Charging process in electron conducting polymers: dimerization model

Abstract

Theory of the charging and discharging process in electron-conducting polymer films at an electrode surface has been presented. It is based on the concept of two coexisting subsystems at the polymer matrix, ‘usual’ sites P which can exchange with the electrode by the electronic charge in a quasi-reversible manner, and sites D where intermolecular bonds between neighboring polymer molecules can be formed. The charging and discharging of the latter subsystem may be realized along different reaction pathways, e.g. via the bond formation after the generation of two cation radicals within such site D in the course of the anodic scan while the bond dissociation may take place via a partially discharged state of the intermolecular bond. This difference leads to a hysteresis in cyclic voltammograms, first of all to a significant mutual shift of the anodic and cathodic peaks of the current originated from the redox transformations of D sites. An important feature of the P sites extracted from experimental CV data is their broad energetic inhomogeneity (dispersion of their redox potentials) responsible for plateaus of the current observed at high charging levels in both directions of the potential scan. Several approaches to the numerical integration of the kinetic equations for the sites' states have been analyzed, and qualitative predictions of the theoretical model have been illustrated.

Introduction

Electronically conducting polymers represent a vast area of modern research since these materials possess a unique combination of physical and chemical properties making them prospective materials for numerous applications such as in batteries and supercapacitors, micro- and nanoelectronic devices, sensors and ion release systems, electrocatalysis, as electroluminescent and electrochromic materials, various conducting and anti-corrosion coatings, non-linear optical materials, etc., see for review Refs. [1], [2], [3], [4], [5], [6], [7]. Most of them are based on the ‘electroactivity’ of these materials prepared in the form of a film at the electrode surface, i.e. on the possibility to charge and discharge them electronically within a very short time scale by varying the electrode potential, and this process can be repeated in a cyclic manner. Alternatively, this charging (mostly, by the film oxidation) can also be achieved by a chemical agent but the charging level of the polymer cannot be varied in a continuous and cyclic way.

In the ‘doped’ state the conjugated polymers possess a very high electronic conductivity, up to 100 or even 1000 S/cm, the mobile species being positively charged. The conventional theory (see, e.g. Ref. [8]) attributes it to a high mobility of single charged ‘polarons’ (whose presence is related to the observation of the ESR signal) and double-charged ‘bipolarons’. Theoretical calculations of the electronic structure of the polymer molecule led to the conclusion that there is gain in energy if two ‘polarons’ form a ‘bipolaron’ [9]. However, experimental studies of several series of solute ‘conducting oligomers’ as a function of their length provided the data for their redox potentials which are at variance with this prediction [10].

Cyclic voltammetry represents the principal source of experimental information on the charging and discharging processes in quasi-static conditions, despite the gradual accumulation of the data concerning this process obtained by alternative techniques, like EQCM [11], [12], [13], [14], [15], [16], probe beam deflection [12], [17], [18], UV–visible and ESR spectroscopy [19], [20], [21], [22], ellipsometry [23], [24], [25], [26], etc.

Cyclic voltammograms of conducting polymer films possess a specific combination of the features [27]: a couple of anodic and cathodic peaks (usually rather broad) in the vicinity of the insulating potential range, with a plateau of the current within a more positive potential interval; practical proportionality between the charging or discharging current at each potential and the scan rate, i–v, the property usually attributed to ‘reversible’ electrochemical processes; significant hysteresis of the current, i.e. a difference between the anodic and cathodic peak potentials (up to 0.4 or even 0.5 V [28], [29]) which is independent of the sweep rate.

The above concept of ‘polarons’ and ‘bipolarons’ was applied to the interpretation of these CV data, see, e.g. Ref. [19] where the hysteresis of the current was attributed to the slow transformation of the neutral sites of the polymer matrix into ‘polarons’ and then ‘polarons’ into ‘bipolarons’. However, the latter explanation fails to describe a practical independence of the peak potentials on the scan rate.

An alternative treatment was proposed by Feldberg [30] who suggested to distinguish between the ‘faradaic’ current to oxidize the polymer matrix itself and a ‘capacitive’ contribution to charge the interface between the charged matrix and the ion-solvent phase. This concept attracted an active interest (see, e.g. Refs. [31], [32], [33]), in particular, attempts were made to separate those terms experimentally within the framework of the assumption that the ‘capacitive’ charge does not give a response to the optical properties of the film. However, the electronic part of the ‘capacitive’ charge is formed by the same types of mobile electronic carriers as the ‘faradaic’ charge so that the optical spectroscopy is useless for this aim, see Ref. [7] for a more extensive discussion. As for the interpretation of CV curves, this concept attributes usually peaks to the ‘faradaic’ process while the plateaus of the current to the ‘capacitive’ term. The latter contribution is too great to be ascribed to the interface between the polymer phase (containing the matrix as well as counterions and solvent molecules between polymer chains) and the solution in macropores. Another variant of this approach attributes the ‘capacitive’ term to the charging of the ‘interface between polymer chains and counterions’ (i.e. this concept considers these components as representing two phases which can hardly be justified physically). However, this explanation of CV plateaus leaves without an explanation the CV data for ‘conducting oligomers’ [28], [34] which can be oxidized up to a similar charging level but their CV curves represent a series of separate peaks without any plateaus. Moreover, a stronger oxidation of such films leads to the chemical dimerization of those molecules, and this process is accompanied with smearing out the peaks, with a gradual appearance of the plateaus typical for conducting polymers [28].

A strong hysteresis of anodic and cathodic peaks may also be a consequence of the specific form of the relation between the energy of the system and its charging level [35] (i.e. S-shape dependence of the film charge vs. electrode potential), e.g. because of attractive interaction between electronic and ionic charge carriers inside the film [36]. Then, the continuous charging or discharging process within certain potential intervals changes at some points to a stepwise one due to the phase transition leading to the jump of the system from the initial state, which has become unstable, to a new stable one. This approach enables one to explain why the drastic change of the electronic conductivity (insulator-to-conductor or vice versa) takes place within the CV peaks. However, high values of the peak potential difference require a very strong attraction between the charge carriers inside the film which is difficult to rationalize.

Studies of the oxidation–reduction process of solute ‘conducting oligomers’ (see Refs. [10], [28], [37], [38], [39], [40] and references therein) have revealed that the cation-radical formation leads to a very rapid dimerization step. A significantly greater stability of the double-charged dimer prevents its dissociation to the same radicals during the reduction scan (if the sweep rate is not too slow) so that its discharge only takes place at a much more negative potential, see Scheme 1 [41].

This finding has led us to assume that a similar physical phenomena might take place inside the polymer films where the creation of radical cations at the matrix may induce the creation of intermolecular bonds whose decomposition can only occur at a much more negative potential, thus leading to a hysteresis in CV curves. This approach is formulated below. Its results have been partially reported at several international conferences [42], [43], [44].

The formation of intermolecular bonds inside the conducting polymer films has recently been confirmed on the basis of spectroelectrochemical data [22]. A similar phenomenon of the coupling between two cation radicals with the formation of the intermolecular bond had also been observed by ESR measurements for other electroactive polymers, TCNQ and TTF [45], [46].

Another group of specific phenomena known as ‘memory effects’ is observed after an sufficiently long exposure of the film to a high cathodic potential [47], [48], [49], [50], [51], [52], [53], [54] which have been interpreted as a manifestation of the percolation in electronic transport [55], [56], [57] or conformational relaxation of the polymer matrix [52], [53], [54]. The latter factors do not seem to play an essential role in the usual conditions of the steady-state cyclic voltammetry, without passing the interval of very high cathodic potentials.