J Agrisuelas
email: jeronimo.agrisuelas@uv.es

C Gabrielli

J J García-Jareño

H Perrot

O Sel

F Vicente

Electrochemically induced free solvent transfer in thin poly(3,4ethylenedioxythiophene) films

Keywords: Poly(3,4-ethylenedioxythiophene), Electrochemical quartz crystal microbalance, Electrochemical impedance spectroscopy, ac-Electrogravimetry, Electrochemically induced conformational changes

In dynamic intrinsically conducting films, counterions transfer and conformational movements stimulated by the electrochemical reactions affect the free water molecules transfer. Poly(3,4-ethylenedioxythiophene) or PEDOT is included in this category. Here, p-doping of PEDOT immersed in LiClO 4 aqueous solution was explored by ac-electrogravimetry. Electrochemical impedance spectroscopy combined with mass impedance spectroscopy proves useful for species identification and kinetics. For PEDOT, new equations have been developed to analyze the ac-electrogravimetry response. Quantitatively, faster free water transfer and slower coupled /free water transfer were separated. Free water transfer plays a key role as a "fingerprint" of conformational movements. This might respond to fundamental questions about the mechanism of PEDOT as well as their implication in technological devices based on this polymer.

Introduction

Since discovery of Poly (ethylenedioxythiophene) or PEDOT, scientific community undertakes several work to prove that this material is historically one of the most successful conducting polymers [START_REF] Groenendaal | Poly(3,4ethylenedioxythiophene) and its derivatives: Past, present, and future[END_REF][START_REF] Kirchmeyer | Scientific importance, properties and growing applications of poly(3,4-ethylenedioxythiophene)[END_REF]. The reversible doping state, excellent stability, regular structure without cross-linking, low band-gap, and electrochemical properties of PEDOT [START_REF] Wang | Research progress on a novel conductive polymer-poly(3,4ethylenedioxythiophene) (PEDOT)[END_REF] allow this conducting polymer to be used in promising practical applications like sensors [START_REF] Resorcarenes | [END_REF], anti-static coatings [START_REF] Jonas | 3,4-polyethylenedioxythiophene (PEDT): Conductive coatings technical applications and properties[END_REF], light-emitting devices [START_REF] Brown | Built-in field electroabsorption spectroscopy of polymer light-emitting diodes incorporating a doped poly(3,4-ethylene dioxythiophene) hole injection layer[END_REF], solar cells [START_REF] Huang | Electrochemical characterization of the solvent-enhanced conductivity of poly(3,4-ethylenedioxythiophene) and its application in polymer solar cells[END_REF], supercapacitors [START_REF] Snook | Conducting-polymer-based supercapacitor devices and electrodes[END_REF], actuators [START_REF] Cho | A solid state actuator based on the PEDOT/NBR system[END_REF] and even as a biological tissue interfacing agent [START_REF] Kim | Effect of immobilized nerve growth factor on conductive polymers: Electrical properties and cellular response[END_REF].

Morphology and electrochemical properties of conducting polymers like PEDOT depend strongly on the experimental conditions of polymerization [START_REF] Niu | Electrochemically controlled surface morphology and crystallinity in poly(3,4-ethylenedioxythiophene) films[END_REF][START_REF] Poverenov | Major Effect of Electropolymerization Solvent on Morphology and Electrochromic Properties of PEDOT Films[END_REF]. In PEDOT films, the role of incorporated free solvent molecules (not structural) during the electrochemical reaction of synthetized polymers is as important as the transfer of ions for charge balance [START_REF] Otero | Artificial Muscles: A Tool To Quantify Exchanged Solvent during Biomimetic Reactions[END_REF]. Free solvent stored by films lubricates the intermolecular movement acting as a plasticizer. On the contrary, film dehydration leads to stiffness of material [START_REF] Bund | Application of PEDOT layers for the electrogravimetric detection of sulphate and phosphate in aqueous media[END_REF][START_REF] Brown | Manipulation of electroactive polymer film viscoelasticity: the roles of applied potential and frequency[END_REF] or increase of conductivity [START_REF] Kriván | Deprotonation and Dehydration of Pristine PPy/DS Films during Open-Circuit Relaxation: an Ignored Factor in Determining the Properties of Conducting Polymers[END_REF].

Mainly, the reversible transfer of anions and solvent between solution and polymer takes place during electrochemical reactions of PEDOT [START_REF] Bund | Effect of the solvent and the anion on the doping/dedoping behavior of poly(3,4-ethylenedioxythiophene) films studied with the electrochemical quartz microbalance[END_REF][START_REF] Plieth | The role of ion and solvent transport during the redox process of conducting polymers[END_REF]. Free-volume inside the film fixes the number of free non-charged molecules, which can be inserted by the films [START_REF] Hillman | Time-Scale-and Temperature-Dependent Mechanical Properties of Viscoelastic Poly(3,4-ethylenedioxythiophene) Films[END_REF]. Simplistically, rigid film oxidation involves anion insertion for charge balancing (p-doping) in this kind of polymers. At the same time, anions exclude free solvent molecules. During film reduction, free solvent occupies rapidly the free space left by anions (undoping). This fact is the so-called anion exclusion effect. In a more realistic view, redox reactions in conducting polymers often involve macromolecular rearrangements of polymer by creation and destruction of double bonds and by the accommodation of the anions. These conformational movements affect the free volume inside the film, which is occupied by free solvent molecules. Thus, doping state of the film and molecular reconfigurations during the electrochemical reactions control the free-volume [START_REF] Bruckenstein | Consequences of Thermodynamic Restraints on Solvent and Ion Transfer During Redox Switching of Electroactive Polymers[END_REF][START_REF] Bruckenstein | Solvent and Salt Transfer Upon Redox Switching of Electroactive Polymers[END_REF][START_REF] Hillman | Solvent effects on the electrochemical p-doping of PEDOT[END_REF][START_REF] Hillman | Kinetics and mechanism of the electrochemical p-doping of PEDOT[END_REF]. Hillman et al. and Bund et al. have specifically explored the ion and solvent transfer in PEDOT films by cyclic electrogravimetric methods [START_REF] Bund | Effect of the solvent and the anion on the doping/dedoping behavior of poly(3,4-ethylenedioxythiophene) films studied with the electrochemical quartz microbalance[END_REF][START_REF] Plieth | The role of ion and solvent transport during the redox process of conducting polymers[END_REF][START_REF] Hillman | Solvent effects on the electrochemical p-doping of PEDOT[END_REF][START_REF] Hillman | Kinetics and mechanism of the electrochemical p-doping of PEDOT[END_REF]. However, the temporal sequence in the transfer of the species and the corresponding mechanisms are not fully explored [START_REF] Hillman | Role of Film History and Observational Timescale on Redox Switching Kinetics of Electroactive Films .1. a New Model for Permselective Films with Polymer Relaxation Processes[END_REF][START_REF] Hillman | Role of film history and observational timescale in redox switching kinetics of electroactive films. Part 2.-Visualizing electrochemical redox switching pathways involving four or more distinct relaxation times[END_REF]. These processes are kinetically inseparable on the timescales accessed by slow transient electrochemical techniques. Electrochemical impedance analysis proves useful to separate temporally different ions/charge transfer, however, this technique is blind for non-charged species transfer [START_REF] Hass | Electrochemical impedance analysis of the redox switching hysteresis of poly(3,4-ethylenedioxythiophene) films[END_REF]. Combining electrochemical and mass impedance spectroscopy, ac-electrogravimetry, allows an objective separation between ions/charge and solvent transfer [START_REF] Agrisuelas | Ionic and Free Solvent Motion in Poly(azure A) Studied by ac-Electrogravimetry[END_REF][START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF][START_REF] Agrisuelas | Effects of anion size on the electrochemical behavior of H2SO4-structured poly(o-toluidine) films. An ac-electrogravimetry study in acid solutions[END_REF].

The aim of this work is to go beyond of the previous electrogravimetric investigations exploiting the ac-electrogravimetry. This technique may separate the dynamic processes (anion transfer and free water transfer) that occur during the redox reactions of thin PEDOT films. Moreover, the study of free solvent transfer can extend the level of detail of the electrochemically induced conformational changes in PEDOT films.

Recently, a refined analytical procedure was proposed to study the anion pdoping of intrinsically conducting polymers (ICPs) by ac-electrogravimetry [START_REF] Agrisuelas | Polymer dynamics in thin p-type conducting films investigated by acelectrogravimetry. Kinetics aspects on anion exclusion, free solvent transfer, and conformational changes in poly(o-toluidine)[END_REF]. Here, the theory section is limited to present basic mathematical developments. The anion exclusion effect is constantly assumed in the analytical equations used to interpret the results. Thus, if the coupled anion/free water electrogravimetric response is removed from the experimental data, the remaining electrogravimetric response is because of the free water transfer stimulated by the conformational changes of the films. The kinetics transfer of this free solvent acts as a "fingerprint".

In addition to the ac-electrogravimetry study, cyclic voltammetry (CV) coupled with the Electrochemical Quartz Crystal Microbalance (EQCM) were exploited to estimate the solvent transfer during PEDOT film electrogeneration in acetonitrile/LiClO 4 solution and during the redox reaction of PEDOT film in aqueous LiClO 4 solution.

Conformational changes have a key role in applications as actuators and few studies have directly addressed the kinetics of conformational changes in electroactive polymers [START_REF] Otero | Biomimetic intracellular matrix (ICM) materials, properties and functions. Full integration of actuators and sensors[END_REF][START_REF] Otero | Structural and Biomimetic Chemical Kinetics: Kinetic Magnitudes Include Structural Information[END_REF]. Therefore, the results presented here may have marked importance for several technological applications involving PEDOT as functional coatings in contact with a liquid phase.

Ac-electrogravimetry theory

In aqueous solution, during the redox reaction of a p-type conducting polymer , monovalent anion, , transfer, which compensates the excess or defect of charge inside the film, can govern the opposite transfer of water molecules (exclusion effect in Figure 1). Assuming a rigid polymer, the number of water molecules, , replaced by the anion insertion depends on anion volume, , therefore, .

As it was demonstrated earlier [START_REF] Gabrielli | Ac-Electrogravimetry Study of Electroactive Thin Films. I. Application to Prussian Blue[END_REF][START_REF] Gabrielli | Ac-Electrogravimetry Study of Electroactive Thin Films. II. Application to Polypyrrole[END_REF], species kinetics in thin films depend on their resistance to cross the polymer|solution interface:

(1)

where is the hydrated polymer and is the doped polymer matrix. The parameter is the kinetic constant of anion expulsion from polymer and is the kinetic constant of anion insertion to polymer from solution.

Changes of anion concentration, , during the small sine wave potential perturbation, , can be defined as a function of perturbation frequency, , [START_REF] Gabrielli | Charge transport in electroactive thin films investigated by ac electrogravimetry[END_REF]:

(

) 2
where is the thickness of the polymer film, is the angular frequency ( ), ,

where, is the maximum concentration of the sites for insertion, is the minimum concentration of the occupied sites and is concentration in solution. is and where is the formal potential and is a preexponential factor of the kinetic rate constants independent of applied potential .

The parameters, and are the Tafel coefficients:

(5)

where is the gas constant and is the absolute temperature. From these coefficients, one can estimate the number of electrons ( ) involved in the faradaic process and the symmetry of direct and reverse transition on the formal redox potential [START_REF] Agrisuelas | Innovative Combination of Three Alternating Current Relaxation Techniques: Electrical Charge, Mass, and Color Impedance Spectroscopy. Part I: The Tool[END_REF][START_REF] Agrisuelas | Innovative Combination of Three Alternating Current Relaxation Techniques: Electrical Charge, Mass, and Color Impedance Spectroscopy. Part II: Prussian Blue reversible arrow Everitt's Salt Process[END_REF].

Often, electrochemical reactions of film induce conformational changes (swelling, shrinking, compaction, or relaxation). Therefore, a constant thickness of films cannot be considered since it may change depending on the polarization potential [START_REF] Kim | Correlation between ion-exchange properties and swelling/shrinking processes in hexasulfonated calix[6]arene doped polypyrrole films: ac-electrogravimetry and electrochemical atomic force microscopy investigations[END_REF][39][START_REF] Lizarraga | Quasi-Equilibrium Volume Changes of Polyaniline Films upon Redox Switching. Formal Potential Distribution and Configurational Modeling[END_REF][START_REF] Kaneto | Contribution of conformational change of polymer structure to electrochemomechanical deformation based on polyaniline[END_REF].

Eq (2) is slightly modified in terms of surface concentration as [START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF][START_REF] Agrisuelas | Effects of anion size on the electrochemical behavior of H2SO4-structured poly(o-toluidine) films. An ac-electrogravimetry study in acid solutions[END_REF]: [START_REF] Brown | Built-in field electroabsorption spectroscopy of polymer light-emitting diodes incorporating a doped poly(3,4-ethylene dioxythiophene) hole injection layer[END_REF] where is .

Based on this model, theoretical electrochemical impedance, is expressed as: [START_REF] Huang | Electrochemical characterization of the solvent-enhanced conductivity of poly(3,4-ethylenedioxythiophene) and its application in polymer solar cells[END_REF] where is the uncompensated solution resistance, is the double layer capacity, is the Faraday constant, and is the active electrode surface area.

The electrical charge/potential transfer function, , is equal to: [START_REF] Snook | Conducting-polymer-based supercapacitor devices and electrodes[END_REF] which is better to compare with the sinusoidal electrogravimetric response.

Considering the participation of anion and water in mass changes, the mass/potential transfer function, , is:

(9)
and by assuming the exclusion effect, and (Figure 1). Then eq [START_REF] Cho | A solid state actuator based on the PEDOT/NBR system[END_REF] is simplified to: [START_REF] Kim | Effect of immobilized nerve growth factor on conductive polymers: Electrical properties and cellular response[END_REF] where is the molar mass of the species involved ( or ) and and have a similar meaning as eq (3) and (4), respectively. is 1 because of insertion during oxidation, whereas, is 1 because of expulsion induced by anion insertion.

In dynamic films, eq [START_REF] Kim | Effect of immobilized nerve growth factor on conductive polymers: Electrical properties and cellular response[END_REF] cannot explain the electrogravimetric response [START_REF] Agrisuelas | Polymer dynamics in thin p-type conducting films investigated by acelectrogravimetry. Kinetics aspects on anion exclusion, free solvent transfer, and conformational changes in poly(o-toluidine)[END_REF].

The conformational changes, which affect the transfer of free water molecules, have different kinetics than anion transfer. A more complete and realistic expression for takes into account both kinds of free water transfers as: [START_REF] Niu | Electrochemically controlled surface morphology and crystallinity in poly(3,4-ethylenedioxythiophene) films[END_REF] where indicates the direction of transfer and the number of molecules of associated with conformational movements ( ) can be equal or different than . and are kinetic parameters of free water transfer from induced conformational movements.

Experimental

Film preparation

The electrochemical polymer deposition and characterization were performed by cyclic voltammetry (CV) using an AUTOLAB potentiostat-galvanostat (PGSTAT302).

A lab-made oscillator acted as an Electrochemical Quartz Crystal Microbalance (EQCM) at room temperature (about 2952 K). The three-electrode cell involved a reference electrode (Saturated Calomel Electrode or SCE, Tacussel XR 600) and a platinum counter electrode. The working electrode was a gold electrode ( 0.3 cm 2 ) patterned on a 9 MHz quartz crystal resonator (TEMEX, France). All the solutions were prepared with deionized and double-distilled water. The potential of the working electrode is referred to the SCE reference electrode in all measurements. PEDOT films were electrodeposited after 10 voltammetric cycles between 0.2 V and 1.1 V at 100 mV s -1 (~ 80 µg cm 2 of the deposited mass). The polymerization solution was 0.1 M LiClO 4 (Sigma-Aldrich) and 0.05 M EDOT (Aldrich) in acetonitrile (Sigma-Aldrich) solution.

Film conditioning

Previously to ac-electrogravimetry experiments, PEDOT film was cycled between 0.4 V and 0.8 V at 100 mV s 1 in 0.1 M LiClO 4 aqueous solution. After the first cycle, changes in the shape of the voltammetric and electrogravimetric responses are almost negligible at least within 10 CV cycles.

ac-Electrogravimetry

ac-Electrogravimetry investigation of the PEDOT films was performed at steady state potentials in the range of 0.7 V to 0.25 V in the same solution. The lower limit was agreed to avoid any significant degradation [START_REF] Zanfrognini | A UV-Visible/Raman spectroelectrochemical study of the stability of poly(3,4ethylendioxythiophene) films[END_REF]. For that, a fast EQCM was coupled with a four-channel frequency response analyzer (FRA, Solartron 1254) and a potentiostat (SOTELEM-PGSTAT Z1). The modified working electrode was polarized at a given potential and a sinusoidal potential perturbation with a small amplitude (10 mV rms) was superimposed between 65 kHz and 0.01 Hz. The microbalance frequency change, and the alternating current response, , were sent to the four channels FRA, which allowed the electrogravimetric transfer function, and the electrochemical impedance, , to be simultaneously obtained. Finally, the experimental data were fitted with the theoretical expressions given in Section 2 by means of Levenberg-Marquardt method [START_REF] Macdonald | Comparison and application of two methods for the least squares analysis of immittance data[END_REF].

Results and discussion

Several works have tried to unfold stoichiometry and mechanisms of electrochemically induced solvent transfer in PEDOT films. Here, the solvent transfer is studied from the cyclic electrogravimetric response (EQCM) of PEDOT in acetonitrile and water solutions. The purpose of the EQCM study is not to make novel claims, but to show that PEDOT produced is a typical film of those studied elsewhere by cyclic voltammetry. However, these results are significant in the sense that they provide a first approximation to interpret ac-electrogravimetry results.

Free acetonitrile transfer during p-doping

In acetonitrile, EDOT radicalization starts when the potential applied reaches to 1 V. The first CV in Figure 2 shows a rising intensity with a mass jump on electrode of about 4 µg cm 2 . The mass/charge ratio is about +150 g mol 1 between 1 V and 1.2 V in both scan directions. Considering the molar mass of monomer ( 142 g mol 1 ),

the ratio points to one electron for one monomer radicalization. The film deposition increase monotonically after the third CV cycle (inset of Figure 2). The final mass deposited after 10 CV cycles is about 8 µg cm 2 . This amount corresponds to a thickness of about 60 nm assuming that the monomer density is ~1.3 g cm 3 . This estimation had not considered the ionic and solvent species population inserted inside film during the electropolymerization. Despite this, we can assume a thin PEDOT film [START_REF] Hillman | Time-Scale-and Temperature-Dependent Mechanical Properties of Viscoelastic Poly(3,4-ethylenedioxythiophene) Films[END_REF].

After few cycles, a pseudo-capacitive behavior appears between 0.2 V and 1 V without distinct redox peaks (Figure 3a). During the oxidation reaction, positive values of mass derivative proves clearly the mass increase owing to insertion of (pdoping) and during the reduction reaction, negative values of mass derivative are because of dedoping.

The instantaneous mass/electrical charge ratio, , has proved especially useful in the analysis of the electrochemical reactions during CV experiments [44]. The mechanism of free acetonitrile transfer can be evaluated with this equation. In acetonitrile, PEDOT film shows a compact structure owing to PEDOTsolvent interactions [START_REF] Chiang | The effects of solvent on the electrochromic properties of poly(3,4-ethylenedioxythiophene)[END_REF]. However, molecular reconfiguration is assumed in the electrochemical mechanisms of conducting polymers [START_REF] Grande | Conformational movements explain logarithmic relaxation in conducting polymers[END_REF]. An approximation to polymer conformational movements consists of solving the stoichiometric relation between the doping molecules, in this case , and the solvent transfer [START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF][START_REF] Agrisuelas | Effects of anion size on the electrochemical behavior of H2SO4-structured poly(o-toluidine) films. An ac-electrogravimetry study in acid solutions[END_REF]. By using the commercial software ChemBio3D Ultra v. 12.0 ChemBioOffice 2010, the volume of fact is observed in the potential range between 0.2 V to 0.2 V when doping level of PEDOT film is lower. In this potential range, PEDOT could not be completely relaxed and acts as a rigid film. However, the molecular arrangements of a relaxed and doped PEDOT film allow the coupled insertion of and between 0.2 V and 1 V.

Free water transfer during p-doping

In water solution (Figure 4a), PEDOT film generated in acetonitrile preserves the capacitor-like shape, and displays not well defined redox peaks with a formal potential around 0 V [START_REF] Bund | Application of PEDOT layers for the electrogravimetric detection of sulphate and phosphate in aqueous media[END_REF][START_REF] Efimov | EQCM study of electropolymerization and redox cycling of 3,4-polyethylenedioxythiophene[END_REF]. However, the electrogravimetric response proves different.

It is expected that the exchange of large solvent molecules ( ) by small solvent molecules ( ) should improve the study of conformational changes in PEDOT films.

Like in acetonitrile, shows two different tendencies in Figure 4b.

is lower than molar mass of between 0.2 V and 0.1 V. Thus, water transfer is in opposite direction of the anion transfer. On the contrary, is higher than between 0.1 V and 0. the exclusion effect can be neglected in this potential range. As the doping level increases, the coulomb repulsion between charged sites becomes stronger, forcing the polymer to expand [START_REF] Chen | Electrochemically Induced Volume Changes in Poly(3,4-ethylenedioxythiophene)[END_REF].

Like in systematically CV experiments [START_REF] Eliseeva | Mass transfer of ions and solvent at redox processes in poly-3,4-ethylenedioxythiophene films[END_REF], conformational changes during electrochemical reaction hinder to reach a complete understanding of the temporal sequence of redox mechanism in PEDOT films. This aspect will be elucidated by acelectrogravimetry.

Kinetic model for PEDOT films in LiClO 4 aqueous media

In a first sight, we can distinguish up to three capacitive processes in the experimental from raw electrochemical impedance. Figure 5 shows all processes at two representative potentials, namely 0.25 V and 0.5 V.

Around 10-1 KHz, a capacitive process ( ) is always observed at all potentials.

This process is considered as a , circuit because this is not associated to the ionic transfer. So, the partial contribution of this process to function is [START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF]: [START_REF] Poverenov | Major Effect of Electropolymerization Solvent on Morphology and Electrochromic Properties of PEDOT Films[END_REF] This faradaic process is faster than transfer in PEDOT film and can be the reason of the pseudo-capacitive current observed in CV experiments (Figure 4). In this time domain, the electrons from electrode may penetrate in the polymer only close to the electrode|polymer interface. Ions in solution are not sufficiently fast to cross the polymer|solution interface. PEDOT film acts as a dielectric material separating both charged planes to form a pseudo-capacitor [START_REF] Snook | Conducting-polymer-based supercapacitor devices and electrodes[END_REF][START_REF] Lei | Effect of poly(3,4-ethylenedioxythiophene) (PEDOT) in carbon-based composite electrodes for electrochemical supercapacitors[END_REF].

At low frequencies domain, shows a quasi-vertical branch at more cathodic potentials (Figure 5). This parallel reaction ( ) is usually observed in conducting polymers deposited on electrodes [START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF][START_REF] Agrisuelas | Vis/NIR spectroelectrochemical analysis of poly-(Azure A) on ITO electrode[END_REF][START_REF] Martinez | Effect of the Electrolyte Concentration and Substrate on Conducting Polymer Actuators[END_REF]. Like above, the partial contribution to is fitted to a , circuit as: [START_REF] Otero | Artificial Muscles: A Tool To Quantify Exchanged Solvent during Biomimetic Reactions[END_REF] In between these two frequency ranges, the partial contribution of associated to transfer can be expressed using eq [START_REF] Snook | Conducting-polymer-based supercapacitor devices and electrodes[END_REF] with some modifications: [START_REF] Bund | Application of PEDOT layers for the electrogravimetric detection of sulphate and phosphate in aqueous media[END_REF] This term considers a constant phase element introduced as an exponent of .

Here, is a mathematical correction to achieve the best fittings because often, real samples do not fit ideal equations ( ) [START_REF] Gabrielli | Impedance Investigation of the Charge Transport in Film-Modified Electrodes[END_REF][START_REF] Mathias | An Alternating-Current Impedance Model Including Migration and Redox-Site Interactions at Polymer-Modified Electrodes[END_REF]. This correction does not cause any change in the physical meaning of the kinetic parameters [START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF].

Accordingly, the equation used for the multiparametric fitting process was:

Reasonable convergences are found using this equation as the simulations show (solid lines in Figure 5). It is important to observe values are close to ideality (0.848±0.006) at all polarization potentials. This corroborates with the low thickness of the PEDOT film. In thicker films, a Warburg-like response due to the charge diffusion inside the film should evolve far from unity [START_REF] Hass | Electrochemical impedance analysis of the redox switching hysteresis of poly(3,4-ethylenedioxythiophene) films[END_REF]. The kinetic parameters for will be used for fittings of .

Up to here, free water transfer does not take part in the charge balance owing to the neutral character of solvent. However, water insertion and expulsion involve in the effective mass changes. Firstly, we consider an exclusion effect ( ) by anions at all potentials. Considering eq [START_REF] Kim | Effect of immobilized nerve growth factor on conductive polymers: Electrical properties and cellular response[END_REF], the partial contribution of of this effect is:

(16)
To detect/separate free water transfer out of exclusion effect, the analysis of real part of as a frequency function at different potentials can be useful (Figure 6). The results together with CV discussion help to propose a theoretical equation of for PEDOT.

As it was expected, shows values above and below of . We However, evolution on frequency provides more information. Up to 1 Hz, exhibits lower values than those that appear at lower frequencies, especially at positive potentials (Figure 6). Thus, the water exclusion by anions is expected. However, the ionic transfer does not occur above 100 Hz because the diffusivity of ions is low. The free water transfer may be governed by a different

Thus, the resulting theoretical expression of transfer function is:

(19)
where is , , or is 1 for species inserted during polymer oxidation or 1 for species inserted during polymer reduction. The and parameters represent the number of water molecules transferred by electron transfer because of changes of free volume inside film driven by electrochemically induced conformational changes.

To reduce the number of free parameters for later fittings, some values are fixed in eq [START_REF] Hillman | Time-Scale-and Temperature-Dependent Mechanical Properties of Viscoelastic Poly(3,4-ethylenedioxythiophene) Films[END_REF] as following:

can be fixed as 1 g mol 1 where 1, 18 g mol 1 and considering and .

-, and come from fittings between experimental and eq [START_REF] Brown | Manipulation of electroactive polymer film viscoelasticity: the roles of applied potential and frequency[END_REF].

is 18 g mol 1 owing to the expulsion from film during insertion in the oxidation.

-18 g mol 1 because is inserted with during the oxidation.

Therefore, six parameters are free for fittings within physically reasonable bounds, namely , , , , and . Figure 7 shows good convergences between experimental curve and eq [START_REF] Hillman | Time-Scale-and Temperature-Dependent Mechanical Properties of Viscoelastic Poly(3,4-ethylenedioxythiophene) Films[END_REF]. Like in , and values obtained are close to ideality (0.89±0.05).

From CV results, the exclusion effect is neglected between 0.1 V and 0.8 V. An alternative to eq [START_REF] Hillman | Time-Scale-and Temperature-Dependent Mechanical Properties of Viscoelastic Poly(3,4-ethylenedioxythiophene) Films[END_REF] may include this fact. However, eq [START_REF] Hillman | Time-Scale-and Temperature-Dependent Mechanical Properties of Viscoelastic Poly(3,4-ethylenedioxythiophene) Films[END_REF] was applied to all studied potentials with an excellent agreement. Later, the analysis of kinetic parameters will show if there is exclusion effect or not.

Identification of electrochemical processes.

The derivative of the surface insertion law for with respect to the potential at , , is calculated as ratio. This ratio has a similar meaning as the theoretical derivation of a voltammetric peak. Therefore, the electrochemical reaction of PEDOT can be positioned on the potential scale (Figure 8). can be mathematically fitted to [START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF][START_REF] Gabrielli | Ions and solvent transport across conducting polymers investigated by ac electrogravimetry. Application to polyaniline[END_REF][START_REF] Agrisuelas | An approach to the electrochemical activity of poly-(phenothiazines) by complementary electrochemical impedance spectroscopy and Vis-NIR spectroscopy[END_REF]: [START_REF] Bruckenstein | Consequences of Thermodynamic Restraints on Solvent and Ion Transfer During Redox Switching of Electroactive Polymers[END_REF] and it can be simulated using the parameters showed in the inset of Figure 8.

Like in CV, PEDOT shows only one electrochemical process with a potential peak around 0 V. About 5.3 nmol cm 2 of can be inserted during the redox conversion of PEDOT. Moreover, a constant amount of (30 nmol cm 2 V 1 ) is transferred between film and solution independently of oxidation state. This fact agrees with the existence of polaronic forms even in reduced and apparently undoped states of PEDOT [START_REF] Zykwinska | ESR spectroelectrochemistry of poly(3,4-ethylenedioxythiophene) (PEDOT)[END_REF].

Obtaining n' and n''

At this point, and are acquired from fittings. The set of transferred out of exclusion effect in the same direction ( ) and in the opposite direction ( by electron transfer are still unknown.

By taking into account the simplistic scheme of anion and free water transfers in

)

Table 1 shows the evolution of the number of on the oxidation state of PEDOT. The number of free water molecules excluded by anion ( ) is assumed constant at 4.7 in the overall studied potentials. However, the transfer of water molecules in both direction ( and ) increases as PEDOT is oxidized owing to the swelling of PEDOT structure [START_REF] Chen | Electrochemically Induced Volume Changes in Poly(3,4-ethylenedioxythiophene)[END_REF]. At potentials where PEDOT is doped, the number of water molecules transferred is about 60. This fact indicates a wide freevolume inside PEDOT favored by two elements, acetonitrile template during the polymerization and anion inserted during the oxidation.

The net water molecules transferred calculated as shows that a net insertion of by anion (hydration of film) takes place from 0 V to positive potentials when PEDOT is predominantly doped. On the contrary, a net loss of (dehydration of film) takes place from 0 V to negative potentials when PEDOT is predominantly undoped. As it was commented above, CV also shows this evolution (Figure 4).

Ease of the species transfer at the polymer|solution interface.

Parameter refers to the ease of species transfer to cross the polymer|solution interface [START_REF] Benito | An electrochemical impedance and ac-electrogravimetry study of PNR films in aqueous salt media[END_REF]. As it is expected, species transfer takes place easier around the formal potential of PEDOT under these experimental conditions (Figure 9). and are 2.0-2.5 µmol s 1 cm 2 V 1 because both species are transferred coupled.

shows values slightly higher indicating an easier transfer of free water in the opposite direction of anions.

has exponential dependence at potentials far from the peak potential as [START_REF] Agrisuelas | Usefulness of F(dm/dQ) function for elucidating the ions role in PB films[END_REF]:

where is , or , represents the maximum value for this function at = , and represent the peak potential of .

By considering eq [START_REF] Jonas | 3,4-polyethylenedioxythiophene (PEDT): Conductive coatings technical applications and properties[END_REF], for the oxidation half-reaction: [START_REF] Hillman | Role of Film History and Observational Timescale on Redox Switching Kinetics of Electroactive Films .1. a New Model for Permselective Films with Polymer Relaxation Processes[END_REF] and for the reduction half-reaction:

Rate of species transfer at the polymer|solution interface.

As it was expounded above, provides the transfer rate of species, eq (3).

Figure 10 shows the evolution of on the potential. The exclusion effect ( ) and the insertion of water molecules out of exclusion effect ( ) have quasi-identical values about 60-65 s 1 . Moreover, the rates decrease as the polymer becomes undoped and, possibly, becomes more compact. Although mathematically can be separated, the results point out to coupled transitions. Unlike CV, anion exclusion can be neglected at all studied potentials because the exclusion is damped by a coupled anion and free water transfer in the same direction. On the contrary, the rate of water expulsion out of exclusion effect ( ) is a faster process of about 90 s 1 at all polarization potentials.

In general, this rate is independent of the oxidation state of PEDOT.

The different rate between both transfers can be caused by the formation of two kinds of charge defects (polarons) previously observed in PEDOT [START_REF] Zykwinska | In situ EPR spectroelectrochemical studies of paramagnetic centres in poly(3,4ethylenedioxythiophene) (PEDOT) and poly(3,4-butylenedioxythiophene) (PBuDOT) films[END_REF] and derivative polymers [START_REF] Visy | Polythiophene puzzle -a plausible solution[END_REF][START_REF] Visy | Direct in situ conductance evidence for non-faradaic electrical processes in poly(3-methylthiophene)[END_REF]. On the one hand, the faster free water transfer can be related to highly mobile polarons delocalized on isolated polymer segments involving fast conformational movements of PEDOT backbone. On the other hand, the localized polarons should be because of insertion inside PEDOT, which fixes polarons on the PEDOT backbone.

Mechanistic model

From results, we suggest an electrochemical mechanism of PEDOT in aqueous solution considering the cube scheme of mechanism and species pathways of PEDOT proposed by Hillman et al. [START_REF] Hillman | Role of Film History and Observational Timescale on Redox Switching Kinetics of Electroactive Films .1. a New Model for Permselective Films with Polymer Relaxation Processes[END_REF][START_REF] Hillman | Role of film history and observational timescale in redox switching kinetics of electroactive films. Part 2.-Visualizing electrochemical redox switching pathways involving four or more distinct relaxation times[END_REF].

To simplify the discussion, we choose to explain the oxidation mechanism but it can be extrapolated to the reduction mechanism. In a first step, the removal of electrons in the molecular structure of PEDOT is the fastest process. Then, double bond formation shortens the distance between EDOT units decreasing the thickness of the film [START_REF] Kim | Electronic Evolution of Poly(3,4ethylenedioxythiophene) (PEDOT): From the Isolated Chain to the Pristine and Heavily Doped Crystals[END_REF][START_REF] Roncali | Conjugated Poly(thiophenes) -Synthesis, Functionalization, and Applications[END_REF]. The free volume of the film is reduced involving a fast expulsion of free water molecules (eq [START_REF] Hass | Electrochemical impedance analysis of the redox switching hysteresis of poly(3,4-ethylenedioxythiophene) films[END_REF]). As there is still anions transfer, this facilitates the transfer of free water (Figure 9). Dehydration step involves an increase of the dielectric constant of the film which could contribute to the behavior of PEDOT [START_REF] Plieth | The role of ion and solvent transport during the redox process of conducting polymers[END_REF][START_REF] Kriván | Key role of the desolvation in the achievement of the quasi-metallic state of electronically conducting polymers[END_REF]. The here-proposed analysis of ac-electrogravimetry results and the mechanistic interpretation for PEDOT films can be used for further investigations on conducting polymers doped with immobile ions or ionomers like the PEDOT:Polystyrene sulfonate system [START_REF] Hong | Transparent graphene/PEDOT-PSS composite films as counter electrodes of dye-sensitized solar cells[END_REF][START_REF] Jonsson | The effects of solvents on the morphology and sheet resistance in poly (3,4-ethylenedioxythiophene)polystyrenesulfonic acid (PEDOT-PSS) films[END_REF][START_REF] Greczynski | Photoelectron spectroscopy of thin films of PEDOT-PSS conjugated polymer blend: a mini-review and some new results[END_REF].

CONCLUSIONS

This work is the first example of an ac-electrogravimetry study on the PEDOT films in LiClO 4 aqueous solutions. The general equations to analyze the electrogravimetric response considering the exclusion effect are successfully applied.

Mechanistic aspects in this p-type polymer prove to be more complicated than expected. Despite this, several interesting conclusions can complete the redox mechanism of PEDOT film in unprecedented detail.

Two different free water transfer processes were recognized and temporally separated by ac-electrogravimetry. The high electron conductivity of PEDOT allows faster molecular movements. The molecular reconfiguration may cause faster free water transfer before the anion transfer occurs. Film doping by anions involves a charge accommodation by repulsive interactions creating free volume. This fact favors the simultaneous free water insertion.

TABLES Table 1. Number of water molecules excluded by anion transfer (

), , number of transferred water molecules owing to conformational changes ( ) in the opposite direction of anions, , calculated from eq [START_REF] Bruckenstein | Solvent and Salt Transfer Upon Redox Switching of Electroactive Polymers[END_REF] and number of transferred water molecules owing to conformational changes in the same direction of anions, , calculated from eq [START_REF] Hillman | Solvent effects on the electrochemical p-doping of PEDOT[END_REF]. The evolution of net water molecules transferred during the electrochemical reaction of PEDOT film was calculated as .

/ Inset is the increment of the mass after each cycle. The solid line is a guide-to-the eye.

FIGURES e 

Figure 3b shows at the 10

 10 Figure 3b shows at the 10 th cycle of electropolymerization. The obtained values are close to the molar mass of ( 99.5 g mol 1 ). Between 0.2 V and 1V, reaches values close to 150 g mol 1 corresponding to the transfer of one together a one acetonitrile molecule ( g mol 1 ) between the film and solution by electron transfer. On the contrary, is close to 70 g mol 1 between 0.2 V and 0.2 V. This value corresponds to the theoretical values of the transfer of one with the opposite transfer of one acetonitrile molecule by electron transfer. Under these experimental conditions, is not involved in the charge balance[17].

  ( ) and acetonitrile ( ) is calculated from the Connolly solventexcluded volume. Considering and , one can replace approximately one acetonitrile molecule as a result of an exclusion effect. This

  8 V. Here, anion and solvent transfer by electron transfer are coupled in the same direction. Considering water volume ( ), can exclude about 4.7 water molecules. At 0.2 V, insertion results in the expulsion of about 3 water molecules. The number of excluded water molecules gradually decrease to 0 at 0.1 V. These values are far from the theoretical values. On the contrary, the number of water molecules accompanying the anion insertion goes from 0 at 0.1 V, to close to 3 water molecules around 0.8 V. Thus,

  can organize the discussion as a function of both parameters, perturbation frequency and polarization potential. As a function of applied potential, trends are similar to those observed in CV experiments. At more negative potentials, is lower than because exclude during the species transfers. On the contrary, reaches values above at more positive values. Film expansion allows the transfer of and in the same direction[48].

  process. PEDOT films have shown faster electrochromic switches up to a modulation frequency of 100 Hz[START_REF] Doherty | Potential-modulated, attenuated total reflectance spectroscopy of poly(3,4-ethylenedioxythiophene) and poly(3,4-ethylenedioxythiophene methanol) copolymer films on indium-tin oxide[END_REF]. The faster electronic transfer between the electrode and PEDOT may lead to macromolecular conformational changes by formation and destruction of double bonds. Therefore, conformational changes can involve a free water transfer because water has a higher mobility than anion.The main question is the flux direction of water molecules regarding anion transfer. By taking the results at 0.25 V as a reference, lower values of than are obtained around 100 Hz. After that, an increase of above occurs up to constant values around 125 g mol 1 in the slow perturbation domain (between 1 and 0.01 Hz). Thus, fast structural movements of PEDOT involve the expulsion of (from now on, ) and a slower free water insertion is expected with anion insertion (from now on, ) during oxidation, opposite during reduction. The partial contribution of of both free water transfers can be expressed as:[START_REF] Bund | Effect of the solvent and the anion on the doping/dedoping behavior of poly(3,4-ethylenedioxythiophene) films studied with the electrochemical quartz microbalance[END_REF]

Figure 1 ,

 1 Figure 1, one monovalent anion transfer involves the transfer of one set of water molecules owing to exclusion effect (). Extrapolating to PEDOT, it is possible to estimate and considering that surface concentration of is equal to surface concentration of and ,[START_REF] Agrisuelas | Kinetic and Mechanistic Aspects of a Poly(o-Toluidine)-Modified Gold Electrode. 2. Alternating Current Electrogravimetry Study in H2SO4 Solutions[END_REF][START_REF] Agrisuelas | Effects of anion size on the electrochemical behavior of H2SO4-structured poly(o-toluidine) films. An ac-electrogravimetry study in acid solutions[END_REF]. Thus,

  5 imply the variation of on the applied potential presents a symmetry on the peak potential, and values for are the same for direct and reverse reaction. In any other case, values are different, and the dependence of on the applied potential should be asymmetric. At 298 K, = 19.5 V 1 for = 1 and = 0.5 since one electrochemical reaction occurs. From the slope of versus plot, values around 3 V 1 are determined, which are close to that obtained in Figure 8 ( V 1 ). Lateral interactions between randomly distributed electroactive sites lessen the theoretical value of considering the Laviron model based on the Frumkin-type isotherm[29]. These low values point to a very intensive lateral interaction between charged sites of PEDOT.

  defects are compensated with the insertion increasing the polarity of PEDOT[START_REF] Chen | Electrochemically Induced Volume Changes in Poly(3,4-ethylenedioxythiophene)[END_REF]. This fact involves a mechanical accommodation of charged polymeric chains and stored anions inside the PEDOT film by repulsive interactions (eq[START_REF] Agrisuelas | Ionic and Free Solvent Motion in Poly(azure A) Studied by ac-Electrogravimetry[END_REF]). Possibly, conformational movements translated themselves as side-chain motions, which create free volume (swelling of the film). Simultaneously, this free volume is rapidly occupied by free water molecules from solution as the similar values of and point out to.

FIGURES CAPTIONSFigure 1 .

 1 FIGURES CAPTIONS Figure 1. Electrode|film|solution cross-section of a rigid polymer showing the exclusion effect caused between anions ( ) and free water molecules ( ). and are the kinetic constants of anion and free water insertion to polymer, respectively. and are the kinetic constants of anion and free water expulsion from polymer, respectively. is the polymer film thickness and the circles represent the molecule volume.

Figure 2 .

 2 Figure 2. Selected cyclic voltammograms of PEDOT electrogeneration in 0.1 M LiClO 4 and 0.05 M PEDOT in acetonitrile between 0.2 V and 1.2 V. Scan rate is 100 mV s 1 .

Figure 3 .

 3 Figure 3. Tenth cyclic voltammogram and corresponding time differential of the mass

Figure 4 .

 4 Figure 4. Representative cyclic voltammogram and corresponding time differential of

Figure 5 .

 5 Figure 5. Experimental (symbols) and theoretical (lines) charge/potential transfer

Figure 6 .

 6 Figure 6. Real part of mass/charge transfer function at low frequency domain,

Figure 7 .

 7 Figure 7. Experimental (symbols) and theoretical (lines) mass/potential transfer function, of a thin PEDOT film in 0.1 M LiClO 4 aqueous solution at 0.25 V (a) and 0.5 V (b). Inset is a cyclic voltammetry of thin PEDOT film in 0.1 M LiClO 4 aqueous solution between -0.4 V and 0.8 V. Scan rate 100 mV s 1 .

Figure 8 .

 8 Figure 8. Evolution of the derivative of the insertion law of , , at different polarization potentials of a thin PEDOT film in 0.1 M LiClO 4 aqueous solution. Solid line is the simulation of eq (20) using the reached parameters by fitting of experimental results. The fitting parameters are included inside the plot.

Figure 9

 9 Figure 9., and evolution with respect to potentials perturbation

Figure 10

 10 Figure 10., and evolution at different polarization potentials

Figure 1 - 4 Figure 3 -

 143 Figure 1

Figure 7 -Figure 10

 710 Figure 7

Electrode Solution Gold Electrode Ionic channel of film

								Ionic channel of film			Solution
	H 2 O	H 2 O	H 2 O	H 2 O	H 2 O			H 2 O	H 2 O	H 2 O	H 2 O	H 2 O		H 2 O
	H 2 O H 2 O	H 2 O H 2 O	H 2 O H 2 O	H 2 O H 2 O	H 2 O H 2 O	k A  k ' A 	A 	H 2 O H 2 O	A 		H 2 O H 2 O	H 2 O H 2 O	k ' H 2 O k H 2 O	H 2 O H 2 O
							e 							H 2 O
			d f							d f

ACKNOWLEDGMENTS

Part of this work was supported by FEDER-CICyT project CTQ2011-28973/BQU.