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Reversible Surface Two-Electron Transfer Reactions in Square Wave Voltcoulommetry: Application to the Study of the Reduction of Polyoxometalate [PMo12O40]3− Immobilized at a Boron Doped Diamond Electrode Joaquin Gonzalez,† Angela Molina,*,† Manuela Lopez-Tenes,† and Fereshteh Karimian‡ †

Departamento de Química Física, Facultad de Química, Regional Campus of International Excellence “Campus Mare Nostrum”, Universidad de Murcia, 30100 Murcia, Spain ‡ Department of Chemistry, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran S Supporting Information *

ABSTRACT: Reversible surface two-electrons transfer reactions (stepwise processes) are analyzed using square wave voltcoulommetry (SWVC), which is a variety of square wave techniques based on the measurement of the transferred charge. Such reversible surface redox processes are exhibited by many two-redox center and multicenter biomolecules (proteins, enzymes, ...) and inorganic molecules like polyoxometalates (POMs), which have very interesting applications, mainly as electrocatalysts. Because of the stationary character of the response obtained, the key parameters that govern the cooperativity degree of the two reversible electron transfers (ETs) are the difference between their formal potentials, ΔE0, and the square wave amplitude, |ESW|, whose combined effect sets the two peaks → one peak transition in the response. Working curves based on the variation of the peak parameters (peak potentials, half-peak widths, and peak heights) with ΔE0 and |ESW| are given, from which the formal potentials and the total surface excess can be accurately determined. SWVC has been applied to the study of the reduction of polyoxometalate [PMo12O40]3− adsorbed at a boron doped diamond electrode (BDD), for which three stable and well-defined reversible charge peaks, corresponding to three cooperative EE processes, are obtained in the interval (0.6, −0.2) V by using low square wave frequencies. From the analysis of these peaks, the values of the total surface excess and the formal potentials of the six ETs have been obtained in aqueous media for two electrolytes: HClO4 and LiClO4. he great field of applications of molecules containing multiple redox centers which are reduced/oxidized in several steps justifies and fuels the considerable efforts being carried out to obtain a better understanding of the electron transfer (ET) processes taking place.1−9 At present, special attention is being paid to the study of these molecules when they are adsorbed onto an electrode and the ETs are direct, without mediators, and avoiding the complexity arising from the consideration of mass transport.1−5,10 Many of these systems present a reversible behavior (or it can be reached by acting on the suitable experimental parameters in the particular electrochemical technique used),1−4,10 which simplifies the study of multielectron transfer processes (themselves complicated) by not having to consider the kinetics of the ETs. To date, cyclic voltammetry (CV) is the most used technique in the study of ETs for adsorbed molecules containing multiple redox centers,1−5,10−13 although more advantageous can be the use of discrete nature potential perturbations as are those based in square wave and staircase waveforms, for which signals with

T

© XXXX American Chemical Society

improved faradaic-to-background ratio, which are much less affected by double layer influences, are recorded. When the ETs behave as reversible, techniques based on charge measurements such as square wave voltcoulommetry (SWVC)14,15 or differential staircase voltcoulommetry (DSVC),16,17 and provide an easily characterizable peak-shaped charge-potential response. On the other hand, more usual techniques based on the recording of currents such as square wave voltammetry (SWV) and staircase voltammetry (SCV) provide negligible measured currents for adsorbed molecules with reversible behavior and therefore cannot be used in these conditions.14,16,18 To use these last techniques, high values of the square wave frequency must be used, for which a quasireversible behavior is exhibited by the system under study.14 The SWVC technique presents the following additional advantages which makes it particularly suitable for the study of Received: June 20, 2013 Accepted: August 7, 2013

A

dx.doi.org/10.1021/ac4019236 | Anal. Chem. XXXX, XXX, XXX−XXX

Analytical Chemistry

Article

In the study of the above process it will be assumed that no surface interactions occur in the monolayer and that heterogeneity of the electroactive monolayer can be ignored (Langmuir isotherm). No desorption takes place on the time scale of the experiment, such that the total excess ΓT is constant and independent of the potential during the whole experiment. In this article, SWVC is applied to the characterization of the reversible surface EE mechanism given by the reaction scheme in eq II. In this technique a square wave potential waveform of height 2|ESW| superimposed on a staircase of amplitude |ΔEs| is applied as (see Scheme S0 in the Supporting Information):12,14

multistep reversible systems: (a) The charge-potential curves present a practically constant baseline; (b) the peak parameters of the SWVC curves show great sensitivity in determining the characteristic parameters of the process; (c) it shows an enhanced resolution for experimental responses. Note also that recording the charge can be easily implemented in traditional electrochemical instrumentation (see the experimental section in the Supporting Information). In this article we will use SWVC to study reversible surface ETs for two-center redox molecules (EE mechanism), whose complete characterization is essential for approaching more complex behaviors like ETs in multicenter molecules, catalytic coupled processes, and intramolecular ETs.3−5,10,19 Moreover, this study is applicable for modeling the noncatalytic voltammetry of redox enzymes10,19 and other catalysts like polyoxometalates (POMs),20,21 attached to the electrode, if the substrate is not present. The theoretical predictions achieved have been applied to the study of the electrochemical reduction of the Keggin heteropolyanion [PMo12O40]3− immobilized at the surface of a boron doped diamond electrode (BDD). This polyoxometalate in solution may present up to five two-electron consecutive reductions in aqueous acidic media in agreement with ref 20. For the first three reductions, the potentials depend on pH as a result of protonation, PMo12O403 − + 2e− + 2H+ ⇌ H 2PMo12O40 3 − ⎫ ⎪ ⎪ H 2PMo12O40 3 − + 2e− + 2H+ ⇌ H4PMo12O403 −⎬ ⎪ H4PMo12O403 − + 2e− + 2H+ ⇌ H6PMo12O40 3 − ⎪ ⎭

⎫ ⎡ ⎛ p + 1⎞ ⎤ ⎟ − 1⎥|ΔE | ⎪ Ep = E initial + ⎢Int⎜ s ⎣ ⎝ 2 ⎠ ⎦ ⎪ ⎬ p+1 + ( − 1) |ESW | ; p = 1, 2, ..., np/2 ⎪ ⎪ Ep = Enp − p + 1; p = (np/2) + 1, ..., np ⎭

where Int(x) is the integer part of the argument, x, and np the total number of potential pulses in a whole cyclic sweep. The charge is measured at the end of each potential pulse and the net response for the mth cycle, ΔQSW, is the difference between the signal corresponding to a pulse with odd index (Qmforward) and the signal of the following pulse with even index (Qmreverse), m m ΔQ SW = Q forward − Q reverse = Q 2m − 1 − Q 2m ;

m = 1, 2, ..., np/2

ΔQ SW QF −

E20

2 K + J ̅ 2m − 1 K + J ̅ 2m − 1 + K (J ̅ 2m − 1 )2

2 K + J ̅ 2m ; K + J ̅ 2m + K (J ̅ 2m )2

m = 1, 2, ..., np/2

where ⎛ F p ⎞ J ̅ p = exp⎜ (E − E ̅ 0 )⎟ ⎝ RT ⎠

E̅ 0 =

THEORY Let us consider a surface EE mechanism in which two reversible electron transfers (ETs) occur as indicated in the following reaction scheme: I + e− ⇄ R

=

(3)

■

E10

(2)

with all the potential pulses having the same time length, τ. By taking into account previous results17 (see also section 2 of the Supporting Information), the above expression for the net charge can be written as

(I)

The immobilization of this complex at an electrode surface was first reported by Wang et al.22 and Rong et al.,23 who pointed out the strong adsorption that this species presents at glassy carbon, edge pyrolytic graphite, gold, and mercury electrodes. In the case of carbon electrodes, in aqueous acidic media, three reversible waves can be observed in the potential range 0.6 to −0.2 V for each of which a global two-electron character has been assigned. As far as we know, no systematic discussion has been carried out on the nature of these dielectronic responses. The electrochemical behavior of this complex has been analyzed, and very accurate values of the total surface excesses and formal potentials of the different ETs have been obtained in two aqueous media (HClO4 and LiClO4) in a very simple way.

O + e− ⇄ I

(1)

(II)

p = 1, 2, ...np

(E10 + E20) 2

(4)

(5)

⎛ F ⎞ K = exp⎜ ΔE 0⎟ ⎝ RT ⎠

(6)

ΔE 0 = E20 − E10

(7)

Q F = FS ΓT

(8)

with E̅ being the average formal potential and S the electrode area. The ΔQSW signal is plotted versus the index potential, defined as the arithmetic average value of the potentials applied in the mth cycle (i.e., the staircase potential), 0

in which O (oxidized), I (intermediate or half-reduced), and R (reduced) refer to the different redox states of the adsorbed molecule O forming a monolayer that we will suppose is totally oxidized at the beginning of the experiment. E01 and E02 are the formal potentials of the first and second steps, respectively. This approach corresponds to a macroscopic description of the system, where O, I, and R refer to “overall” redox states, and no differentiation between possible microstates corresponding to a particular oxidation state is considered.

m E index = E2m − 1 + ( − 1)2m |ESW | ;

m = 1, 2, ..., np/2 (9)

So, eq 3 can be rewritten in terms of the index potential as B


Analytical Chemistry ΔQ SW QF −

=

Article

m 2 K + J index /A ̅

K 2

m + J index /A + ̅ m K + J index ̅ A

m K + J index ̅ A+

conditions the charge response has amply reached its maximum value corresponding to reversible behavior (see Figure S1 in the Supporting Information).

m /A)2 K (J index ̅

m 2 K (J index ̅ A)

■

RESULTS AND DISCUSSION Theoretical Results. From the above study of a reversible surface EE mechanism in SWVC, it results from eq 10 that the key parameters to be considered for its analysis are the difference between the formal potentials of both steps in the reaction scheme in eq II, ΔE0, (through K, see eqs 6 and 7), and the square wave amplitude, |ESW| (see eq 12). Figure 1 shows the cyclic normalized ΔQSW−Eindex curves ((ΔQSW/QF)−(Eindex − E̅0) curves), calculated from eq 10, for

;

m = 1, 2, ..., np/2

(10)

where ⎛ F ⎞ m = exp⎜ J index (E m − E ̅ 0 )⎟ ̅ ⎝ RT index ⎠

m = 1, 2, ...np/2 (11)

⎛ F ⎞ |E |⎟ A = exp⎜ ⎝ RT SW ⎠

(12)

Note that (ΔQSW/QF) given by eq 10 is an even function of (Emindex − E̅0), i.e., the function takes the same values for (Emindex − E̅0) and (E̅ 0 − Emindex) (by changing Jmi̅ ndex for (1/Jmi̅ ndex)), which is a consequence of the behavior for species O and R of the reaction scheme in eq II in a reversible process (see also eq S4 in section 2 of the Supporting Information). It is worth highlighting that the stationary character of the ΔQSW−Eindex response (see section 2 of the Supporting Information) leads to the net charge-potential curves were logically independent of the square wave frequency, f(= 1/ (2τ)), and the staircase amplitude, |ΔEs|, and only dependent on the square wave amplitude |ESW|. Therefore, they are superimposable on those obtained for any differential electrochemical technique of double pulse (double differential pulse voltammetry, DDPV) or multipulse potential (differential multipulse voltammetry, DMPV)24 provided that the difference between the successive potential pulses coincides with 2|ESW|. Moreover, when the value of this difference is less than RT/F, the response obtained with any of the above techniques is identical to those in cyclic voltammetry (CV), alternating current voltammetry (ACV), potentiometric stripping analysis (PSA), and also it is transferable to that in any reciprocal derivative chronopotentiometric technique,25 that is ⎛ ΔQ SW ⎞ ⎜ ⎟ ⎝ |ESW | ⎠|E

SW | −71.2 mV, only one peak is obtained for any value of |ESW| and a nonlinear fall of W1/2 with ΔE0 is always obtained and is more pronounced as |ESW| decreases. Thus, by working at E2peak

Figure 3. Evolution of the peak potentials, Epeak − E̅ 0 (a), half-peak width, W1/2 (b), and normalized peak charge, ΔQSW,peak/QF, with ΔE0, calculated from eq 10 for an adsorbed molecule presenting two reversible ETs according to the reaction scheme in eq II. These curves have been calculated for different |ESW| values shown in the curves (in mV). The red lines correspond to the particular case |ESW| = 75 mV. The dashed blue line in parts b and c separates the regions for one or two peaks in the SWVC response. Other conditions are the same as in Figure 1.

3 for the same values of |ESW| as in Figure 2, which are shown on the curves. Figure 3a shows the variation with ΔE0 of the peak potentials of the square wave voltcoulograms, referred to the average formal potential (E̅0) value. Thus, a horizontal line, located at E

E1peak)



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small values of |ESW|, values of ΔE0 in the interval (−71.2 < ΔE0 < 50) mV can be determined. For more positive values of ΔE0, the limit W1/2 = 45 mV for an E mechanism with two electrons is obtained.14 A dashed blue line separates the regions for one or two peaks in the SWVC response. This line has a slope equal to 2 (i.e., W1/2 = 2|ΔE0|, see Figure 2a,b). If ΔE0 has been determined from Figure 3a and/or Figure 3b, the total surface excess, ΓT, can be obtained from Figure 3c. This figure shows that the peak heights always increase with |ESW|, and it takes constant values for extreme values of ΔE0 which coincide with that corresponding to a simple reversible ET for very negative values of ΔE0 (for which two peaks are obtained) and with that corresponding to an apparent simultaneous two-electron transfer for very positive values of ΔE0 (for which one peak is obtained). Note that, as in the previous case for the half-peak width, the peak height is greatly influenced by the value of ΔE0, with its value being multiplied 2.5 times for |ESW| = 50 mV and 3.3 times for |ESW| = 25 mV. Therefore, in the case in which the normalized peak charge ΔQSW,peak/QF was accurately known by another method, a very precise measurement of ΔE0 was obtained from the peak height. As in Figure 3b, the regions of one or two peaks in the SWVC response are separated with a dashed blue line. Experimental Results. The reduction of the Keggin heteropolyanion [PMo12O40]3− immobilized at the surface of a BDD electrode has been studied to illustrate the theoretical analysis carried out in the previous section. In the case of carbon electrodes like glassy carbon or pyrolytic graphite electrodes, in aqueous acidic media, three reversible waves can be observed in the potential range (0.6, −0.2) V, for each of which a two-electron transfer has been assigned (see the reaction scheme in eq I in the introduction section and ref 20). We will analyze the nature of these reduction processes of the [PMo12O40]3− complex under reversible conditions by applying SWVC in aqueous media with two electrolytes, HClO4 1.0 M and LiClO4 0.1 M, in order to prove the capabilities of this technique of elucidating the mechanism of the charge transfer processes taking place. First, the stability of the [PMo12O40]3− monolayer at a BDD electrode formed by direct immobilization of this complex has been checked with CV (see Figure S2 in the Supporting Information), which shows the cyclic voltammograms of this monolayer for three scan rates). When comparing the direct and inverse scans, the voltammograms show three stable and practically symmetrical peaks with the peak potentials being independent of the scan rate for values of vCV below 0.5 V s−1 (maximum differences of 5 mV, see Table S1 in the Supporting Information), such that these reductions can be considered as reversible under these conditions. Cyclic square wave charge−potential curves corresponding to [PMo12O40]3− monolayers in the same electrolytes are shown in Figure 4 for different pulse times in the range 50−100 ms (i.e., frequencies in the range 10−5 Hz) and |ESW| = 25 mV. From these curves it can be seen that very well-defined peaks are obtained in both electrolytes at the BDD electrode, with a nearly constant baseline. Actually, the resolution achieved in the three peaks greatly improves on that obtained at the cyclic voltammograms (see Figure S2 in the Supporting Information) and even on that corresponding to SWVC at other carbon electrodes such as glassy carbon or edge plane pyrolytic graphite (see Figure S3 in the Supporting Information). It can be also seen in Figure 4 that the converted charge increases

Figure 4. Cyclic square wave ΔQSW−Eindex curves of a [PMo12O40]3− monolayer at a BDD electrode for aqueous HClO4 1.0 M (A) and LiClO4 0.1 M (B) media and time pulses τ = 50, 75, and 100 ms (i.e., f = 10, 6.7, and 5 Hz) shown in the curves. |ESW| = 25 mV, |ΔEs| = 5 mV. T = 298 K.

with the pulse time length until for τ ≥ 75 ms no significant differences in the peak charges are observed in the ΔQSW−Eindex curves (which are negligible in Figure 4A and are below 5% in Figure 4B), so the response can be considered as reversible under these conditions (i.e., for low frequencies). The symmetry of the curves with respect to the zero charge axis also confirms the reversibility of these processes under these conditions, in line with the discussion in Theoretical Results (see Figure 1). Note that this behavior is opposite to that observed for the current potential curves in SWV (ΔISW−Eindex), for which an increase of the pulse time (that is, a decrease of the frequency) leads to a decrease of the response which, for long enough times, becomes indistinguisable from the background current (see Figures S1 and S3 in the Supporting Information and ref 14). In order to analyze the curves in Figure 4, we will assume that each peak corresponds to an isolated EE process with a cooperative character, i.e., with a not very negative or even a positive value of ΔE0 (see Theoretical Results and refs 10 and 28), such that each one (denoted as processes I, II, and III) can be treated separately from the others. The values of the peak parameters (peak potentials, peak charges, and half peak widths) of the three peaks corresponding F



Article

Γ[PMo12O40]3− (LiClO4) = 1.6 × 10−11 mol cm−2. In both cases, the values obtained indicate submonolayer coverages for which deviations from ideal behavior due to intermolecular Coulombic repulsions between the adsorbed molecules would not be significant. (5) Once QF is known, the values of ΔE0I and ΔE0II can be accurately determined from curves in Figure 3c (see Table 1). (6) By combining the values of E̅ 0i and ΔE0i , the individual formal potentials of the six ETs are obtained (see Table 1). From the values obtained for the formal potentials, theoretical ΔQSW−Eindex curves have been calculated by using eq 10 for each of the three processes. The overall response will be the sum of the three individual ones (as shown in Figure S6 in the Supporting Information). From these results it can be concluded that the above assumption of three isolated cooperative EE processes is justified in both electrolytes since no significant difference between the three different individual processes and the overall response is obtained (with relative errors between individual and overall responses below 3%). In order to check the goodness of the results obtained, in Figure 5 the experimental SWVC curves of a [PMo12O40]3−

to the direct response appear in Table S2 in the Supporting Information. A time pulse of 100 ms (frequency of 5 Hz) and a value of |ESW| = 25 mV have been chosen in order to minimize overlappings between peaks (see Figure 2). From the data shown, the difference between peak potentials for processes II and III is higher than 170 mV for both electrolytes, and the difference between peak potentials for processes I and II is around 100−130 mV. Therefore, the above assumption of considering three isolated cooperative EE processes is justified, at least in the case of process III. We will discuss below the validity of this assumption for processes I and II. Our purpose is to obtain, from the analysis of the peak parameters of the ΔQSW−Eindex curves of the [PMo12O40]3− monolayers, the value of the total surface excess together with the formal potentials of the two monoelectronic reductions involved in each of the three EE processes observed. Thus, it is necessary to obtain the average formal potentials E̅0i (eq 5) and the difference between formal potentials, ΔE0i (eq 7), for the three processes (i = I, II, and III). After removing the nonfaradaic contribution of the ΔQSW− Eindex curves in the way discussed in the Experimental Section (see section 1 and Figure S5 of the Supporting Information), the following steps have been followed: (1) The average formal potential for each particular process (E̅ 0I , E̅ 0II, and E̅ 0III) has been considered equal to the corresponding peak potential (see Table 1) . (2) From half peak widths values of the three peaks Table 1. Average Potentials E̅0i and ΔE0i = E02,i − E01,i for the Three Peaks (i = I, II, and III), Corresponding to the Direct Response of [PMo12O40]3− Monolayer Shown in Figure 4a HClO4 1.0 M process

E̅0i /mV

vs

SCE

ΔQSW,peak,i/QF

ΔE0i /mV vs SCE

17 1.21b 1.41b 85 1.07 −10 LiClO4 0.1 M

E01,i, E02,i/mV vs SCE 447, 463 305, 385 180, 170

I II III

451 348 173

process

E̅0i /mV vs SCE

ΔQSW,peak,i/QF

ΔE0i /mV vs SCE

E01,i, E02,i/mV vs SCE

I II III

255 120 −65

0.77b 1.32b 1.01

−55 46 −19

282, 227 97, 143 −55, −74

τ = 100 ms. bObtained from the value of QF determined with ΔE0III and Figure 3c. a

shown in Table S2 in the Supporting Information, we estimated the value of ΔE0i (i = I, II, and III) by using the working curves in Figure 3b. Note that for processes I and II the half-peak width cannot be obtained directly from the experimental ΔQSW−Eindex curves because they partially overlap (see Figure 4). For this reason, a Gaussian fitting has been used and the values of W1/2 thus obtained (see Table S2 in the Supporting Information) should be considered only as rough estimations, and another procedure will be used for obtaining more accurate 0 values of ΔE0I and ΔEII0 (see below). The value of ΔEIII 1/2 obtained from the direct measurement of W of the SWVC curves in both electrolytes is shown in Table 1 and can be considered as accurate. (3) Once ΔE0III is known, the total charge QF can be obtained from Figure 3c: HClO4 1.0 M, QF = 35.1 nC and LiClO4 0.1 M, QF = 109 nC. (4) By taking into account eq 8, the above charge values lead to the following total excesses: Γ[PMo12O40]3− (HClO4) = 5.1 × 10−12 mol cm−2 and

Figure 5. (Lines) Experimental ΔQ SW −E index curves of a [PMo12O40]3− monolayer at a BDD electrode for aqueous HClO4 1.0 M (A) and LiClO4 0.1 M (B) media. τ = 100 ms ( f = 5 Hz). (Black dots) Theoretical ΔQSW−Eindex curves calculated from eq 10 by using the data shown in Table 1 for the two media above. Other conditions as in Figure 4. G



■

monolayer obtained for |ESW| = 25 mV and τ = 100 ms (lines) have been compared with theoretical curves calculated from eq 10 by using the data shown in Table 1 (black dots). From this comparison it can be concluded that an excellent agreement has been obtained in both electrolytes. Only small deviations can be observed for process I (mainly in the halfpeak width). From these results (see Table 1) it can be concluded that an aprotric electrolyte leads to a shift in the formal potentials of the different steps, which is more notorious for process III (shift of 240 mV in ΔE0III). This could be due to the increasing formal charge of the immobilized molecules, which cannot be compensated by the addition of protons. On the other hand, the change of protons by cation Li+ also causes a decrease of the cooperative character of the different EE processes (i.e., a higher estabilization of the intermediate species in each of the three reductions, which leads to a lower value of ΔE0i ), which mainly affects process I. This last behavior is also observed in the case of the solution soluble complex,29 although in this case the peaks transform from dielectronic to monoelectronic. In order to understand clearly the effect of the cation in the response of the monolayer of [PMo12O40]3−, a broader essay would be required and may be the consideration of the whole process as a global six-electron transfer reaction. These results show SWVC to be an excellent technique for analyzing these processes since it presents high sensitivity in the elucidation of the charge transfer events taking place, because it provides accurate values of the formal potentials of the different steps in a very simple way.

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Article

ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors greatly appreciate the financial support provided ́ y Técnica by the Dirección General de Investigación Cientifica (Project Number CTQ2012-35700) and the Fundación SENECA de la Región de Murcia (Project Number 08813/ PI/08). Also F. K. thanks Ferdowsi University of Mashhad.

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REFERENCES

(1) Bard, A. J., Stratmann, M., Fujihira, M., Rusling, J. F., Rubinstein, I., Eds. Encyclopedia of Electrochemistry, Vol. 10; Wiley-VCH: Weinheim, Germany, 2007. (2) Vos, J. G.; Forster, R. J.; Keyes, T. E. Interfacial Supramolecular Assemblies; Wiley: Chichester, U.K., 2003. (3) Hammerich, O., Ulstrup, J., Eds. Bioinorganic Electrochemistry; Springer: Dordrecht, The Netherlands, 2007. (4) Bartlett, P. N. Bioelectrochemistry: Fundamentals, Experimental Techniques and Applications; Wiley: Chichester, U.K., 2008. (5) Willner, I.; Katz, E. Bioelectronics: From Theory to Applications; Wiley-VCH: Weinheim, Germany, 2005. (6) Cahen, D.; Kodes, G. Adv. Mater. 2002, 14, 789−798. (7) Repo, E.; Ahlberg, E.; Murtomäki, L.; Kontturi, K.; Schiffrin, D. J. Electrochim. Acta 2009, 54, 6584−6593. (8) Ulgut, B.; Abruña, H. Chem. Rev. 2008, 108, 2721−2736. (9) Astruc, D.; Boisselier, E.; Ornelas, C. Chem. Rev. 2010, 110, 1857−1959. (10) Leger, C.; Bertrand, P. Chem. Rev. 2008, 108, 2379−2438. (11) Gulaboski, R.; Mirceski, V.; Bogeski, I.; Hoth, M. J. Solid State Electrochem. 2012, 16, 2315−2328. (12) Scholz, F., Ed. Electroanalytical Methods: Guide to Experiments and Applications, 2nd ed.; Springer: Heidelberg, Germany, 2010. (13) Gonzalez, J.; Lopez-Tenes, M.; Molina, A. J. Phys. Chem. C 2013, 117, 5208−5211. (14) González, J.; Molina, A.; Abenza, N.; Serna, C.; Moreno, M. M. Anal. Chem. 2007, 19, 7580−7587. (15) Molina, A.; Soto, C. M.; González, J. J. Electroanal. Chem. 2009, 634, 90−97. (16) Molina, A.; Gonzalez, J.; Abenza, N. Electrochim. Acta 2007, 52, 4351−4362. (17) González, J.; Molina, A.; Soto, C. M.; Serna, C. J. Electroanal. Chem. 2012, 664, 54−62. (18) Gonzalez, J.; Abenza, N.; Molina, A. J. Electroanal. Chem. 2006, 596, 74−86. (19) Leger, C.; Lederer, F.; Guigliarelli, B.; Bertrand, P. J. Am. Chem. Soc. 2006, 128, 180−187. (20) Sadakane, M.; Steckhan, E. Chem. Rev. 1998, 98, 219−237. (21) Dolbecq, A.; Dumas, E.; Mayer, C. R.; Mialane, P. Chem. Rev. 2010, 110, 6009−6048. (22) Wang, B.; Dong, S. Electrochim. Acta 1996, 41, 895−902. (23) Rong, C.; Anson, F. C. Inorg. Chim. Acta 1996, 242, 11−16. (24) Molina, A.; Laborda, E.; Martinez-Ortiz, F.; Bradley, D. F.; Schiffrin, D. J.; Compton, R. G. J. Electroanal. Chem. 2011, 659, 12− 24. (25) Gonzalez, J.; Molina, A. J. Electroanal. Chem. 2003, 557, 157− 165.

CONCLUSIONS

In this article, the study of a reversible surface two-electron transfer process has been carried out by using the SWVC technique. The key parameters that govern the whole reversible surface EE process (and then the “cooperativity degree between ETs”) have been shown to be the difference between the formal potentials of both ETs, ΔE0 (= E02 − E01), and the square wave amplitude |ESW|. Hence, the ΔE0 value at which the transition two peaks → one peak takes place has been given as function of |ESW|. It has been also shown that the values of the formal potentials and the total surface excess can be easily and very accurately obtained from the peak parameters of the SWVC curve, i.e., from peak potentials, half-peak widths, and peak heights. SWVC has been applied to the study of the reduction of the Keggin polioxometalate [PMo12O40]3− immobilized at the surface of a BDD electrode. The six formal potentials involved in the whole process and the total surface coverage have been obtained in aqueous media for two electrolytes: HClO4 and LiClO4. Because of the stationary character of the SWVC response for reversible processes, these curves become indistinguishable from those obtained for any other differential electrochemical technique of double pulse or multipulse potential if the difference between the successive pulses coincides with 2|ESW|. Furthermore, at the continuous limit (i.e., |ESW| ≪ RT/F), all the above-mentioned techniques lead to a unique response that coincides with those obtained in CV, in alternating current voltammetry (ACV), in potentiometric stripping analysis (PSA), and it is also transferrable to that for any reciprocal derivative chronopotentiometric technique. H



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(26) Molina, A.; Serna, C.; Lopez-Tenes, M.; Moreno, M. M. J. Electroanal. Chem. 2005, 576, 9−19. (27) Molina, A.; Moreno, M. M.; Serna, C.; Lopez-Tenes, M.; Gonzalez, J.; Abenza, N. J. Phys. Chem. C 2007, 111, 12446−12453. (28) Hoke, K. R.; Cobb, N.; Armstrong, F. A.; Hille, R. Biochemistry 2004, 43, 1667−1674. (29) Maeda, K.; Himeno, S.; Osakai, T.; Saito, A.; Hori, T. J. Electroanal. Chem. 1994, 364, 149−154.

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