Application of Several Multipotential Step Techniques to the Study of Multicenter Molecules at Spherical Electrodes of Any Size

Journal of Electroanalytical Chemistry

Journal of Electroanalytical Chemistry 603 (2007) 249–259 www.elsevier.com/locate/jelechem

Application of several multipotential step techniques to the study of multicenter molecules at spherical electrodes of any size

Manuela Lo´pez-Tene´s, A´ ngela Molina *, Carmen Serna, Marie´n M. Moreno, Joaquı´n Gonza´lez

Departamento de Quı´mica Fı´sica, Universidad de Murcia, Espinardo 30100, Murcia, Spain

Received 28 November 2006; received in revised form 5 February 2007; accepted 9 February 2007 Available online 15 February 2007

Abstract

Several multipotential step techniques such as staircase voltammetry (SCV), additive diﬀerential staircase voltammetry (ADSCV) and cyclic voltammetry (CV) have been applied to the study of the reversible reduction/oxidation of molecules with multiple redox centers (interacting or not) using spherical electrodes of any size. The theoretical predictions have been tested with two experimental systems: quinizarine in acetonitrile and pyrazine in aqueous acid media, founding an excellent agreement between theory and experiments. A crit- ical analysis of the response with each technique allows us to conclude that, although all of them are powerful qualitative tools, ADSCV, proposed in this paper, is the most suitable technique to study such multistep processes quantitatively, and it can be used to determine the formal potentials easily for any number of electrochemical steps in the case of molecules with strongly interacting centers, and also in the case of molecules with two redox centers whatever the interaction degree between them. The formal potentials for the systems mentioned above have been evaluated with this technique. The advantages of using microelectrodes in order to obtain characteristic parameters of the system are also discussed. 2007 Elsevier B.V. All rights reserved.

Keywords: Multicenter molecules; Interacting and noninteracting redox centers; Multipotential techniques; Cyclic voltammetry; SCV; ADSCV; CV; Spherical electrodes; Microelectrodes

1. Introduction devices, design of new materials, information storage, chemiluminescent analytical methods, biomedical imaging, In a recent paper we deduced a simple explicit analytical etc. [1–3]. expression for the current obtained at spherical electrodes In this work we particularize the general equation for the reversible reduction/oxidation of molecules with deduced in [1] to analyse the response of molecules contain- multiple redox centers such as fullerenes, linear polymers, ing multiple redox centers with any interaction degree supramolecular species and dendrimers, in any multipoten- using the well-known staircase voltammetry (SCV) and tial step technique [1]. The study of such multicenter mol- cyclic voltammetry (CV) techniques [4,5], and a new ecules is of great interest and very topical on account of technique – additive diﬀerential staircase voltammetry their present and potential applicability in energy conver- (ADSCV) – which is introduced in this work on the basis sion, sensor development, molecular electronic and optical of SCV and the double pulse technique additive diﬀerential pulse voltammetry, ADPV [6–8]. The equations here are valid for spherical electrodes of any size, from planar to ultramicrospherical electrodes, which is of great interest, * Corresponding author. Tel.: +34 968 367524; fax: +34 968 364148. since mercury electrodes such as the SMDE are widely used E-mail address: [email protected] (A´ . Molina). in the study of multicenter molecules [9].

In the literature, only in CV has a rigorous analytical 2. Experimental solution been developed for the simplest case of a molecule with two redox centers (EE mechanism) in planar diffusion All computer programs were written in our laboratory. [10]. Here, we establish the equivalence between the non- A three electrode cell was employed in the experiments. explicit integral equations in this reference and those A home-made static mercury drop electrodes (SMDE) with obtained by us in the particular case of planar diffusion, different radius values served as working electrode. The and we conclude that classical expressions for the current electrode radii of the SMDE were determined by weighing can be used although by changing the integral equations a large number of drops. The counter electrode was a Pt by our simpler, explicit and easy to be programmed wire and the reference and quasireference electrodes were expressions. aAgjAgCljKCl 1.0 M electrode in the experiments with The analysis of the response in each technique allow us pyrazine and a silver wire for the quinizarine in acetonitrile to conclude that, despite the fact that CV has been widely solution, respectively. used over the years to study the experimental behaviour of Pyrazine, NaClO4 and HClO4 were of Merck reagent multicenter molecules and that is unquestionably a power- grade. Quinizarine (1,4-dihydroxy-9,10-anthraquinone), ful qualitative tool, it is not the most appropriate technique anhydrous acetonitrile and tetrabutylamonium perchlorate to carry out a quantitative study of these interesting mole- (TBAP) were of Aldrich reagent grade. All reagents were cules, particularly when they present strongly interacting used without further purification. Acetonitrile inhibits the redox centers since, as the response develops over a wide adsorption of quinizarine in such a way only diffusive range of potential, the non-desired effects in CV are behaviour is observed. Water was bidistilled and nitrogen enhanced [4,5], especially in the reversal scan. gas was used for deaeration. In pyrazine experiments the Conversely, the additive technique, ADSCV, has been ionic strength has been adjusted to 1 M. In all the experi- shown to be very suitable for studying these multistep pro- ments the temperature was kept constant at 20 ± 0.1 C. cesses quantitatively. The technique presents a response We used different digital noise filters of the instrument showing zero-current points from which, in the case of supported software in the experimental voltammetric mea- strongly interacting centers, the formal potentials of all surements. The experimental ISCV/E curves were smoothed electrochemical steps can be determined directly for any by applying the moving average smoothing procedure pro- value of the electrode radius, sweep rate and pulse ampli- posed by Savitzky and Golay [12]. tude. For molecules with intermediate interactions between For the experimental curves shown in Fig. 6, the back- the centers, working with electrodes of small size has the ground current has been corrected. The diffusion coefficient effect on the ADSCV curves of separating the electrochem- value used in the theoretical adjustment of this figure, ical steps in such a way that the formal potentials can also D = (7.5 ± 0.1)106 cm2 s1, was previously obtained from be evaluated in this case from the zero-current points, pro- chronoamperometric experiments and is in good agreement vided the interactions are not very weak. When microelec- with that previously reported in the literature [7,13]. trodes are used, the stationary response obtained is Cross potentials in ADSCV have been calculated from identical to that in the double pulse technique ADPV [6– linear interpolations of the zone around the zero-current 8] and in the triple pulse technique DDPV [11]. Neverthe- points in the differential staircase voltammograms. less, ADSCV presents, in contrast to the double and triple pulse techniques, the clear advantage of avoiding the exper- 3. Expression of the current for any multipotential step imental inconvenience of having to reach the equilibrium technique every two or three potentials applied, which needs a delay time when solid electrodes are used, or, in the case of a In this paper we apply several multipotential step tech- SMDE, a new mercury drop. niques to study the reduction of a molecule containing n In the particular case of a molecule with two redox cen- electroactive redox centers shown in Scheme 1. ters, the formal potentials can be determined from the ADSCV response for any interaction degree between them. We have illustrated these results by working with two experimental systems of molecules containing two redox centers, with different interaction degrees between them, namely quinizarine in acetonitrile and pyrazine in aqueous acid media, and we have found an excellent agreement between the theoretical predictions and the experimental data. Finally, once the formal potentials are known, the stationary response obtained in SCV when using microelectrodes can be used to determine characteristic parameters of the system like analytical concentrations and diffusion coefficients. Scheme 1. M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259 251

We will assume that only the higher oxidation state, On, 4. Expression of the current for different multipotential step of the molecule is initially present in solution with a techniques concentration c*, and that all reactions of the process (Scheme 1) are reversible. We also suppose that the diffu- Eq. (1), which corresponds to the rigorous solution for a sion coefficients of the (n + 1) redox states of the molecule reversible multistep mechanism in any multipotential step are equal (=D), in such a way that the possible (n 1) technique [1], will be particularized in this paper for two reproportionation/disproportionation homogeneous elec- extensively used electrochemical techniques – staircase vol- tron-transfer reactions have no effect on the response in tammetry (SCV) and cyclic voltammetry (CV) [4,5] – and any voltammetric technique of single or multipotential for a new technique derived from SCV, additive differential step, be the diffusion field planar, spherical or cylindrical staircase voltammetry (ADSCV), which is proposed in this [8]. In this paper, we consider a spherical electrode of any paper. In the above techniques, all the potential pulses have radius, r0. the same duration s (t1 = t2 = = tp = s) and therefore Under these conditions, we derived in Ref. [1] the Eq. (4) can be rewritten as expression for the current corresponding to the application tk;p ¼ðp k þ 1Þs ð5Þ of any pulse ‘‘p’’ (p P 1), in any sequence of consecutive potential steps designed, which is given by P 4.1. Staircase voltammetry 1=2 Xp n1 k1 k D ðn jÞ½c ðr0Þc ðr0Þ I ¼ FA j¼0 j j p p 1=2 In the cyclic version of this technique, the sweep is made k¼1 ðtk;pÞ between the initial potential, Ein = E1, and the reversal Xn1 FAD potential E = E at which the direction sweep is reversed, þ ðn jÞ½c0ðr Þcpðr Þ ð1Þ r N r j 0 j 0 as shown in Scheme 2a [4,5]. The absolute value of the dif- 0 j¼0 ference DE = Ek+1 Ek (1 6 k 6 p 1) is kept constant where F and A have their usual electrochemical meanings, and its sign is negative or positive according to the direc- and the surface concentrations of the different oxidation tion of the potential sweep. p states of the molecule, cj ðr0Þ, are The potential sweep rate is defined as Q 9 n c J p > jDEj p f ¼jþ1 f > v cj ðr0Þ¼ P Q ; j ¼ 0; 1; ...; n 1 > ¼ ð6Þ n n p = s 1þ J f j¼1 f ¼j p P 1 and by inserting Eqs. (5) and (6) in Eq. (1), we deduce the p c > c ðr0Þ¼ P Q > n n n ;> following expression for the current at spherical electrodes 1þ J p j¼1 f ¼j f of any size:

ð2Þ ISCV ¼ Ip P ! p 1=2 Xp n1 k1 k with the functions J j depending on the potential in the way Dv ðn jÞ½c ðr0Þc ðr0Þ ! ¼ FA j¼0 j j 00 p DE 1=2 F ðEp E Þ j j k¼1 ðp k þ 1Þ J p ¼ exp j ðj ¼ 1; 2; ...; nÞð3Þ j RT Xn1 FAD 0 p þ ðn jÞ½cj ðr0Þcj ðr0Þ ð7Þ 0 0 r0 and cj ðr0Þ¼0 for j 6¼ 0 and c0ðr0Þ¼c . tk,p in Eq. (1) is the j¼0 time elapsed between the beginning of the kth potential where Ip is the current measured at the end of the pth pulse, step and the end of the pth potential step, i.e., which is plotted versus the potential Ep (see Scheme 2b). Xp tk;p ¼ tm ð4Þ 4.2. Additive differential staircase voltammetry m¼k The idea for the new multipulse technique named addi- with tm being the duration of the potential step Em. Note that current in Eq. (1) has been expressed as the tive differential staircase voltammetry (ADSCV) is based in sum of two contributions with different temporal and the double pulse technique additive differential pulse vol- radial dependences. Indeed, whereas the first contribution tammetry (ADPV) [6–8]. In this multipulse technique the depends on time and does not depend on electrode radius applied potential–time waveform is the usual staircase in (this is the characteristic response for a planar electrode), SCV (see Scheme 2a) and the signal is obtained by adding the second one is independent of time but dependent on two differential currents: DIp in the direct branch of the electrode radius (this is the current obtained for an ultra- applied staircase perturbation, and DI2Np in the reverse microspherical electrode). This different temporal depen- branch, defined as (see plots (a) and (c) in Scheme 2) dence reflects in that planar contribution depends on all DIp ¼ Ipþ1 Ip ð8Þ the potentials applied until the potential pulse p, while DI ¼ I I ð9Þ radial contribution depends only on the present potential 2Np 2Npþ1 2Np step applied, Ep [1]. with each current given by Eq. (7). 252 M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259

IADSCV ¼ DI p þ DI2Np

¼ Ipþ1 I p þ I2Npþ1 I2Np; 2 6 p 6 ðN 1Þ ð10Þ which is plotted versus the common potential in the two scan directions, Ep = E2Np (see Scheme 2(d)). Note that since the signal in ADSCV is obtained from differences of currents, the background current is significantly reduced with respect to SCV. In Scheme 2 we represent the potential–time waveform in SCV, plot (a), and the typical responses in SCV (plot (b)) and ADSCV (plot (d)), through the intermediate response in differential staircase voltammetry, DSCV, (plot (c)) [14,15]. The solid curves in plots (b)–(d) have been obtained for a molecule with three noninteracting redox centers [1] but they show the typical shape for a nernstian simple charge transfer process (E mechanism), corresponding to a molecule with a single redox center, whose response is shown in dotted lines. In general, for a molecule with ‘‘n’’ noninteracting centers, the shape of the response in any potential step technique is effectively that of a reversible one-electron transfer but with the particularity that the signal is amplified by a factor of ‘‘n’’ [1], which is three in our case. The cross potential (zero-current point) in ADSCV (plot (d)), which for a simple E mechanism coin- 00 cides with the formal potential E P, is coincident in this case 1 n 00 of noninteracting centers with n j¼1Ej , since the global multistep process develops as a simple E process with the formal potential being the average of the formal potentials of all the electrochemical steps [1].

4.3. Cyclic voltammetry

Eq. (7) is valid for any value of DE in the staircase. Clearly, staircase experiments with good potential resolu- tion (small jDEj) should present very similar responses to those from linear sweep experiments with the same scan rate. Thus, at the limit jDEj!0, the results obtained by using Eq. (7) should be coincident with those corresponding to the well-known cyclic voltammetry technique. In practice, it is suﬃcient to select jDEj < 0.01 mV to obtain the CV signal [16,17]. In fact, the modern digitally con- trolled devices use staircase functions with very small jDEj to generate ‘‘linear’’ scan waveforms [5]. Eq. (7) can be written as function of the sweep rate a, deﬁned by [18] Fv a ¼ ð11Þ RT

Scheme 2. (a) Potential–time waveform and points of current measure- in the following form: ment for SCV. (b)–(d) Responses in SCV (Eq. (7)), DSCV (Eqs. (8) and I I planar Iradial (9)) and ADSCV (Eq. (10)), respectively, for a molecule with three CV ¼ CV þ CV ð12Þ noninteracting redox centers (solid lines) [1] and for a molecule with only with one center (dotted lines). "#P 1=2 Xp n1 k1 k planar DFv j¼0 ðn jÞ½cj ðr0Þcj ðr0Þ ICV ¼ FA RT pas ðp k þ 1Þ1=2 The signal in the additive technique is given by (Eqs. (8) k¼1 and (9)) ð13Þ M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259 253

Fig. 1. Inﬂuence of electrode radius, r0, on the ISCV/E curves (a and c, Eq. (7)), and on the IADSCV/E curves (b and d, Eq. (10)), for a molecule containing 0 0 0 0 0 0 * 5 2 1 two strongly interacting redox centers ðDE ð¼ E2 E1 Þ¼250 mVÞ. jDEj = 10 mV, m = 100 mV/s, c = 1 mM, D =10 cm s , T = 298 K. The values of r0, in cm, are given on the curves. and account Eq. (2) and applying the derivative deﬁnition in

Xn1 the limit corresponding to CV (jDEj!0), we can write radial FAD 0 p "# I ¼ ðn jÞ½c ðr0Þc ðr0Þ ð14Þ CV r j j 2 1=2 Xp k k k k k k 0 j¼0 EE; planar F DFv 2½J 1J 2ð2 þ J 2Þ þ J 2ð1 J 1J 2Þ ICV ¼Ac RT RT pas ðp k þ 1Þ1=2ð1 þ J k þ J k J k Þ2 In spite of the fact that CV has been widely used in k¼1 2 1 2 studying the experimental behaviour of multicenter mole- ð17Þ cules, a rigorous analytical solution has been developed only for the simplest case of a molecule with two redox cen- where the double sign refers to the direction sweep, with ters (EE mechanism) in planar diﬀusion, by Polcyn and the upper sign corresponding to the cathodic sweep Shain [10], who gave the following expression for the CV (DE < 0) and the lower sign to the anodic one (DE > 0). signal: By comparing Eqs. (15) and (16) with Eq. (17) we deduce that I ¼ 2I1ðwÞþI2ðvÞð15Þ Xp k k k where F J 1J 2ð2 þ J 2Þ ) wðatÞ¼ 1=2 1=2 2 RT pðasÞ ðp k þ 1Þ ð1 þ J k þ J k J k Þ I ðwÞ¼FAcðpDaÞ1=2wðatÞ k¼1 2 1 2 1 ð16Þ 1=2 ð18Þ I2ðvÞ¼FAc ðpDaÞ vðatÞ Xp k k k F J 2ð1 J 1J 2Þ where a is given by Eq. (11) and the w(at) and v(at) func- vðatÞ¼ RT pðasÞ1=2 ðp k þ 1Þ1=2ð1 þ J k þ J k J k Þ2 tions are two non-explicit integral equations (see Eqs. (9) k¼1 2 1 2 and (10) in Ref. [10]). ð19Þ In order to compare our results with those in Ref. [10], the explicit equation (13) will be particularized for the case and hence, we conclude that Eq. (17) should be used in- of an EE mechanism by making n = 2. Thus, taking into stead of Eqs. (15) and (16) [10] since Eq. (17) has the 254 M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259 advantages of being explicit, simpler and easier to redox centers. Nevertheless, we will refer especially to mol- programme. ecules with two redox centers, not only for the sake of sim- plicity but also because it is a frequent experimental case and the results obtained may be easily generalized for more 5. Results and discussion complex molecules.

The number and shape of the waves obtained in the I/E response for a multistep process depend on the relative 5.1. Strongly interacting centers values of the formal potentials of each step. In the case of molecules with strongly interacting centers 5.1.1. Influence of electrode radius, r0 00 00 00 Fig. 1 shows the influence of the electrode radius on the it is hold that E1 E2 En and according to Refs. [1,19], the intermediate oxidation states in Scheme 1 are SCV response (Fig. 1a and c) and on the corresponding stable, which leads to well separated waves in the I/E ADSCV curves (Fig. 1b and d) for a molecule with two 00 00 00 response. Thus, in SCV and CV, well defined peaks for strongly interacting redox centers ðDE ð¼ E2 E1 Þ¼ each charge transfer are obtained for sweeps in both direc- 250 mVÞ. The curves have been obtained with tions, and in ADSCV two peaks with a different sign for jDEj = 10 mV and v = 100 mV/s at conventional spherical each charge transfer are observed (see Figs. 1–4). For electrodes of different radii, r0,(Fig. 1a and b) and at a 4 multicenter molecules with intermediate interactions, the microelectrode with r0 =10 cm (Fig. 1c and d). It can values of formal potentials of the different steps are closer be observed that, whereas the impact of the electrode size and the intermediate oxidation states of the molecule on the shape of the curves is very important in SCV, the become unstable. Thus, the I/E response obtained goes curves in ADSCV (Fig. 1b and d) are qualitatively similar from non-well separated waves for the different charge and the most interesting feature in these figures is that the transfers (see Figs. 4–6) to totally overlapped waves [1]. potential at the three cross points (zero-current points) when using microelectrodes is exactly coincident with Eq. (1) and those derived from it (Eqs. (7), (10) and 0 0 0 E0 E0 0 0 1 þ 2 0 (12)–(14)), are valid for molecules with any number of E1 ; 2 (central cross potential, Ecc) and E2 , as shown

Fig. 2. Influence of pulse amplitude, jDEj (a and b) and sweep rate, m (c and d) on the ISCV/E curves (a and c, Eq. (7)) and on the IADSCV/E curves (b and d, Eq. (10)), for the same molecule in Fig. 1. r0 = 0.01 cm. The values of jDEj, in mV, and m, in mV/s, are given on the curves. Other conditions as in Fig. 1. M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259 255 in Fig. 1d, and this behaviour hardly depend on the elec- These characteristic points will be used to estimate trode radius (see Fig. 1b). Thus, the formal potentials can unknown parameters of the system studied (see below). be accurately determined from a linear interpolation of The response in the ADSCV technique (Fig. 2d) shows the central zone of the curve around each cross potential. that the cross points are also independent of the sweep rate, Note that, according to Eq. (7), as the electrode radius v. Therefore, the formal potentials of both charge transfer decreases the radial contribution to the current is more reactions can be determined directly from the cross points important and hence, for sufficiently small electrodes, the obtained in ADSCV, for any value of the electrode radius, response in SCV (and also in CV, see Eqs. (13) and (14)) sweep rate and pulse amplitude. should present the characteristic stationary shape corre- In order to corroborate the theoretical predictions, in sponding to the radial contribution, as shown in Fig. 1c. Fig. 3 we have plotted the experimental curves obtained Thus, the current, Iss, taking into account Eqs. (2) and for different values of the radius of a mercury electrode (3) is given by (see Eqs. (7) and (14)) in SCV (Fig. 3a) and in ADSCV (Fig. 3b) for the quinizar- FADc 2 þ J ine in acetonitrile system. In Fig. 3a the typical curves cor- Iss ¼ 2 ð20Þ responding to well separated steps are observed and the r0 1 þ J 2 þ J 1J 2 00 00 values of the formal potentials E1 and E2 can be easily In this particular case of well separated steps it is fulfilled determined from the curves in Fig. 3b. Thus, the values 00 00 00 00 00 that E1 E2 and hence, for E ¼ E1 it holds that J1 =1 obtained are E1 ¼0:5750 0:001 V and E2 ¼1:050 00 and J2 !1, and the current (Eq. (20)) becomes in 0:001 V ðDE ¼0:475 0:002 VÞ. We have also determined the central cross potential, Ecc, obtaining Ecc = 0 FADc 1 IssðE ¼ E0 Þ¼ ð21Þ 0.815 ± 0.001 V, which practically coincides with the 1 r 2 0 semisum of formal potentials. 00 whereas for E ¼ E2 , J1 = 0 and J2 = 1, and Eq. (20) simpli- fies to ss 00 FADc 3 I ðE ¼ E2 Þ¼ ð22Þ r0 2 Thus, we could estimate the formal potentials from the value of the current given by Eqs. (21) and (22), as indicated in Fig. 1c. However, they can be more accurately obtained from the ADSCV response in Fig. 1d. In these conditions, for r0 ! 0, the ADSCV response is identical to that in the double pulse technique ADPV (as is indicated by the same current peaks for the two steps [7,8]). Once the formal potentials are thus known, Eqs. (21) and (22) can be used to determine D and c*.

5.1.2. Influence of the characteristic parameters of SCV: pulse amplitude, DE, and sweep rate, v Fig. 2a and b shows the influence of pulse amplitude, jDEj, on the current obtained in SCV and ADSCV, respectively, at a conventional spherical electrode of radius r0 = 0.01 cm for the same molecule as in Fig. 1 (Eqs. (7) and (10) with n = 2). In Fig. 2a it is observed that on dimin- ishing jDEj, the peak currents increase in absolute value and the limit currents are independent of jDEj. In this figure the curve for jDEj!0 corresponds to the CV technique. In Fig. 2b it is observed that the cross points, from which the formal potentials can be directly determined, are independent of the value of jDEj. Fig. 2c and d shows the influence of sweep rate, v, on the ISCV/E (Eq. (7)) and IADSCV/E (Eq. (10)) curves, respectively, obtained for jDEj = 10 mV at a spherical electrode of radius r0 = 0.01 cm, for the molecule with two strongly interacting redox centers considered in previous figures. Fig. 3. Influence of the radius of a SMDE, r , on the experimental I /E Note that the curves in Fig. 2c present one common point 0 SCV curves (a), and on the IADSCV/E curves (b) obtained for quinizarine or ‘‘isopoint’’ of non zero current in the reverse branches, 1 mM + TBAP 0.1 M in acetonitrile. jDEj = 5 mV, m = 0.5 V/s, T = 293 K. which is obviously independent of the sweep rate [17]. The values of r0, in cm, are given on the curves. 256 M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259

In Fig. 4a and b we have plotted the experimental stair- and case voltammograms obtained with quinizarine in acetoni- FADc 2 þ J iso trile by applying several values of sweep rate to a SMDE of Iiso ¼ 2 ð25Þ right r iso radius r0 = 0.01 cm. In Fig. 4a one isopoint in the reverse 0 1 þ J 2 branches is obtained [17] (see Fig. 2c), whereas in Fig. 4b the scan is reversed at a less negative value of E and then Thus, once the values of formal potentials are known, the r * three isopoints are observed. At these characteristic points, values of D and c can be estimated by using Eqs. (24) independent of the sweep rate, the planar contribution to and (25). In this way, we have obtained for the quinizarine in acetonitrile system the value of the diffusion coefficient the current is zero and the current is simply given by (see 5 2 1 Eq. (7)) D = (2.50 ± 0.35)10 cm s . Fig. 4c and d are com- mented below. FADc 2 þ J iso The above comments are also valid for the isopoints Iiso 2 ¼ iso iso iso ð23Þ obtained in CV, but this technique is less advantageous r0 1 þ J þ J J 2 1 2 than SCV, particularly in the case of strongly interacting iso centers, since the response develops in a wide potential where J j ðj ¼ 1; 2Þ is given by Eq. (3) for Ep = Eiso. In this case of molecules with strongly interacting centers interval, and in these conditions the cumulative non- 00 00 desired effects in CV are enhanced, especially in the reverse ðE1 E2 Þ, for the left and the right isopoints in Fig. 4b, iso iso scan [4,5]. which hold J 2 !1 and J 1 ! 0, respectively, Eq. (23) becomes in 5.1.3. Any number of redox centers FADc 1 iso The results in Sections 5.1.1 and 5.1.2 for molecules with Ileft ¼ iso ð24Þ r0 1 þ J 1 two strongly interacting centers are valid in general for

Fig. 4. Influence of sweep rate, m, on the experimental ISCV/E curves obtained with quinizarine 1 mM + TBAP 0.1 M in acetonitrile in (a) and (b), and with pyrazine 1.0 mM at pH = 0.35 in HClO4 + NaClO4 adjusted to ionic strength 1.0 M in (c) and (d). r0 = 0.01 cm, jDEj = 0.01 V (a) Er = 1.4 V, (b) Er = 1.2 V, (c) Er = 0.6 V, (d) Er = 0.45 V. The values of m, in V/s, are given on the curves. M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259 257 molecules with any number of redox centers. Indeed, we steps [20]. From Fig. 5b and d it can be seen that the cross can conclude that the formal potentials for any charge points only coincide with the formal potentials when using transfer can be obtained directly from the cross points in microelectrodes (Fig. 5d). This behaviour is observed pro- 00 00 00 the ADSCV response, for any value of the electrode radius, vided it is fulfilled that DE ð¼ E2 E1 Þ < 100 mV. the sweep rate and the pulse amplitude, and even if the dif- Therefore, the use of ADSCV, together with the use of fusion coefficient, D, and the analytical concentration, c*, microelectrodes permits an accurate and easy determina- are unknown. These parameters can be determined from tion of formal potentials since a decrease of the radius the value of the stationary current obtained with microelec- has the effect on the ADSCV curves of separating the electrodes in SCV since in general, for any charge transfer step trochemical steps. This effect can also be observed in 0 j (j =1,2,...,n) it is fulfilled that IssðE ¼ E0 Þ¼FADc j 1 Fig. 5c where the current at the formal potentials is given j r0 2 (see Eqs. (21) and (22)). by Eqs. (21) and (22) despite these equations having been obtained for well separated steps. Thus, the formal poten- 5.2. Moderately interacting redox centers tials can also be estimated from stationary SCV curves like those in Fig. 5c. Moreover, by comparing Figs. 5c and d it The conclusions in Section 5.1 are not valid, in general, is clear that using microelectrodes, ADSCV has a zero for molecules with intermediate interactions between their when SCV has an inflection point, independently of the redox centers. As an example, Fig. 5 shows the influence degree of interaction of the redox centers and of the poten- of the electrode radius on the curves for a molecule with tial step, DE, used in the staircase perturbation. 00 00 00 two centers ðDE ð¼ E2 E1 Þ¼125 mVÞ in SCV Once the formal potentials have been determined from (Fig. 5a and c) and in ADSCV (Fig. 5b and d). Note that ADSCV curves, the isopoints obtained in SCV (or CV) using in Fig. 5a, for conventional spherical electrodes, two non- conventional spherical electrodes could be used to estimate well resolved peaks are observed, whereas in Fig. 5c, for the values of D or c*, as explained in Section 5.1.2.In lower values of the radius, a stationary response is Fig. 4c and d we have plotted the experimental staircase obtained, which presents the typical shape of overlapped voltammograms obtained with pyrazine in aqueous acid

Fig. 5. Inﬂuence of electrode radius, r0, on the ISCV/E curves (a and c, Eq. (7)), and on the IADSCV/E curves (b and d, Eq. (10)), for a molecule containing 00 00 00 two partially interacting redox centers ðDE ð¼ E2 E1 Þ¼125 mVÞ. The values of r0, in cm, are given on the curves. Other conditions as in Fig. 1. 258 M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259

since, as has been pointed out (see p. 14), when r0 ! 0 the expression for the current in ADSCV coincides with that for ADPV and so, both techniques present the same features. In Fig. 6 we have plotted the experimental curves (dotted lines) obtained at several values of the radius of a mercury electrode, r0, in SCV (Fig. 6a) and in ADSCV (Fig. 6b) for the system pyrazine in aqueous acid media, at pH = 0.35. In the solid lines appear the corresponding theoretical curves, which have been calculated for 00 00 00 DE ð¼ E2 E1 Þ¼0:126 V. As can be seen, for this value an excellent adjustment between theoretical and experimental curves is reached. In these conditions the ADSCV curves present three cross potentials, of which those at the extremes do not correspond to the formal potentials (see Fig. 5b) but from the central one 0 0 E0 E0 1 þ 2 Ecc ¼ 2 , the value Ecc = 0.327 ± 0.001 V was obtained by a linear interpolation of the central zone of the experimental curves. Thus, from the values of Ecc and 00 00 00 DE we have obtained for E1 and E2 the values 00 00 E1 ¼0:264 0:001 V and E2 ¼0:390 0:001 V. These values are approximately 40 mV more positive than that reported in a previous paper [7], because pyrazine solutions at diﬀerent pH were used in each work [13] (pH = 0.35 in the present paper and pH = 1 in the previous work).

Acknowledgements

Fig. 6. Comparison between experimental curves for pyrazine 1.0 mM at The authors greatly appreciate the financial support pH = 0.35 in HClO4 + NaClO4 adjusted to ionic strength 1.0 M (dotted lines) and theoretical curves for the case of a molecule with two redox provided by the Direccioń General de Investigacioń Cientı´- 0 centers with DE0 = 126 mV (solid lines), obtained for different values of fica y Tećnica (Projects Number BQU2003-04172 and the radius of a SMDE, r0. (a) Curves in SCV (Eq. (7) with n = 2), (b) CTQ2006-12552/BQU) and by the Fundacioń SENECA Curves in ADSCV (Eq. (10) with n = 2). jDEj = 0.005 V, m = 0.1 V/s, (Expedients number PB/53/FS/02 and 03079/PI/05). 5 1 T = 293 K, D = 0.75 · 10 cm s . The values of r0, in cm, are given on M.M.M. thanks the Fundacioń CAJAMURCIA for the the curves. postdoctoral grant received. media. The difference with that observed for strongly inter- References acting centers (Fig. 4a and b) is that in the present case only one isopoint in the reverse branches is obtained whatever the [1] A. Molina, C. Serna, M. Lo´pez-Tene´s, M.M. Moreno, J. Electroanal. Chem. 576 (2005) 9 and references therein. potential Er at which the scan is reversed. Thus, only one [2] A.J. Bard, Nature 374 (1995) 13. parameter could be estimated from Eq. (23), which no sim- [3] B.K. Roland, W.H. Flora, H.D. Selby, N.R. Armstrong, Z. Zheng, J. plifications admits for overlapped steps. Am. Chem. Soc. 128 (2006) 6620. In the case of two redox centers, ADSCV also makes it [4] Z. Galus, Fundamentals of Electrochemical Analysis, second ed., Ellis possible to determine simultaneously and accurately the Horwood, Chichester, 1994 (Chapter 11). [5] A.J. Bard, L.R. Faulkner, Electrochemical Methods. Fundamental two formal potentials for any interaction degree between and Applications, second ed., Wiley, New York, 2001. 00 the centers (i.e., for any value of DE ). The procedure, [6] A. Molina, M.M. Moreno, C. Serna, L. Camacho, Electrochem. already described in ADPV [7,8], consists of measuring Commun. 3 (2001) 324. the potential at the central cross point (zero-current point) [7] A. Molina, M.M. Moreno, M. Lo´pez-Tene´s, C. Serna, Electrochem. 0 0 E0 E0 0 0 Commun. 4 (2002) 457. 1 þ 2 0 0 of the ADSCV curves, Ecc ¼ 2 and then, E1 and E2 [8] C. Serna, A. Molina, M.M. Moreno, M. Lo´pez-Tene´s, J. Electroanal. can be easily determined by adjusting the experimental Chem. 546 (2003) 97. ADSCV curve to the theoretical one for the corresponding [9] G. Diao, Z. Zhang, J. Electroanal. Chem. 414 (1996) 177. 0 0 0 DE0 ð¼ E0 E0 Þ value. It is proved numerically that this [10] L. Polcyn, I. Shain, Anal. Chem. 38 (1966) 370. 2 1 [11] A. Molina, M. Lo´pez-Tene´s, C. Serna, M.M. Moreno, M. Rueda, behaviour is fulfilled approximately in spherical electrodes Electrochem. Commun. 7 (2005) 751. with conventional size (see Fig. 5b), whereas it is an analyt- [12] A. Savitzky, M.J.E. Golay, Anal. Chem. 36 (1964) 1627. ical solution in the case of microelectrodes (see Fig. 5d) [13] J. Swartz, F.C. Anson, J. Electroanal. Chem. 114 (1980) 117. M. Lo´pez-Tene´s et al. / Journal of Electroanalytical Chemistry 603 (2007) 249–259 259

[14] F. Scholz, L. Nitschke, G. Henrion, Fresenius Z. Anal. Chem. 332 [18] R.S. Nicholson, I. Shain, Anal. Chem. 36 (1964) 706. (1988) 805. [19] J.M. Hale, J. Electroanal. Chem. 8 (1964) 181. [15] J.-S. Yu, Z.-X. Zhang, J. Electroanal. Chem. 427 (1997) 7. [20] C. Serna, M. Lo´pez-Tene´s, J. Gonza´lez, A. Molina, Electrochim. [16] A. Molina, C. Serna, L. Camacho, J. Electroanal. Chem. 394 (1995) 1. Acta 46 (2001) 2699. [17] M.M. Moreno, A. Molina, Collect. Czech. Chem. Commun. 70 (2005) 133.