Innovative Combination of Three Alternating Current Relaxation

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Innovative Combination of Three Alternating Current Relaxation Techniques: Electrical Charge, Mass, and Color Impedance Spectroscopy. Part II: Prussian Blue / Everitt’s Salt Process Jeronimo Agrisuelas, Jose Juan Garcıá-Jarenõ,* David Gimenez-Romero, and Francisco Vicente Department of Physical Chemistry, UniVersity of Valencia, Dr. Moliner 50, 46100 Burjassot, Spain ReceiVed: January 28, 2009; ReVised Manuscript ReceiVed: March 25, 2009

The simultaneous recording of three impedance functions (electrochemical impedance, color, and mass impedance) allows the role of different species to be distinguished easily during electrochemical processes in conducting and electrochromic films. Herein, this technique has been applied to the study of the Prussian blue films at several potentials between the blue form (Prussian blue) and the colorless form (Everitt’s salt). At these potentials, these electrochemical reactions take place by means of exchange of different ions. Thus, the exchange of potassium cations is related to the changes of absorbance at 690 nm, whereas the exchange of protons does not introduce color changes at this wavelength. There is also another site for potassium insertion that does not produce any color change at this wavelength. The analysis of experimental results obtained from this technique has allowed these contributions to be distinguished. Besides, the fitting of the different impedance signals has allowed independent information on the kinetics of electron motion, ion exchange, and color changes to be obtained. Introduction Prussian Blue Films. Prussian blue (PB, ferric hexacyanoferrate) is one of the most studied hexacyanometallates in the literature due to its ease of generating controlled quality films on the surface of very different conducting materials, from metals to composite materials, or different conducting transparent metal oxides.1-9 Redox processes associated with PB films are accompanied by color changes.2,10-16 PB films can be electrochemically reduced to the colorless Everitt’s salt (ES) form in a KCl solution

KFeIIIFeII(CN)6 + 1e- + K+ a K2FeIIFeII(CN)6 (i) Prussian blue (blue color) Everitt’s salt (colorless) This electrochromic character together with the high stability of electrogenerated deposits has led to an increasing technological interest in this material. The near ultraviolet-visible (UV-vis) and near infrared (IR) absorption spectra of PB films show changes at three different spectroscopic bands centered at 380, 690, and 1000 nm, during the reduction process from the PB blue form to the ES colorless form.17 The electronic transition at 690 nm is related to the electronic charge transfer from Fe(II)low spin atoms surrounded by cyanide units to Fe(III)high spin atoms, so monitoring the amount of Fe(II)low spin, CN, and Fe(III)high spin electronic states (change of color from blue to colorless). This same charge transfer also has a forbidden transition at 1000 nm. On the other hand, the transition detected at 380 nm is related to the electronic charge transfer from Fe(II)high spin atoms to Fe(III)low spin atoms.17 These electronic transitions make this material an excellent candidate to be studied by color impedance (CIS) at different potentials between the mixed valence state (PB) and the fully reduced form (ES). We will focus our research on the changes of the electronic * To whom correspondence [email protected].

should

be

addressed.

E-mail:

transition at 690 nm, which is related to the main process in the PB a ES reaction.18 Moreover, these electrochemical reactions are related to the ion exchange. During the reaction, the exchange of potassium ions between the solution and the PB film takes place to balance the electrical charge of conducting films in a KCl solution.2,19 Nonetheless, this is only a simplified scheme of reaction because there is also the minor participation of other cations during these electrochemical reactions.19-22 Thus, the mass impedance (MIS) together with the electrochemical impedance (EIS) provides information on the nature and role of the different participating species. The aim of this work is to apply didactically the theoretical methodologies explained in Part I.23 For that purpose, Prussian blue films have been studied by analysis of experimental data of EIS + CIS + MIS at intermediate potentials between the mixed valence form (PB) and the fully reduced form (ES). This information allows the electron motion across the conducting film to be studied as well as the kinetics of the electrochemical reaction (reaction i). Theory: A Model for the Impedance Response of Conducting Films. The results of the EIS for Prussian blue films together with the alternating current (ac) electrogravimetry or mass impedance (MIS) have been analyzed on the basis of a kinetic model that considers an electrode-conducting film-solution system.20,21,24,25 At the electrode-conducting film interfacial region, there is always an electron transfer that introduces a potential drop. At the same time, there is the potential drop due to the ion exchange at the conducting film-solution interfacial region. Furthemore, the potential drop across the conducting polymer should be considered, but it is commonly assumed that for these cases it is a very thin film. This last contribution was neglected. According to this model, we can deduce theoretical mathematical expressions for the faradaic impedance function or the electrical

10.1021/jp900824w CCC: $40.75  2009 American Chemical Society Published on Web 04/20/2009

Alternating Current Relaxation Techniques: Part II

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charge impedance function (∆q/∆E)(ω) and the ac electrogravimetric transfer function or the mass impedance (∆m/∆E)(ω).20,21,23,25 Models that consider electron transfer and more than one ion species may be found in the literature,21,24,25 and they explain the results of the electrochemical impedance spectroscopy. However, their application for mass impedance and color impedance functions is not obvious, and some simplifications should be considered. One possibility is to neglect the electron transfer contribution at the electrode-polymer interphase. Accordingly, the expressions for the electrical charge impedance, mass impedance, and color impedance functions are, respectively,

∆q 1 (ω) ) ∆E jω

∆m 1 (ω) ) ∆E jω

∑

FGi

[ ∑ [

∆Aλ 1 (ω) ) ∆E jω

i

√

i

δMiMiGi

Ki coth(√jωτi) 1+ d jω ⁄ τ

i

∑ i


√

i

] ]

(1)

]

(3)

δεiεiλGi

[


√

i

(2)

Another possibility is to consider only the exchange of one ion and the electron transfer, which has been successfully used in a previous analysis of EIS and MIS results of PB films.21 This model is used in this work to fit the experimental data because introducing more processes implies many free parameters for the fitting procedure. Furthermore, these expressions may be simplified, if one of the time constants proves large enough when compared to the other

ZF )

[

] [ ]

Ke coth(√jωτe) 1 1 1+ + 1+ FGe d FG 1 jω ⁄ τ

√

e

K1 coth(√jωτ1) d jω ⁄ τ

√

(

)

τe.τ1

≈

1

K1 coth(√jωτ1) Ke√τe 1 1 1 + + + FGe FG1 dFG1 dFGe √jω jω ⁄ τ

√

∆m 1 (ω) ) ∆E jω

(( ((

δM1M1

) (

K1 coth(√jωτ1 Ke coth(√jωτe 1 1 1+ + 1+ G1 d Ge d jω ⁄ τ jω ⁄ τ

1 jω

√

)

1

(

δM1M1

(4)

1

√

)(

e

))

Ke√τe 1 K1 coth(√jωτ1 1 1 + + + G1 Ge dG1 jω ⁄ τ dGe √jω √ 1

)

τe.τ1

)

≈

(5)

∆Aλ 1 (ω) ) ∆E jω

(( ((

δε1ε1λ

) (

K1 coth(√jωτ1 Ke coth(√jωτe 1 1 1+ + 1+ G1 d Ge d jω ⁄ τ jω ⁄ τ

1 jω

√

)

1

(

√

δε1ε1λ

)(

e

Ke√τe 1 K1 coth(√jωτ1 1 1 + + + G1 Ge dG1 jω ⁄ τ dGe √jω

√

1

) ))

)

τe.τ1

≈

(6)

In these expressions, the δM and δε parameters can only reach values of +1 and -1. δM ) +1 indicates that the mass increases if the polymer is oxidized. This means that an anion participates as a counterion in the electrochemical process. However, δM ) -1 if a cation exchange takes place. It is similar for the color impedance parameter δε. At a given wavelength, this parameter is +1 if the oxidized form of the electrochromic material is the colored form at this wavelength, whereas δε ) -1 if the opposite occurs. The general model considering all situations should be the appropriate model for the analysis of this system. However, it introduces many free parameters and many variables even for a simulation procedure. For that, we have chosen in this work the first possibility for the fitting and simulation procedures (two species, two processes) because there is no possibility to obtain a good simulation for the crossed impedance functions unless two or more species and processes are considered. Experimental Section The complete description of the methodologies and equipment used to simultaneously obtain the three impedance functions is described in Part I.23 All experiments were carried out in a three electrode electrochemical cell. An auxiliary electrode was platinum mesh, and the reference electrode was Ag/AgCl/KCl (sat). The working electrode was a high-reflectance gold-quartz crystal electrode (AT cut quartz crystal, 6 or 9 MHz, MatelFordahl, France), which allows the current, mass (from the frequency resonance), and reflectance (from the light intensity received on the photodiode surface) to be simultaneously measured. The cell temperature was controlled by means of Peltier thermoelectric modules, and the cell was a hightransmittance glass cell from Hellma (OG). For the impedance measurements, a small potential perturbation was applied to the stabilization potential of the working electrode (25 mV rms). Color change was measured by the change in the light intensity reflected on the gold electrode of the electrochemical quartz crystal microbalance (EQCM). The photodiode produces a current intensity proportional to the light intensity, which is converted by means of a current-to-voltage converter into an analogical signal. This voltage reflectance was turned into an apparent absorbance (Aλ), which is better for comparison with the changes of mass and electrical charge. All chemical products used were Scharlau analytical reagent quality. Prussian blue was deposited from 0.02 M K3Fe(CN)6, 0.02 M FeCl3, and 0.01 M HCl freshly prepared dissolutions by applying a controlled cathodic current of 40 µA cm-2 for 150 s. The film thickness was estimated as about 115 nm.6,25,26 The PB deposits were sufficiently thin to ensure a precise relationship between the frequency variation of the quartz crystal and the mass change without any viscoelastic artifacts.25 PB films freshly prepared (insoluble PB) were stabilized and

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Figure 1. Voltammetric cycle between 0.6 and -0.2 V for a stabilized PB film in an aqueous solution of KCl 0.5 M, pH 2.98, and T ) 298 K. Scan rate ) 20 mV s-1. (a) Current and mass changes represented as derivative dm/dt. (b) Current and absorbance changes at 690 nm represented as derivative dA/dt.

converted into the soluble form by means of 15 cycles around the PB a ES system5,27-29 in a KCl solution until narrow and sharp peaks appeared. All experiments were carried out in a KCl 0.5 M solution at pH 2.98 and a controlled temperature of 25 C. Results dm/dt and dA/dt Funtions during a Voltammogram. Freshly deposited Prussian blue films were stabilized by means of the procedure described by Itaya,2,5,29,30 cycling around the PB a ES system for 15 times until narrow and sharp peaks appear. The near UV-vis and near IR absorption spectra of PB films are characterized mainly by the spectroscopic band centered at 690 nm.17 This transition is related to the electronic charge transfer from Fe(II)low spin atoms surrounded by cyanide units to Fe(III)high spin atoms, so monitoring the amount of Fe(II)low spin, CN, and Fe(III)high spin electronic states is important. Thus, Figure 1a shows voltammograms together with the dm/ dt, changes and current dA690/dt changes at the characteristic 690 nm wavelength in Figure 1b. Plotting derivative curves of mass and absorbance is preferred because the current represents the derivative of electrical charge, and it is better to compare them. Figure 1a shows that the shape of both curves is similar

Agrisuelas et al. but with some differences. These differences indicate that more than one species may be exchanged during the electrochemical reactions of PB films to balance the electrical charge, depending on the applied potential.19,20 Changes of color at 690 nm (blue) are directly related to the main electrochemical process during the reduction of the PB to the ES form. In spite of a good correlation between current and derivative absorbance changes at this wavelength, there are also some differences. The most significant is that the current in the potential range between 0.30 and 0.50 V seems to not be related to color changes at this wavelength. In panels a and b of Figure 1, at potentials near -0.2 V, derivative curves of absorbance and mass reach values near 0, while the current proves the presence of a cathodic current. This process has been described as a catalytic process due to the presence of molecular oxygen in the solution.31 Impedance Analysis: Electrical Charge Impedance (EIS), Color Impedance (CIS), and Mass Impedance (MIS). Electrochemical impedance spectroscopy has been used during the last years for the characterization of conducting films. Their ability to separate among different processes by changing the frequency of the potential perturbation makes of this technique one of the most powerful tools in the analysis of the kinetics of redox processes in conducting films. During the past few years, the possibility of obtaining the classical impedance function and also an impedance response for other modulated analogical signals such as mass (frequency changes of the EQCM) or color (transferred light intensity) increases the possibilities of impedance techniques.32-39 Electrochemical reactions in PB films involve mass changes (due to the balance of electrical charge4,33) and also color changes11,29 (because the reduced form, ES, is transparent, whereas the PB form is blue), which is due to changes of absorbance at 690 nm.17 EIS + MIS were used to monitor the kinetics of changes of mass and electrical charge and to identify the exchanged ions between the solution and the conducting film by means of the crossed impedance function F(∆m/∆q).20,40 Furthermore, this technique was used to discern between fast and slow ionic species during the electrical charge balance.41 Thus, the EIS, MIS, and CIS studies of this conducting film may provide interesting and different information that may be helpful in understanding the electrochemical behavior of this material. Prussian blue films were studied simultaneously by EIS, CIS, and MIS at different stabilization potentials between the fully reduced form (Everitt’s Salt, ES) and the mixed valence compound (Prussian blue, PB). Figure 2a shows an example (0.325 V) of the EIS represented as faradaic capacitance, CF, or electrical charge impedance, (∆q/∆E)(ω)

CF(ω) )

1 ∆q Z (ω) ) (ω) jω F ∆E

(7)

The faradaic impedance, ZF, was obtained from the electrical impedance function by subtracting the contribution due to the uncompensated resistance from the the double-layered capacitance obtained from EIS at high frequencies. MIS and CIS at 690 nm spectra obtained for PB films at 0.325 V are also plotted in panels b and c of Figure 2, respectively. At first glance, there seems to be good correlation among panels a, b, and c of Figure 2. It could be said that electrochemical impedance for PB films presents classical capacitor behavior at lower frequencies and that mass and color impedance functions follow the capacitance behavior. The MIS in the third quadrant indicates the main participation of a cation as a


Figure 2. Electrochemical impedance spectroscopy represented as electrical charge impedance (a), mass impedance (b), and color impedance (c) for a PB film in an aqueous KCl 0.5M, pH 2.98 solution. Stabilization potential is E ) 0.325 V, and wavelength for color impedance is 690 nm.

counterion, while the CIS in the first quadrant clearly indicates that absorbance at this wavelength decreases for the reduced form (δε1ε1690 > 0), given that the oxidized form of this film is blue (PB), whereas the reduced form is colorless (ES). The analyses of the crossed impedance functions introduce some different information. Figure 3 shows F(∆m/∆q)(ω),


Figure 3. Crossed impedance functions (a) F(∆m/∆q)(ω), (b) F(∆Aλ/ ∆q)(ω), and (c) (∆Aλ/∆m)(ω) for a PB film in an aqueous KCl 0.5M, pH 2.98 solution. Stabilization potential is E ) 0.325 V, and wavelength for color impedance is 690 nm. Simulations (lines) were calculated by considering two cation species, K+ (faster) and H3O+(slower), and each of these cations has a different molar absorptivity (zero for the protonassociated process) (eqs 1-3). No delay was considered among the different impedance functions. HF means high frequency, and LF means low frequency.

F(∆A/∆q)(ω), and (∆A/∆m)(ω) impedance functions for this film at 0.325 V. Figure 3a shows that the F(∆m/∆q)(ω) function

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has values between -26 and -30 g mol-1. These values may be explained by the exchange of two cation species.19-21,42 However, there is also the possibility of a delay between the mass response and electrical charge response to the same potential perturbation. At these potentials, the electrochemical behavior of Prussian blue films has been described in terms of the exchange of two ions: potassium ions and a smaller participation of hydrated protons.19-21,42 The participation of an anion is not considered because the mass impedance function (Figure 2b) shows only one loop in the third quadrant (cation participation). For the case of the F(∆Aλ/∆q)(ω) impedance function, it is similar. The shape of this function may be obtained by a simulation considering two different processes that produce changes of color at this wavelength, where the faster one produces more color changes than the slower one. Finally, the shape of the (∆Aλ/∆m)(ω) function may be reproduced by considering the same hypotheses. Figure 3 also shows all these simulations. The shape of these functions has been obtained for the case where the faster process corresponds to a larger molar mass and the slower process to the smaller molar mass. It is similar for the F(∆Aλ)/(∆q)(ω) impedance function, where the faster process is associated with a larger molar absorptivity and the slower process with the smaller molar absorptivity. In previous papers, it has been proved that at this potential there is a residual participation of protons together with the main participation of potassium.20 At other potentials, the participation of protons may be neglected; this is the case at 0.175 V, which is near the peak potential.20,40 However, at this potential the F(∆m/∆q)(ω) impedance function also shows a loop (Figure 4). In this case, if only one species participates, the only possibility for obtaining this loop is a delay between mass and electrical charge responses.23 Looking at the shape of the F(∆m/ ∆q)(ω) impedance function, the electrical charge response is faster than the mass response. Accordingly, the simulation reproduces this shape quite well considering this hypothesis (Figure 4). The case of the F(∆Aλ/∆q)(ω) impedance function seems a little different because a loop appears in the first quadrant. The shape of this loop seems to be more similar to the shape obtained for the two processes with different molar absorptivities than to the shape obtained by a single process and a delay between the electrical charge and color changes.23 Simulations included in Figure 4 consider two processes for the electrochromic process. This case will be discussed later. Therefore, it should be considered that all three signals analyzed (current, mass, and color) are not synchronized, i.e., the rates for the electron motion through the electrode (electron hopping between neighboring centers), mass changes associated with the charge balance (ion exchange), and color changes (electron configuration changes due to the electrochemical reactions of a chromophore center) are different. Herein, the main doubt may be whether or not this delay among different signals is caused by the different electronics of the different analogical signals. Current and color changes (first converted into a current) have similar electronics (current to potential converter), which do not introduce any significant delays at these frequencies (from 100 to 0.01 Hz). Mass changes were obtained from the difference between the reference frequency and working electrode frequency using frequency comparator equipment and a frequency to voltage converter. This assembly introduces some delay, but it is corrected by a calibration procedure.32,33 Thus, the nonsynchronized response of the different signals should be attributed to the physical properties and to the electrochemical behavior of Prussian blue films and not to the electronics.

Agrisuelas et al.

Figure 4. Crossed impedance functions (a) F(∆m/∆q)(ω) and (b) F(∆Aλ/∆q)(ω) for a PB film in an aqueous KCl 0.5M, pH 2.98 solution. Stabilization potential is E ) 0.175 V, and wavelength for color impedance is 690 nm. Simulations (lines) were calculated by considering two active processes and eqs 1-3. Both processes were associated with potassium cations, but the slower one is associated with a zero molar absorptivity. This is considered a delay between different impedance functions, following this order: τCIS ) (1/2)τEIS ) (1/4)τMIS for both processes. HF means high frequency, and LF means low frequency.

The above presented methodology represents a fast way to identify processes taking place during electrochemical reactions of electroactive films. One of the most interesting topics in conducting and electrochromic films is the study of the kinetics of these processes. The single observation in Figure 4 allows a sequence for the electron conduction through the electroactive film to be proposed. The first step is associated with the color change, and it corresponds to an electron configuration change in an electroactive center fast step, where electrons move into different bands. The second step or intermediate step is the electron hopping between neighboring centers (electron motion through the film), and finally, the last and slower process is the balance of the electrical charge by the counterion exchanges. This hypothesis may be corroborated by the fitting of experimental data to the simplified theoretical model proposed.21,23 This has been chosen as the case for the two exchanged species (eqs 1-3). Herein, we will analyze values obtained for the main process because values obtained for the other process are accompanied by a large indetermination. Therefore, it is possible to obtain information on the following parameters from the



Figure 5. Dependence of time constants calculated from the fitting of the experimental impedance data to eqs 4-6 for (∆q/∆E)(ω), (∆m/ ∆E)(ω), and (∆Aλ/∆E)(ω).

Figure 6. Color impedance for a PB film in an aqueous KCl 0.5M, pH 2.98 solution. Stabilization potential is E ) 0.250 V, and wavelength for color impedance is 690 nm.

fitting: 1/(FG), τ1 and K from the EIS, and 1/(ε1λG1), K1, and τ1 from the CIS, and 1/(M1G1), K1, and τ1 from the MIS. Figure 5 shows the dependence of the time constants on the potential. It should be noted that the time constant obtained from the color impedance function proves smallest at most of the studied potentials, while the time constant associated with the mass impedance function proves the largest. This result is in good agreement with the observations of the previously mentioned crossed impedance functions. The order from slower to faster processes inferred from the crossed impedance functions corresponds to the order here obtained from the fitting of the experimental data to the theoretical model (Introduction). Values of the time constants for the mass exchange processes corroborate that this is the slower process at any studied potential except at 0.250 V, where the color change at 690 nm is apparently slower. This potential corresponds to a Fe(III)/[Fe(II) + Fe(III)] ratio near 0.31. At this ratio and according with the covalent exchange model, we have observed an abrupt change of physical properties of this film42,42 that may be explained by means of an electron configuration reordering, which apparently makes this color change slower than the mass and current changes because of the optimization of the double-exchange mechanism.42-44 The shape of the MIS, EIS and CIS are slightly different at this potential showing a quasi double loop (Figure 6). The analyses of the crossed impedance functions at this potential are interesting (Figure 7). The shape of the F(∆A/ ∆q)(ω) function is very different from the shape of this function at other potentials (Figure 3). It is not easy to obtain a good simulation considering only a slower color change than electrical charge changes. It should be noted that the very different shape of the color impedance function at these potentials indicates the presence of another parallel process that affects the color response at this wavelength, and that is not considered in eqs 1-3. On the other hand, the shape of the F(∆m/∆q)(ω) function is well simulated by considering the same hypothesis as that at 0.175 V. At larger cathodic potentials than 0.100 V, there is a catalytic process due to the presence of molecular oxygen in the solution,31,45 which causes no mass change and no color change but a net current change. This fact causes an apparently faster impedance response for the current. This case is similar to some studies of color changes in LixWO3 films, where color changes

apparently are slower than electrical charge changes because of the presence of parallel reactions46 or the presence of coloring ionic trapping states.47 The dependence on the potential of the G1 -1term obtained from the fitting of the experimental impedance data to the proposed model is plotted in Figure 8. Thus, we observe an exponential dependence at potentials far from the peak potential, which agrees with the proposed theoretical model48

G1 )

G1,max B1 cosh (E - E0 1) 2

(

)

(8)

where G1,max represents the maximum value for this function (at E ) E10′), E10′represents the formal potential for the redox process k1

PB + e- + K+ {\} ES k-1

B1 nR ) F (direct reaction) 2 RT

(9)

B1 n(1 - R) ) F (reverse reaction) 2 RT

(10)

or

Values of R ) 0.5 imply that the variation of G on the applied potential presents a symmetry with respect to the formal redox potential, and values for B1 are the same for the direct and reverse reactions. In any other case, B1 values are different, and the dependence of G on the applied potential should be asymmetrical. At 298 K, (B1)R)0.5/2 ) 19.5 V-1 for n ) 1 electron. Thus, it is possible to obtain an estimation of this parameter for the reverse and forward reactions from the slope of log(G1) versus E plot (Figure 8). Values obtained for the different slopes are about 20 V-1 in all the cases, except for the G parameter obtained for the color impedance at potentials between 0.250 and 0.375 V, where the slope reaches values near 39 V-1. The G parameter has been interpreted for the EIS case as the inverse of a charge transfer resistance. By analogy, those G parameters obtained from MIS may be interpreted as the inverse of a mass transfer resistance, and for the case of G parameters obtained from CIS, they may be interpreted as the inverse of a color transfer resistance. The

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Agrisuelas et al.

Figure 8. Dependence on the potential of FG, MG, and ε690G parameters obtained from the fitting of the experimental impedance data to eqs 4-6.

Figure 7. Crossed impedance functions (a) F(∆m/∆q)(ω) and (b) F(∆Aλ/∆q)(ω) for a PB film in an aqueous KCl 0.5M, pH 2.98 solution. Stabilization potential is E ) 0.250 V, and wavelength for color impedance is 690 nm. Simulations (lines) were calculated by considering two active processes and eqs 1-3. Both processes were associated with potassium cations. It is considered a delay between different impedance functions, following this order: τEIS ) (1/2)τMIS for both processes. It was not possible to obtain a good simulation for the F(∆Aλ/ ∆q)(ω) function. HF means high frequency, and LF means low frequency.

mass transfer resistance may be located at the polymer-solution interfacial region, where the counterion insertion and expulsion processes take place. The color transfer resistance is not easy to locate because color changes take place by a change in the electronic configuration of the chromophore center and perhaps may be related to the energy barrier for the electronic configuration change. In this last case, the asymmetry of the dependence of G on the applied potential is related to the fact that at potentials in the range of 0.30-0.40 V color changes are very small at this wavelength, when compared with mass and electrical charge changes (Figure 1b). Another interesting parameter that may be obtained from the fitting is FGd/K (EIS), MGd/K (MIS), or ελGd/K (CIS). These parameters have been interpreted as the derivatives of the insertion law for the counterion species.20 It is clear that electrical charge changes and counterion motion are related; however, it is not always the same for color change at a given wavelength because in PB films there are different Fe(III) sites that may be active for redox processes but not for color change at this wavelength. In other words, these parameters are related

Figure 9. Dependence on the potential of FGd/K, MGd/K, and ε690Gd/K parameters obtained from the fitting of the experimental (∆q/ ∆E)(ω), (∆m/∆E)(ω), and (∆Aλ/∆E)(ω) impedance data to eqs 4-6. These parameters are multiplied by different factors for the purpose of comparison.

with the maximum number of sites active for each one of the studied impedances. Figure 9 shows the variation of these parameters on the applied potential. Looking at Figure 9, we observe good correlation between the mass and electrical charge impedance; differences in the voltage (0.30 and 0.40 V) may be attributed to the participation of protons and potassium cations together in this range of potentials that make the mass response smaller. The analysis of the color impedance function proves slightly different. On the one side, there is the maximum displaced to more cathodic potentials, and on the other side, there is the very small response between 0.30 and 0.40 V. This effect is better observed when we analyze the ratio between the mass and electrical charge and the ratio between the color and electrical charge (Figure 10). Figure 10 shows that the mass/electrical charge ratio keeps more or less constant in a wide range of potentials from 0.000 to 0.300 V, indicating good correlation between the mass and electrical charge changes in this range of potentials. This ratio


J. Phys. Chem. C, Vol. 113, No. 19, 2009 8445 Finally, the molar mass and molar absorptivity, at potentials in the range of 0.0-0.1 V, do not vary with the potential and reach maximum values. Conclusion

Figure 10. Dependence of the ratios (MFGd/K)MIS/(FGd/K)EIS (apparent molar mass of participating species) and (ε690FGd/K)CIS/(FGd/ K)EIS (apparent molar absorptivity of participating species). All of these parameters were obtained from the fitting of the experimental impedance data (∆q/∆E)(ω), (∆m/∆E)(ω), and (∆Aλ/∆E)(ω) to eqs 4-6.

may be interpreted as a mean value for the molar mass of the species participating in the redox processes. Thus, in this range, there appears to be very important participation of potassium cations because the molar mass are near 40 g mol-1. In the voltage range of 0.300-0.400 V, this ratio decreases due to the participation of protons.20 Therefore, two zones can be distinguished from this ratio. On the other hand, the color/electrical charge ratio proves very small in the range of potential voltage (0.300-0.400 V), so indicating that most of current passed causes no color change at this wavelength. This ratio may also be interpreted as a first estimation of the molar absorptivity, ελ. The physical interpretation of this behavior is not obvious. It should be considered that the PB crystal structure presents different Fe(III) sites. It should be noted that the main structure of this crystal has been described with one-fourth of the Fe(CN)64- vacancies.49-51 This fact generates different Fe(III) surrounding sites. It is known that Fe(CN)5H2O complexes, where one of the cyanides is substituted by other anions such as OH-, does not present the classical blue color.52 Thus, the change of the oxidation state of this center does not produce any color change at 690 nm. The color change in the range of potentials of 0.300-0.400 V is very small. It also proves interesting that the molar mass of the exchanged species does not vary significantly in the range of 0.000-0.300 V, which corresponds to the potassium exchange. However, it is important to emphasize that the molar absortivity only keeps constant in the range of 0.000-0.100 V. This means there is also another redox process, where the potassium participates as a counterion, that produces a smaller or no color change. This is also related to different Fe(III) sites in the PB crystal structure. Thus, at least three different processes can be identified. The first one at potentials of 0.30-0.40 V, where the proton participates as a counterion, and color changes are very small at 690 nm. Another process occurs at potentials near the peak potential, where potassium participates mainly as a counterion. Here, there are color changes, but molar absorptivity changes with the potential. Therefore, at these potentials, there is only one cation species, but at least two different color changes are associated with the processes. It may be that there are two different sites for potassium insertion.18

By obtaining and simultaneously analyzing the three impedance functions, we open new possibilities for the knowledge of the kinetics of electrochemical processes taking place in conducting films. A fast and only qualitative analysis of the shape of the experimental impedance functions and crossed impedance functions evaluated from the experimental ones has allowed different species participating in the electrochemistry of PB films to be detected. Besides, results allowed fast and slow processes to be discerned. It has been proved that color changes are faster than electrical charge changes through the electrode and that there is participation of counterions for the electrical charge balance. This conclusion is not easy to obtain by other experimental techniques, and in this case, information is obtained at the electronic level from electrochemical and spectroscopic in situ techniques. In PB films, the first step during an electrochemical process corresponds to an electron configuration change associated with changes of absorbance at 690 nm. Then, the electron moves to a neighboring center (electron conduction), and finally, cations reach or leave their site in the PB structure to balance the electrical charge. Because mass changes and electrical charge are not exactly coupled, we have a nonlocal electroneutrality condition. The analysis of the apparent molar absorptivity and molar mass dependence on the applied potential has allowed at least three overlapped electrochemical processes or different sites for cations insertion in the PB film structure to be postulated: one site for proton insertions, another site for potassium that does not cause color changes, and a third site for potassium that does cause color change at 690 nm. Acknowledgment. This work is supported by FEDER-CICyT project CTQ2007-64005/BQU. D.G.-R. acknowledges his position with the Generalitat Valenciana. References and Notes (1) Neff, V. D. J. Electrochem. Soc. 1978, 125, 886–887. (2) Itaya, K.; Akahoshi, H.; Toshima, S. J. Electrochem. Soc. 1982, 129, 1498–1500. (3) Mortimer, R. J.; Rosseinsky, D. R. J. Chem. Soc., Dalton Trans. 1984, 2059, 2061. (4) Feldman, B. J.; Melroy, O. R. J. Electroanal. Chem. 1987, 234, 213–227. (5) Roig, A.; Navarro, J.; Garcia, J. J.; Vicente, F. Electrochim. Acta 1994, 39, 437–442. (6) Garcia-Jarenõ, J. J.; Navarro, J. J.; Roig, A. F.; Scholl, H.; Vicente, F. Electrochim. Acta 1995, 40, 1113–1119. (7) Navarro-Laboulais, J.; Vilaplana, J.; Lopez, J.; Garcia-Jarenõ, J. J.; Benito, D.; Vicente, F. J. Electroanal. Chem. 2000, 484, 33–40. (8) Cox, J. A.; Jaworski, R. K.; Kulesza, P. J. Electroanalysis 1991, 3, 869–877. (9) Malik, M. A.; Kulesza, P. J.; Wlodarczyk, R.; Wittstock, G.; Szargan, R.; Bala, H.; Galus, Z. J. Solid State Electrochem. 2005, 9, 403– 411. (10) Mortimer, R. J.; Rosseinsky, D. R.; Glidle, A. Solar Energy Mater. and Solar Cells 1992, 25, 211. (11) Mortimer, R. J. J. Electrochem. Soc. 1991, 138, 633–634. (12) Kulesza, P. J.; Zamponi, S.; Malik, M. A.; Miecznikowski, K.; Berrettoni, M.; Marassi, R. J. Solid State Electrochem. 1997, 1, 88–93. (13) Rosseinsky, D. R.; Glasser, L.; Jenkins, H. D. B. J. Am. Chem. Soc. 2004, 126, 10472–10477. (14) Itaya, K.; Uchida, I. Inorg. Chem. 1986, 25, 389–392. (15) Itaya, K.; Ataka, T.; Toshima, S. J. Am. Chem. Soc. 1982, 104, 4767–4772. (16) Araci, Z. O.; Runge, A. F.; Doherty, W. J.; Saavedra, S. S. Isr. J. Chem. 2006, 46, 249–255. (17) Robin, M. B. Inorg. Chem. 1962, 1, 337–342.

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