discharging process has features of a phase transition. It may lead to a considerable hysteresis during the cycling process, even if it is realized in a quasi-equilibrium way. Variable behaviour has been found for the partial interfacial potentials versus electrode polarization, φ m/p (E) and φ p.s (E), depending on individual charges of electronic and ionic species, on the value of the global interaction parameter as well as on the ratio of different contributions to the free energy, due to electron-electron, electron-ion and ion-ion short-range interactions. These curves may be of an S- or Z-shape, possess extrema or even a loop with the self-crossing point. Highly narrow peaks are characteristic of these systems with a strong attraction between the species. There is again an asymmetry between the anodic and cathodic peaks as well as with respect to peak potentials, due to the film/solution potential variation. The ratio of anodic and cathodic peak widths depends on the particular type of the rate-determining process, eg slow electron or ion interfacial transfer or “droplets” formation.

Conductivity and space charge phenomena in solid electrolytes with one mobile charge carrier species, a review with original material

Abstract Phenomenological space charge polarization theory, involving the dependences of mobility and diffusion coefficient on the concentration of charge carriers, is developed for solid electrolytes with carriers of one kind mobile. The results are used to describe the equilibrium, transient and frequency response of capacitors and dc and ac characteristics of electrochemical cells with solid electrolyte.

Multi-component diffusion approach to transport across electroactive-polymer films with two mobile charge carriers

Abstract This paper aims to apply general relations between the thermodynamical forces (gradients of electrochemical potentials) and resulting fluxes of the species to transport phenomena in a uniform film of the electroactive polymer in contact with some other conducting media, metal(s) and/or solution(s), in the case of a low-amplitude perturbation imposed. Two kinds of mobile charged species are assumed to be present inside the film, the “electronic” and “ionic” ones. The coefficients in the above relations (friction coefficients) are expressed through the experimentally measurable macroscopic transport parameters, the total high-frequency conductivity, migration transference numbers, binary diffusion coefficient and differential redox capacitance of the film. The non-stationary diffusion equation is found to be valid for several local characteristics of the film, in particular for electron or ion charge density, or for the low-frequency current density. This equation has been solved analytically for three usual geometries of the system, metal/film/metal, metal/film/solution and solution/film/solution, upon a sinusoidal variation of the electrode potential. The final expressions for complex impedance contain contributions of the bulk film, interfacial charge-transfer resistances and (in contact with solution(s)) bulk solution. The functional form of their frequency dependence as well as the shape of complex-impedance plots has turned out to be highly simple for all geometries, being in accordance with those derived earlier within the framework of the Nernst-Planck-Einstein equations. However, the parameters of those dependences have a form different with respect to the previous expectations, leading to a modification of the procedure to interpret experimental data.

Influence of ionic size on the mechanism of electrochemical doping of polypyrrole films studied by cyclic voltammetry

Charging/discharging process of a polypyrrole film has been studied in contact with a large-size anion (tetraphenylborate) solution in acetonitrile with a comparison to that in perchlorate solutions. The overall redox activity in the former case is significantly reduced. Nevertheless, we have been able to give a clear cyclic-voltammetry characterization of the film at various bulk-electrolyte concentrations for different sweeping rates. Those data reveal two well separated waves in each potential scan direction located in the 0.1 M NaBPh4 solution at −0.38 V and −0.1 V (vs Ag/AgBPh4 0.1 M in CH3CN) in the anodic branch. The first oxidation wave obeys an ultra-thin layer mass transfer mode (temporal mode), while the second one is diffusional for sufficiently high scan rates but it approaches the same quasi-equilibrium charging regime at lower sweeping rates. Decrease of the bulk electrolyte concentration leads to a shift of both peaks in opposite directions from the merging point, keeping their shapes and intensities unchanged, with the positive or negative 60 mV slope in the semi-logarithmic coordinates. Both peaks have been attributed to a single redox transition with participation of single-charged electronic species but with different mechanisms of the charge compensation by ions. Splitting the curve into two peaks is assumed to be due to the existence of two different forms of ionic species inside the polymer phase, “free” and “bound” ones. Presence of some amount of bound anions in the reduced state is accompanied by the corresponding concentration of cations which are removed from the file during the first step of the charging process. The second redox wave is related to the free-anion insertion into the film. This approach is able to reproduce properly all features of experimental data.

Transport across an electroactive polymer film in contact with media allowing both ionic and electronic interfacial exchange

Abstract In this paper, the general theory of coupled electron-ion transport inside a film having a mixed electron-ion conductivity is applied, and the a.c. impedance expressions have been calculated for the situations where the film can exchange electrons and/or ions with the surrounding media. Important example of such system is given by a conducting polymer film between two solutions containing a redox active couple (“redox active solutions”) which is subjected to a faradaic process at the film surface with the participation of electronic species inside the film. As particular cases, the general formula describes also the systems where one or both interfacial boundaries can only be crossed by one type of charged species, electrons or ions. Besides the previously analysed situations, metal/film/metal, metal/film/background solution, or a film between two background solutions, we have obtained expressions for impedance of the film between a redox active solution and a background (without redox species) one, or between a metal and a redox active solution. Theoretical predictions for the shapes of complex impedance plots in the case of a redox active solution have been demonstrated.

Field-induced interfacial relaxation and electrical properties of the compact layer

Abstract The physical mechanisms which determine the equilibrium distance of the closest approach of solvent molecules to the electrode are discussed. Emphasis is given to the relaxation of this distance with variation of the metal electronic profile upon charging. The importance of this phenomenon in the charge dependence of the compact-layer capacity is demonstrated. Model consideration shows that new information on the subtle quantum-mechanical electronic properties of the interface can be obtained from classical capacitance measurements. In particular, it is possible to estimate the derivative of the electronic profile decay length upon charge, the parameters of the repulsion of the closed electronic shells of solvent molecules from the metal free-electron cloud, and some other quantities. At the same time, crucial qualitative conclusions about the character of the non-linear response of the metal surfaces in contact with the polar solvent can be drawn prior to a self-consistent calculation directly from basic features of the capacity curve, such as its asymmetry, the slope at the pzc, etc.