Mechanism for Interplay between Electron and Ionic Fluxes in KhFek

Jan 21, 2006 - Kinetic Aspects of Ion Exchange in KhFek[Fe(CN)6]l·mH2O Compounds: A Combined Electrical and Mass Transfer Functions Approach. D. GimÃ...
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J. Phys. Chem. B 2006, 110, 2715-2722

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Mechanism for Interplay between Electron and Ionic Fluxes in KhFek[Fe(CN)6]l‚mH2O Compounds D. Gime´ nez-Romero,† P. R. Bueno,‡ J. J. Garcı´a-Jaren˜ o,§ C. Gabrielli,*,† H. Perrot,† and F. Vicente§ UPR 15 du CNRS, Laboratoire Interfaces et Syste` mes Electrochimiques, UniVersite´ Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France, Instituto de Quı´mica, Departamento de Fı´sico-Quı´mica, UniVersidade Estadual Paulista, P.O. Box 355, 14801-907, Araraquara, Sa˜ o Paulo, Brazil, and Departament de Quı´mica Fı´sica. UniVersitat de Vale` ncia, C/ Dr Moliner, 50, 46100, Burjassot, Vale` ncia, Spain ReceiVed: October 27, 2005; In Final Form: December 13, 2005

This paper develops a framework for the interpretation of ionic insertion/deinsertion reactions in an aqueous 2+ (CN) ] ‚ environment taking place in transition-metal hexacyanoferrates of the general formula KhFe3+ 6 l k [Fe mH2O, also called Prussian Blue. Three different processes were fully separated in the electrochemistry of these films. It was clearly identified that one of these electrochemical processes involves the insertion/deinsertion 2+ (CN) ] ‚mH O structure to reach the of H3O+ (hydrated protons) through the channels of the KhFe3+ 6 l 2 k [Fe film electroneutrality during the electron transfer between Everitt’s Salt and Prussian Blue. The other electrochemical processes involve K+ or H+ (proton) exchange through the water crystalline structure existing 2+ in the channels of the KhFe3+ k [Fe (CN)6]l‚mH2O structure.

Introduction The blue pigment compound known as Prussian Blue (PB) is the classical prototype of a transition-metal hexacyanoferrates of general formula AhMk[Fe(CN)6]l (where h, k, and l are stoichiometric numbers, A ) alkali metal cation, M ) transition metal) and represents an important mixed valence compound.1-7 In the special case of Prussian Blue, or iron(III) hexacyanoferrate(II), A corresponds to one monovalent cation (i.e., K+) and M corresponds to Fe+3 in the above generic formula. Several hexacyanoferrates have raised intense interest because of their electrocatalytic, electrochromic, ion-exchange, ionsensing, or photomagnetic properties.8-28 Mainly because these compounds present an important predisposition for ion intercalation10,11 they are also used as battery electrodes.18,19 Ionexchange features combined with ion-sensing properties enable the use of these compounds as probes for applications in the biosensor fields.20,21 Furthermore, the ion-exchange properties of these compounds are specifically important and it is not hardly surprising that a huge amount of studies have been devoted to this topic.10,11,18,19 Their selective intercalation trends take advantage of applications as amperometric and potentiometric sensors.12,13 It is important to point out that the electrochromic features of electroactive PB compounds and analogues have also been studied2-7 because of their technological importance in applications concerning photoinduced image formation (displays development) on targeted areas.8,9 Classically, PB compounds are described in two ideal stoichiometric formulations, the so-called soluble form, 2+ KFe3+[Fe2+(CN)6] and insoluble form, Fe3+ 4 [Fe (CN)6]3. These common names have a historical structural connotation rather than actual solubility implications.29 These stoichiometric formulations are considered to present different crystalline * To whom correspondence should be addressed. E-mail: [email protected]. † Universite ´ Pierre et Marie Curie. ‡ Universidade Estadual Paulista. § Universitat de Vale ` ncia.

structures. In fact, from a historical point of view, Keggin and Miles30 have suggested a face-centered cubic lattice structure for the soluble form in which the high-spin ferric and low-spin ferrocyanide sites are each octahedrally surrounded by -NC and -CN units, with the potassium counterion occupying an interstitial site. The simple Keggin-Miles structure model reflects the polymeric nature of PB albeit the actual structure is rather more complicated. In other words, according to the general formula, AhMk[Fe(CN)6]l, considering A ) K and M ) Fe3+, Keggin-Miles have described the three-dimensional 2+ framework considering that the h, k, cubic Fe3+ k -NC-Fel and l numbers in the general formula represent the unit value. Alternatively, the single-crystal PB insoluble structure has been studied in detail by Buser et al.,1 who have also considered the structure as a (primitive) cubic lattice. However, one-fourth of the [Fe2+(CN)6]4- units are missing, with their nitrogen sites occupied by water molecules coordinated to the Fe3+ sites and with as many as eight additional water molecules interstitially located. Because the space group symmetry for this compound usually corresponds to Fm3m, a random distribution of [Fe2+(CN)6]4- vacancies is expected to exist in 2+ 1 the Fe3+ 4 [Fe (CN)6]3 structure of iron atoms. It was shown by neutron diffraction study31 that there are two parts in the hydrated structure of the insoluble form. First, the well-known structure of the iron atoms, Fe4[Fe(CN)6]3, and second, the crystalline structure of water molecules. Thus, the ideal stoichiometry expected for the hydrated structure is Fe4[Fe(CN)6]3‚mH2O,31 with m set as 14 in the general formula. Two crystallographically and chemically distinct kinds of structural water molecules exist within the relatively open cubic Fe3+-N-C-Fe2+ of the PB framework. One kind of these structural water molecules is part of the Fe(CN)46 vacancies. The second kind occupies interstitial positions and represents, therefore, uncoordinated water. For instance, for the ideal expected stoichiometry, that is, Fe4[Fe(CN)6]3‚14H2O, the unit

10.1021/jp0561773 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/21/2006

2716 J. Phys. Chem. B, Vol. 110, No. 6, 2006 cell contains six coordinated and eight uncoordinated water molecules.31 It has also been argued that during ionic electrochemical insertion/deinsertion cycling, in KCl solution from -0.20 to 0.60 V, the PB insoluble form is fully irreversibly converted to the soluble form.32-34 The data of Lundgren et al.29 support this conversion; however, it is clearly not fully quantitative, due to the fact that the stoichiometry of the PB soluble form cannot exactly be described as that shown in the chemical formula presented above. Consequently, after reductive cycling, the electroactive films probably present a composition intermediate between the insoluble and soluble form.29 The oxidized PBforms can be reduced to the colorless form called Everitt’s Salt (ES). In general, the PB films in their 2+ insoluble structure, Fe3+ 4 [Fe (CN)6]3‚mH2O, can be reduced to a colorless compound ES corresponding to the insoluble structure by means of the following reaction:35 2+ + Fe3+ 4 [Fe (CN)6]3 ‚mH2O + 4K + 4e a 2+ K4Fe2+ 4 [Fe (CN)6]3‚mH2O (1) 2+ Nevertheless, the soluble form, Fe3+ 4 [Fe (CN)6]3‚mH2O, can be reduced to a ES form corresponding to the soluble structure, in potassium chloride solution environment, by means of the following reaction:35

KFe3+[Fe2+(CN)6]3‚mH2O + K+ + e- a K2Fe2+[Fe2+(CN)6]‚mH2O (2) It is important to emphasize that it is not common to write the above equations with the compounds containing the mH2O structural water. However, it is very important to consider this part of the structure (mH2O) when dealing with the solid-state chemistry mechanism for ion flux in transition-metal hexacyanoferrate compounds because it will be discussed in detail in this work. As a result, we present the chemical equations in that form to facilitate the discussion to be done in the following sections and also to insist on the structural water contained in this kind of compound. Thus, the main goal of the present work was to study the electrochemical mechanisms that control the ion fluxes in KhFek[Fe(CN)6]l‚mH2O compounds during the ES T PB electron transfer by electrogravimetric and electric combined measurements. Experimental Section 1. Mass and Electrochemical Measurements. The experiments were carried out in a typical three-electrode cell, where one of the gold electrodes of a quartz crystal resonator (CQE Troyes, France) of about 25 mm2 was used as a working electrode, a platinum plate was used as a counter electrode, and finally a saturated calomel electrode (SCE) was used as a reference electrode. All EQCM experiments were carried out by using a homemade UPR15/RT0100 9 MHz oscillator, a TC-110 Yokogawa frequency meter and an AUTOLAB-Ecochemie (PGSTAT100) potentiostat/galvanostat. Current and mass changes were measured simultaneously thanks to this specific equipment; a high quality frequency/voltage converter was included in the frequency counter and allows microbalance frequency changes to be stored through the AUTOLAB device in electronic files. The EQCM was calibrated by means of galvanostatic copper electrodeposition, which gave an experimental Sauerbrey con-

Gime´nez-Romero et al. stant equal to 16.3 × 107 Hz‚g-1‚cm2. This calibration procedure has been commonly used and described.36-39 2. Film Preparation. PB electroactive films were galvanostatically deposited on gold electrodes35 from FeCl3 (A. R., R. P., NORMAPUR), K3Fe(CN)6 (A. R., R. P., NORMAPUR), and HCl (A. R., R. P. Normapur). The galvanostatic experiments were carried out using the AUTOLAB (PGSTAT100) potentiostat-galvanostat. The gold electrodes were immersed into 0.02 M K3Fe(CN)6, 0.02 M FeCl3, and 0.01 M HCl solutions, and a controlled cathodic current of ic ) 40 µA‚cm-2 was applied for 150 s for PB electrodeposition. The estimated film thickness is around 90 nm, and it was corroborated by a theoretical estimations.40 This method allowed the insoluble form of the PB structure to be deposited on the working electrode. The PB films were stabilized before gravimetric and electric measurements by means of cyclic voltammetry around the ES T PB transition [0.60, -0.20] V in 0.25 M KCl (A. R., R. P., NORMAPUR) solution, pH ) 2.23. These PB films were sufficiently thin to allow the Sauerbrey’s equation41 to be used without limitation coming from viscoelastic properties of the film according to references 42 and 43. Other nonideal contributions that could cause frequency shifts, like roughness, were not expected for these very thin films.44 Furthermore, the validation of the mass response of a quartz crystal microbalance coated with PB thin films in these experimental conditions has been realized in a previous paper.43 3. Experimental Conditions for the Measurements. All of the electrochemical experiments were conducted in 0.25 M KCl or 0.25 M KNO3 (PROLABO, analytical grade) solutions, pH ) 2.23. Finally, the PB films were partly dehydrated by heating the film in an oven (MEMMERT) at 393 K for 24 h. Results and Discussion Before any experiment, the PB compound films were cycled around the potential of the electron-transfer ES (K4 3+ 2+ 2+ Fe2+ 4 [Fe (CN)6]3‚mH2O) T PB insoluble (Fe4 [Fe (CN)6]3‚ mH2O) (from 0.60 to -0.20 V) in a solution containing potassium ions. After 15 cycles, it was shown that the films 2+ were converted from the insoluble form (Fe3+ 4 [Fe (CN)6]3‚ mH2O), free of potassium ions as initially deposited, to the soluble form KFe3+[Fe2+(CN)6]‚mH2O.32-34 During this reaction or structural change, the PB films lose one-quarter of the high spin iron(III) and the potassium ions occupy interstitial sites in the structure of the soluble PB films (conversion process of insoluble PB to soluble PB stoichiometry).2,29 1. Voltammetric Measurements. Figure 1 shows the electrochemical response of the PB films in different aqueous solutions. According to the literature,35 in Figure 1a, the soluble PB compound form, KFe3+[Fe2+(CN)6]‚mH2O, is reduced to the ES compound form in potassium chloride solution in agreement with reaction 235 and the response is stable. On the contrary, Figure 1b shows that the soluble PB structure is not stable during voltammetric cycling in an HCl environment that does not contain potassium ions in this case (pH ) 2.23). The instability of the film in this solution was confirmed by the fact that the current was not the same for each cycle and, in addition, the mass balances decreased during the successive cycles. Therefore, the potassium ions are not only important as the counterions needed to maintain electroneutrality of the PB film but they are also important to maintain the crystalline structure completeness during the cation insertion from aqueous solution in cyclic voltammetry experiments (because the entrance of potassium cations from the solution is impossible and, as a result, this film is not stable in a HCl solution). The potassium

Fluxes in KhFek[Fe(CN)6]l‚mH2O Compounds

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Figure 2. Curves of the F(dm/dQ) function vs potential during the linear potential scan of the voltammogram of Figure 1a. The experimental conditions were the same as those in Figure 1a. The continuous line is the voltammogram, and the circles are the experimental values of this function. (O) are the values of the F(dm/dQ) function during the cathodic scan and (b) are the values of the F(dm/dQ) function during the anodic scan.

Figure 1. Current and mass response as a function of potential obtained during a linear potential scan in PB stabilized film for ES T PB conversion. The pH of electrolyte solutions was 2.23. (a) 0.25 M KCl environment and (b) 0.006 M HCl in the solution (without KCl, pH ) 2.23). (Solid lines are the five cycle, and the dashed line is the fifteen cycle.) Continuous lines are due to voltammogram responses, and dashed lines are due to mass vs potential. The scan rate used was 10 mV‚s-1.

ions effectively take part in the crystalline structure of the stabilized PB film KFe3+[Fe2+(CN)6]‚mH2O. This explains the fact that the transition-metal hexacyanoferrate films present selective properties of ion separation with respect to the alkali cations present in solution45 because the potassium ion occupies a specific structural localization inside this structure. It is important to mention that the narrow current peaks observed in the voltammogram when measurements are made in potassium chloride solutions (Figure 1a) almost disappear in a hydrochloric acid solution without KCl (Figure 1b). Therefore, these two peaks (reduction and oxidation peaks) are related to the redox processes involved in the K+ insertion/deinsertion process according to eq 2. Moreover, the very narrow shape of the peaks indicate that the potassium motion, inside the PB structure (as well as inside the film/electrolyte interface), is very fast and, therefore, at these potentials, the KFe3+[Fe2+(CN)6]‚ mH2O structure possesses a high electronic conduction (almost metallic conductivity), as has also been observed by means of the evolution of the EIS spectra with respect to temperature.46 However, the insertion/deinsertion redox process involved in the potassium ion exchange is not the only insertion/deinsertion mechanism taking place when an electrochemical potential is applied to PB films (KFe3+[Fe2+(CN)6]‚mH2O). In fact, the electrochemical process of PB film presents three overlapped insertion/deinsertion reactions (or charge compensation). Evidence for the presence of three reactions has been seen occurring in PB films because the voltammetric curves can be simulated in these experimental conditions only by considering three overlapped waves.47 Besides, the unusual width of the peak base observed in the curve of Figure 1a is also explained by Feldman et al. by considering the presence of at least two overlapped

waves in the voltammetric curve.22,23 The redox potentials of these electrochemical processes have been shown to be at about 0.14, 0.21, and 0.32 V,47 but these processes have not been clearly identified in the literature. 2. EQCM Measurements. The faradaic mechanisms are better studied by an analysis of the ratio between the mass and the electrical charge passed during a voltammetric experiment (F(dm/dQ) function). This analysis allows information on the molecular weight of the species that adsorbs (inserts) or desorbs (deinserts) during the electrochemical process to be obtained by means of the following expression48

F

dm ) dQ

zi

∑Rixi MWi νi ( mass changes due to uncharged species (3)

where xi is the charge of the exchanged species, Ri is a constant assumed to be -1 when there is an insertion/deinsertion process of cationic species (the guest species is positively charged) occurring in the host and +1 when there is an insertion/ denisertion process of anionic species (the guest species is negatively charged), the sign indicating the direction of the ionic or cationic motion during the ionic insertion/deinsertion process, F is the Faraday constant (96 500 C/mol), dQ is the electric charge change that crosses the film, dm is the concomitant mass change of the film, MWi the molecular weight of the charged species involved in the i faradaic process, zi is the number of electrons involved in ith faradaic process, and νi represents a percentage of the electrical charge balanced by the participation of the ion involved in the global electrochemical process. In electrochemical systems, it is also important to consider uncharged species such as the free solvent molecules that could participate indirectly in the electrochemical process. This participation could produce mass changes but their motion does not cause an electrical charge flux and, therefore, no faradaic current is associated. Nonetheless, the participation of these species could modify the obtained mass/charge ratio. The first step to calculate the mass/charge function, during a cyclic voltammetric experiment, is to obtain from the experimental mass versus time curve, m versus t, the dm/dt versus t curve. This curve is obtained numerically after an initial smoothing of the experimental data by a FFT procedure.48 Accordingly, Figure 2 shows the variation of the F(dm/dQ) function during the voltammetric scan of the PB film in 0.25

2718 J. Phys. Chem. B, Vol. 110, No. 6, 2006 M KCl solution (corresponding to Figure 1a). In this experiment, the negative sign of the F(dm/dQ) function during both scans indicates that the main ionic flux, necessary to reach the film electroneutrality during the electrochemical processes, corresponds to a cationic motion (the positve zone is due to the fact that the current density is zero in this potential interval (zone 4 during the anodic scan), given that the calculation of the F(dm/dQ) function does not make sense when the current density is zero). Furthermore, the F(dm/dQ) function is not constant during the voltammetric scan; therefore, different ions are involved during the ES T PB electron transfer, as commented above. The F(dm/dQ) function divides the ES T PB transition (Figure 2) in four potential intervals associated with four different electrochemical processes: (1) Between 0.60 and 0.40 V (zone 1), the value of the F(dm/dQ) function barely varies and keeps more or less constant with a value of about -10 g‚mol-1. (2) Between 0.25 and 0.15 V (zone 2), the F(dm/dQ) function reaches a value of about -40 g‚mol-1. (3) Between 0.15 and 0.00 V (zone 3), the F(dm/dQ) function has a value about -30 g‚mol-1. (4) Between 0.00 and -0.20 V (zone 4), the F(dm/dQ) function decreases to a value equal to about 0 g‚mol-1. The corresponding reaction was considered to be the catalysis of the molecular oxygen reduction by Itaya et al.16 Therefore, as this function tends to 0 g‚mol-1, a possible explanation is that this one is a reaction that takes place mainly on the surface of the PB film and, consequently, it does not change the mass of the working electrode although it contributes to the current measurement. The first three potential intervals corroborate the presence of three different ionic fluxes associated with the ES T PB electron transfer, as commented above. These potential intervals coincide with the redox potentials associated with the three overlapped waves, which allow one to simulate the voltammetric curves in these experimental conditions.47 Accordingly, these three different ionic fluxes will be unmasked later during the discussion of this article. The ions present in the solution are the potassium cations, the protons, and the chloride anions (0.25 M KCl, pH 2.23). Therefore, because the values of the F(dm/dQ) function are about -40 g‚mol-1 in zone 2 of the voltammetric scan, the ES T PB electron transfer involves mainly the potassium cation exchange at these polarization potentials (MWK+ ) 39 g‚mol-1) (the central zone of the voltammetric peak). According to this value, the global motion of the potassium cations takes place without their solvation shell. Therefore, this result corroborates the structural localization of the potassium ions inside the hydrated PB crystalline structure. Indeed, if the potassium ions were only countercations, then they should be moved with their solvation shells because the size of the channels of the PB structure is bigger than the size of the potassium molecule. Figure 3 shows the voltammetric response for the KFe3+[Fe2+(CN)6]‚mH2O compound in two different solutions (0.25 M KCl and KNO3). These solutions differ only by the anion (nitrate and chloride anion) because the cation is the same (potassium). The voltammetric responses of the compound in these solutions are practically the same. Consequently, the anion exchange does not take place during this electron transfer because the variation of the molecular weight of the anions present in the working solution does not imply the variation of mass and current. As a result, the electrochemical processes involved in the ES T PB electron transfer that do not involve the K+ motion (zones 1 and 3) must only be related to the exchange of protons. This result is corroborated by the influence of the pH in the impedance spectra of the PB films in the zone

Gime´nez-Romero et al.

Figure 3. Current and mass response as a function of the potential obtained during a linear potential scan in PB stabilized film for ES T PB conversion. The pH of the electrolyte solutions was 2.23. Solid lines are the 0.25 M KCl environment, and dashed lines are the 0.25 M KNO3 solution. The scan rate used was 10 mV‚s-1.

Figure 4. Curves of the F(dm/dQ) function vs potential during the linear potential scan of the voltammogram of Figure 1b. The experimental conditions were the same as those of Figure 1b. The continuous line is the voltammogram, and the circles are the experimental values of this function.

1 of the voltammogram in KCl solutions because this influence is minimal at other potentials.49 To discern the ionic exchange that accompanies the K+ motion, Figure 4 shows the variation of the F(dm/dQ) function during the voltammetric scan corresponding to a PB film in a HCl solution without K+ cations (Figure 1b). In this experiment, the redox processes of the PB are well separated during the anodic scan because the processes that involved the motion of K+ cations are a minority. The K+ motion can be seen only during the anodic scan and because of the few K+ ions initially present inside the PB film structure, because these ions are not in the solution. Thus, the motion of the H+ (MWH+ ) 1 g‚mol-1) takes place in zone 1 of the voltammogram during this scan because the value of the F(dm/dQ) function tends to about -1 g‚mol-1 at these potentials (Figure 4). Therefore, the proton exchange between the solution and the KFe3+[Fe2+(CN)6]‚ mH2O structure takes place at these potentials by means of proton hoppings from one water molecule to the next, as in aqueous solution. Accordingly, the H+ motion is responsible for the decrease of the F(dm/dQ) function from 0.25 V and, consequently, the electrochemical processes that involves the H+ motion take place between 0.25 and 0.60 V. H+ has a smaller atomic size than K+. Consequently, this ion cannot occupy the structural vacancies of the potassium cations. The H+ ion must occupy its own structural vacancy inside the KFe3+[Fe2+(CN)6]‚mH2O compound structure. Because the iron and ferricyanide vacancies inside the PB structure are too large for the size of the proton and there is no solvent

Fluxes in KhFek[Fe(CN)6]l‚mH2O Compounds motion during this electron transfer, these H+ must be exchanged, from the solution, with the water crystalline structure of the film and not with the KFe3+[Fe2+(CN)6] structure of the iron atoms. In the PB structure, the crystalline water molecules that are interacting with the electroactive iron atoms are the structural water, which is part of the coordination shell of Fe3+. This structural water fills empty nitrogen sites of the 31 Consequently, it is probably this one Fe(CN)46 vacancies. that is the water participating to the H+ exchange because they are the only water molecules that can compensate the charge of the crystalline part of the KFe3+[Fe2+(CN)6] structure. These water molecules participate in the energy bands of the iron atoms given that they form part of their coordination shell. The water that is interacting with the electroactive iron atoms must be formed by four molecules of hydroxyl ions and two water molecules to compensate for the positive charge of the PB structure due to the Fe(CN)46 vacancies. The presence of hydroxyl anions in the water crystalline structure existing in empty nitrogen sites of the Fe(CN)4vacancies in the 6 2+(CN) ] ‚mH O compound explains the 1/1.3 ratio [Fe Fe3+ 6 3 2 4 between the oxygen and hydrogen atoms (O/H) in the hydrated PB structure proposed by Herren et al.31 (the ideal ratio to considerer water molecules would be 1/2). So, the mechanism that involves the H+ motion would be the protonation (H2O)/ deprotonation (OH-) of these water molecules of the Fe3+ coordination shell (occurring inside the PB structure) to compensate for the oxidation state of the iron atoms in this structural environment (i.e., Fe(II)-H2O/Fe(III)-OH). Accordingly, this mechanism in the H+ insertion/deinsertion to compensate for the charge of the OH- anions present in the KFe3+[Fe2+(CN)6]‚mH2O structure can explain the reduction of the electrical charge involved in the voltamperograms of the ES T PB electron transfer when the working solution pH increases.52 So, as happens in the case of the potassium cations, this PB film destabilization, with the decrease of the proton concentration, supports the structural localization of these protons into the PB structure. The electrical charge decrease as the pH increases has been explained in the literature by the formation of ferric hydroxide at more basic pH45 but, at these pH levels, the values of pKs indicate that the chemical formation of this species is not allowed and besides, the anion motion does not take place through the PB structure, as shown in Figure 3. So, this process would be the stabilization of the Fe(III)-OH present in the PB crystalline structure due to the fact that these hydroxides are more stable as the pH increases (a sort of passivation process of the film). The proposed localization of these molecules inside the film can also explain the fact that this reaction is less important in PB electrochemistry than the reaction involving K+ cation motion because the occupancy of the Fe(CN)46 sites is 75%, leaving 25% of ferricyanide vacancies.31 The ratio between both processes can be observed easily in Figure 1a and b because the voltammetric charge of the peak due to K+ motion is higher than the charge of the voltammetric peak due to H+ motion. Accordingly, the electroneutrality of the PB stabilized films is reached during the [0.25, 0.60] V potential interval by means of the H+ motion, which occupy the hydroxylic vacancies of the structural water contained in the KFe3+[Fe2+(CN)6]‚mH2O compound. The other ions contained in the solution environment do not fulfill the requirements to occupy these vacancies or other structural sites inside this structural water. 3. Dehydrated PB. By the experiments presented previously, it is still not possible to know if there is some protonic motion

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Figure 5. Curve of the F(dm/dQ) function vs potential during the first linear potential scan of the voltammogram of PB film dehydrated during 24 h at 393 K. The experimental environment was 0.25 M KCl and pH 2.23. The dashed line is the voltammogram before the partly dehydration process of the PB film, and the solid line is the first voltammogram after this process. (O) are the values of the F(dm/dQ) function during the cathodic scan of the partly dehydrated PB film, and (b) are the values of the F(dm/dQ) function during the anodic scan of the partly dehydrated PB film.

coupled to the potassium cationic motion in potential zone 3. Figure 2 indicates that there are two different electrochemical processes overlapped in this potential interval in KCl solution, given that the values of the F(dm/dQ) function are different (about -30 g‚mol-1) to the molecular weight of the potassium cations. Nevertheless, in this potential interval, the main electrochemical process involves the K+ cation exchange to reach the film electroneutrality because the values of the F(dm/dQ) function are about -40 g‚mol-1 (MWK+ ) 39 g‚mol-1). To separate the ion motions, the system is partly dehydrated to eliminate the influence of the K+ motion in the [0.00, 0.20] V potential interval. It was already shown that the K+ motion depends on the amount of water present inside the PB structure.52 When the PB compound films suffer a complete dehydratation process, the voltammetric responses observed are very different from the first cycles to the last.52 During the first scans, the wave shape does not show any voltammetric peak and a limiting current appears, which suggests that the process is controlled by the transport of some species. As the number of cycles increases, the films partially recover their inner water content,52 given that the global mass change during the cathodic scan of the first voltammetric cycle is equivalent to the exchange of about one water molecule for each redox sites present. Concomitantly, the peaks become narrower and higher showing an increase of the electric charge enclosed within the peak.52 As a result, the potassium ion localization inside the hydrated PB crystalline structure, as well as their motion, depend on the structural water present inside this structure. Figure 5 shows the voltammetric signal of the partly dehydrated KFe3+[Fe2+(CN)6]‚mH2O film. First, the hydration of the film must take place during the cathodic scan of the PB film because the voltammetric signal during the anodic scan is more similar to the voltammetric signal of the hydrated PB film. Second, Figure 5 also shows that the current densities in the potential intervals of zones 1 and 2 disappear during the cathodic scan when the PB film is partly dehydrated. Therefore, the H+ and K+ motions inside the KFe3+[Fe2+(CN)6]‚mH2O structure takes place through the crystalline water existing in the channels of this structure. Such diffusional or migrational motion occurs according to solid-state rules (self-diffusion of the cations in the structural hydrated water). This kind of motion could explain the dehydratation of the alkali metal cations before their entrance into the PB structure.36,38,51 As commented above, in case

2720 J. Phys. Chem. B, Vol. 110, No. 6, 2006 contrary the potassium cation must come in the PB structure with its coordination shell. Third, the current density corresponding to the secondary reaction in the potential interval corresponding to zone 3 clearly increases. Therefore, this secondary process is favored by the dehydration of the KFe3+[Fe2+(CN)6]‚mH2O film. Furthermore, this motion must take place through the channels of the PB structure itself, KhFek[Fe(CN)6]l because it occurs even when the water structure does not exist (when the film is partly dehydrated, Figure 5, or it is totally dehydrated52). Because the electrodic mechanisms are better studied by the analysis of the F(dm/dQ) function during the voltammetric scan, Figure 5 also shows the variation of the F(dm/dQ) function during the voltammetric scan of the partly dehydrated PB film. This function effectively indicates that, during the anodic scan, the PB structure is more hydrated than thatduring the cathodic scan because the values of the F(dm/dQ) function are more similar to the K+ motion in the hydrated film (MWK+ ) 39 g‚mol-1). However, during the cathodic scan, the values of the F(dm/dQ) function are about -20 g‚mol-1. Accordingly, because the K+ motion is impeded during this voltammetric scan given that the film is dehydrated, the film hydration must occur during the cathodic scan and, thus, this hydration favors the K+ motion during the anodic scan. As seen in Figure 5, the motion of the water molecules depends on the applied potential because it is localized mainly in the potential interval between 0.00 and 0.20 V (zone 3, Figure 5). Therefore, to reach the film electroneutrality, these water molecules must be accompanied by a positive charge because the cations are the only species that can come in the PB structure to reach this electroneutrality during the cathodic scan. Accordingly, at these potentials, the exchange of the hydrated proton (H3O+, MWH3O+ ) 19 g‚mol-1) is demonstrated. As the other ions exchange during the ES T PB electron transfer, H3O+ must occupy the structural vacancies of the KFe3+[Fe2+(CN)6]‚mH2O structure because all electrochemical processes disappear when the KFe3+[Fe2+(CN)6]‚mH2O film is completely dehydrated.52 Furthermore, the localization of H3O+ in the PB structure must be similar to the localization of the K+ cations because the amount of electricity of the voltammogram is similar before and after the partial dehydration of the PB film (Figure 5). The charge compensation that involves the K+ exchange can be partly replaced by the H3O+ exchange (these processes partly take place with H3O+ because the PB film is destabilized when there are not K+ cations in the working solution, as commented above). Thus, the H3O+ localization must be into the cationic vacancies of the water crystalline structure present into the interstitial positions of the KFe3+[Fe2+(CN)6]‚mH2O film, a similar localization to the structural localization of the K+ cations.30 4. Film Stability. As mentioned previously, the electron transfer between a high-spin iron(III) and a high-spin iron(II), occurring for the ES T PB transition, involves the exchange of three ionic species (H3O+, K+, and H+) depending on the applied potential. Furthermore, the electronic structure of KFe3+[Fe2+(CN)6]‚mH2O is not separated in different parts (both structures are linked because the elimination of the hydrated part decays the conductivity of the film,52 for instance, the PB structure itself and the hydrated part (i.e., the compound may be imagined as just one from the electronic point of view). Therefore, the ionic counterpart for electronic balance depends on the specific crystalline sites and positions of the ions inside the host structure. This means that the ionic counterpart depends on different stoichiometries (compositions) presented by the

Gime´nez-Romero et al.

Figure 6. Current and mass responses with respect to the potential obtained during the linear potential scan of a stabilized PB film. The scan rate used was 10 mV‚s-1. The continuous line represents the PB voltammogram obtained in 0.25 M KCl, the dashed line represents the first voltammogram of the same film in 0.01 M KCl, and the dotted line represents the 15th voltammogram in this solution. The solid line in the mass response is the first voltammogram in 0.01 M KCl, and the dashed line is the mass response is the 15th voltammogram.

hydrated PB crystalline structure. Thus, these different stoichiometries (compositions) change the equilibrium potential of the hydrated PB crystalline structure. Consequently, the electrochemical reactions and kinetics involved in the ionic exchange through the host depend on the experimental conditions. As a result, the PB film stability depends on the solution in which the compounds are immersed. In general, the structural and chemical stability of the KhFek[Fe(CN)6]l‚mH2O compound depends on the solution environment and, particularly, on the chemical potential equilibrium between the ions in solution and those inside the crystalline structure. It is well known that for any species partitioned between a solid phase and solvent their electrochemical potentials must be equal.53 So, if the chemical potential of the solution for some cations, for example, potassium is low, then the tendency is to affect the stoichiometry of KhFek[Fe(CN)6]l‚mH2O to low values of h. However, the chemical potential of K+ in solution must also alter the stability of other ions in the structure such as that pertaining to part of hydrated structure of KhFek[Fe(CN)6]l‚mH2O. All of these points evidence that the stoichiometry of the compound depends strongly on the synthesis conditions54 and that the stoichiometry of the structure may change with time if the measurement conditions are strongly different from the synthesis conditions. Thus, the structural changes dictated by changes in solution composition (ionic activity) with which the film will ultimately become equilibrated may take some time to occur because the kinetics of solid-state reactions may be slow, much slower than typical voltammetric time scales. This dependence of the PB film stability on the solution environment is experimentally corroborated by the fact that the stabilized PB films are not stable when the chemical potential of K+ in the working solution is lower (0.01 M) than the one existing in the stabilization solution (0.25 M) (Figure 6). In this case, the nonstability of the PB films is due to a decreasing amount of potassium ions in the PB structure, which occurs to equilibrate the chemical potential of K+ in the working solution. Consequently, the stabilized PB film may be destabilized quickly in such a situation. These data are in concordance with the decrease of the current density and mass observed during the decrease of the K+ chemical potential in solution (Figure 6). In addition, Figure 6 shows that there is an increase of the current density in the potential interval related to the H+ and H3O+ exchange in 0.01 M KCl. This one corroborates the fact that the K+ chemical potential in solution alters the stability of

Fluxes in KhFek[Fe(CN)6]l‚mH2O Compounds other ions on the structure, such as H+, which are part of the hydrated structure of KhFek[Fe(CN)6]l‚mH2O. 5. Discussion. According to what was discussed previously, all of the evidence presented above shows that there is no other structural difference between soluble or insoluble PB forms except by the h stoichiometry number and Fe3+ amount. In other words, these forms of compounds differ only by the number of occupied positions in the unit cell because, in the soluble structure, the positions of some ions are only partially occupied. This is only one KhFek[Fe(CN)6]l‚mH2O compound with various h stoichiometric numbers. So, the name PB soluble used in the literature is just related to a particular stoichiometry of a more general compound, that is, KhFek[Fe(CN)6]l‚mH2O. The soluble term just indicates a PB structure containing a higher amount of K+ ions and a lower amount of spin iron(III) species. Consequently, this explains why some authors postulate an intermediate composition between the insoluble and soluble form of the PB compounds.29 The coexistence of different stoichiometric possibilities and hydrated degrees in the hydrated part of the PB structures leads to very important consequences besides those already discussed previously. In fact, this structural picture explains why the synthesis conditions and solution environment are so important in defining the electrochemical response of these compounds.54 In other words, the synthesis parameters and solution environment determine the “equilibrium” stoichiometry and hydratation degrees and explain why the electrochemical features of the PB compounds are so sensible to the preparation parameters of the compounds. Finally, the possibility of the existence of different stoichiometries and hydratation degrees explains why there is no consensus about the exact lattice constants of PB crystalline structure in the literature.55 Alternatively, the difference between the values of the F(dm/dQ) function and the molecular weight of the potassium cation cannot be due to the simultaneous motion of solvent molecules during the ES T PB electron transfer. This motion would take place for two reasons: by a volume change during the ES T PB transition and/or by the osmotic forces due to the cation concentration increase inside the PB structure during this electron transfer. Thus, the first hypothesis is rejected because the PB compound is an ionic crystalline solid, that is, a rigid structure differing greatly from polymer electroactive structures/films where the solvent molecule may contribute to mass change of the electroactive film.43 In addition, there is no change of the volume of the PB crystalline structure during the ES T PB electron transfer, given that the unit cell dimensions of the PB and ES structures are the same, within experimental error, for these compounds.30,56 In the same way, the second hypothesis is rejected because the water entrance depends on the applied potential; and besides, this entrance also takes place when the PB film is partly hydrated (when the motion of the other cations (K+ and H3O+) do not take place), as is seen in Figure 5.52 Most of the articles that postulate a water motion consider that the ES T PB transition takes place only by means of the exchange of the potassium cations inside the structure. For that reason, differences were observed between the experimental and theoretical values explained by some authors by solvent molecule motions entering the PB structure.57,58 However, from the EQCM results, these differences can be explained in another way. However, the hypothesis of solvent molecule motions during the redox process of PB is in disagreement with the practically identical electrochemical results obtained in D2O and H2O solutions of NaClO4 in nickel hexacyanoferrate films.50

J. Phys. Chem. B, Vol. 110, No. 6, 2006 2721

Figure 7. Schematic representation of chemistry mechanism proposed for ion fluxes that take place in KhFek[Fe(CN)6]l‚mH2O compound electrochemistry.

On the basis of all of the evidence mentioned and discussed previously, a new mechanism can be proposed for the interpretation of the insertion reactions in aqueous environment taking place in transition-metal hexacyanoferrates of the general formula KhFek[Fe(CN)6]l‚mH2O (Prussian Blue). It is summarized by the electrochemical reactions involved in the conversion PB T ES as follows: KhFek[Fe(CN)6]l‚mH2O + nK+ solution + ne a Kh+nFek-nFen[Fe(CN)6]l‚mH2O (4)

KhFek[Fe(CN)6]l‚mH2O(nOH-) + nK+ solution + ne- a KhFek-nFen[Fe(CN)6]l‚mH2O(nH2O) (5) KhFek[Fe(CN)6]l‚mH2O + nHO+ 3solution + ne a

KhFek-nFen[Fe(CN)6]l‚mH2O(nH3O+) (6) To illustrate the mechanism postulated in this paper, we have adopted a very simple approach based on the scheme of Figure 7, which shows the hydrated part, that is, mH2O, and the PB structure itself, that is, KhFek[Fe(CN)6]l. According to what was discussed above, the hydrated part occupies the interstitial sites located in the channels of the KhFek[Fe(CN)6]l‚mH2O structure. From the literature, it seems that these interstitial sites are similar to those occupied by K+ intercalated ions. Finally, during the ES T PB transition, the K+ and H+ exchanges, accompanying the charge compensation processes to reach the electroneutrality condition inside the film, take place through the crystalline structure of the water molecules. On the contrary, the H3O+

2722 J. Phys. Chem. B, Vol. 110, No. 6, 2006 motion to reach this electroneutrality takes place through the channels of the KhFek[Fe(CN)6]l‚mH2O structure. Conclusions In this paper, it was shown that the insertion/deinsertion mechanism of the ES T PB electron transfer in transition-metal hexacyanoferrates of the general formula KhFek[Fe(CN)6]l‚mH2O (Prussian Blue) occurs by means of three different ionic exchanges involving three different ionic sites inside the crystalline structure. The existence of different processes related to two distinct structural environments inside the crystalline structure of KhFek[Fe(CN)6]l‚mH2O compounds was demonstrated. Two ionic exchanges were identified as being related to K+ and H+. These exchanges occur through the structural water pertaining to the PB framework. The other charge-transfer process is related to interstitial sites where H3O+ can be exchanged between its interstitial position in crystalline structure of the KhFek[Fe(CN)6]l‚mH2O compound and the aqueous environment (electrolyte) through the channels of the PB structure itself, KhFek[Fe(CN)6]l. The site occupation and the structural stability of the compound depend strongly on the concentration of the ions in the solution (electrolyte concentration and pH conditions). Several approaches in the literature propose the existence of different redox processes in PB electrochemical systems.22,23,47 However, our approach provides an immediate explanation of the different ionic exchanges and clearly identifies all of them thanks to simultaneous current and mass changes with respect to the potential. Furthermore, this paper proposes, probably for the first time, the participation in an electrochemical process of a crystalline structure constituted by water molecules embedded in a rigid skeleton. Finally, this work will be complemented by another related paper in which more detailed aspects of the solid-state kinetics of ion fluxes that take place in KhFek[Fe(CN)6]l‚mH2O compounds electrochemistry and its interpretation based on combined aspects of mass and electrical transfer function will be deeply discussed. Acknowledgment. This work has been supported by FEDERCICyT project CTQ 2004-08026/BQV. D.G.-R. acknowledges a Fellowship from the Generalitat Valenciana, Postdoctoral Program. P.R.B. acknowledged Sa˜o Paulo state research funding institution (FAPESP) by the project under no. 02/06693-3. J.J.G.-J. acknowledges his position to the Ramon y Cajal Program (Spanish Minestry of Education and Science). We appreciate the very useful discussions with Nuria PastorNavarro. References and Notes (1) Buser, H. J.; Shwazenbach, D.; Petter, W.; Ludi, A. Inorg. Chem. 1977, 16, 2704. (2) Neff, V. D. J. Electrochem. Soc. 1978, 125, 886. (3) Itaya, K.; Akahoshi, H.; Toshima, S. J. Electrochem. Soc. 1982, 129, 1498. (4) Mortimer, R. J.; Rosseinsky, D. R. J. Chem. Soc., Dalton Trans. 1984, 2059. (5) Feldman, B. J.; Murray, R. W. Anal. Chem. 1986, 58, 2844. (6) Garcı´a-Jaren˜o, J. J.; Navarro-Laboulais, J.; Vicente, F. Eletrochim. Acta 1996, 41, 2675. (7) Kulesza, P. J.; Galus, Z. Electrochim. Acta 1997, 42, 867. (8) Nishizawa, M.; Kuwabata, S.; Yoneyama, H. J. J. Electrochem. Soc. 1996, 143, 3462. (9) de Tacconi, N. R.; Rajeswar, K. Chem. Mater. 2003, 15, 3046. (10) Kelly, M. T.; Arbuckle-Keil, G. A.; Johson, L. A.; Su, E. Y.; Amos, L. J.; Chun, J. K. M.; Bocarsly, A. B. J. Electroanal. Chem. 2001, 500, 311. (11) Amos, L. J.; Schmidt, M. H.; Sinha, S.; Bocarsly, A. B. Langmuir 1986, 2, 559.

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