A comparison of the multistep consecutive reduction mode with the multicomponent system reduction mode in cyclic voltammetry

Computers and Chemistry 26 (2002) 333– 340 www.elsevier.com/locate/compchem

A comparison of the multistep consecutive reduction mode with the multicomponent system reduction mode in cyclic voltammetry Przemysław Sanecki *, Piotr Skitał Faculty of Chemistry, Rzeszo´w Uni6ersity of Technology, ul. W. Pola 2, 35 -959 Rzeszo´w, Poland Received 12 May 2001; received in revised form 20 September 2001; accepted 23 October 2001

Abstract e

kf1

e

e

kf2

e

The multistep consecutive ECE–ECE reduction process A “ B“ C “ D “ E“ F“ G has been compared with e e e e reduction in multicomponent system A “ B, C“ D, D“ E, F“ G. A simple method of transformation has been devised to disclose the subtle structure of the complex cyclic voltammetry (CV) responses and illustrated by the ECE–ECE process modeled earlier. The method can be applied to any multi-electron CV experimental curve for which a numerical modeling has been done. Electroreduction processes similar to those considered here are often met in practice. An attempt of unification of consecutive electroreduction and electroreduction of multicomponent system has been made. Interrelation between research and analytical voltammetry aspects of the problem is also discussed. © 2002 Elsevier Science Ltd. All rights reserved. Keywords: Electroreduction; Voltammetry; Multistep electron transfer; Reduction of multicomponent systems

1. Introduction The cyclic and linear sweep voltammetry is a very important tool for both analytical and mechanismrevealing purposes. In this paper, we present a new way of analysis of cyclic voltammetry (CV) curves in order to reveal their subtle structures and simultaneously to pass from experimental consecutive reduction to simulated multicomponent system reduction. The transformation seems to be of particular importance for multi-electron reactions studied by voltammetry methods where one-electron steps are very close to each other and unrevealed. The electroreduction of intermediates is displayed on the transformed voltammogram. After the transformation, advantages of simulation are particularly well seen. The problem of multistep charge transfer (kinetic problem) overlaps the problem of mul* Corresponding author. Tel.: +48-17-865-1261; fax: + 4817-854-3655. E-mail address: [email protected] (P. Sanecki).

ticomponent charge transfers (analytical problem) (Bard and Faulkner, 1980). The aim of this paper is an attempt of unification of both reduction modes. The procedure presented and the example helps to understand the relationship between the consecutive multistep reduction mode and multicomponent reduction mode. It shows how to pass from the consecutive multistep reduction, interesting for kinetic investigations, to the multicomponent reduction interesting for analytical purposes. In practice we have a consecutive experimental CV multielectron curve and we are interested to see the respective CV curve of multicomponent system. Not everyone seems aware that on the consecutive reduction voltammogram, the peak potential of an intermediate rarely presents its true value as for the single free substance in a solution. It takes place even for two-electron peaks numerically resolved into oneelectron ones (Sanecki and Kaczmarski, 1999, 2001). When kh,n + 1 \ kh,n, Ep does not reflect the real electrochemical properties of the intermediate. After transformation into the multicomponent system, the picture

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corresponds to that of a single intermediate reduced separately or to that of a mixture of all species occurring in the sequence. Peak potentials (naturally or numerically resolved) of all species correspond to that of pure substances. The first simple example of such a transformation was shown in (Sanecki, 2001) and now another example as well as more general approach is presented. The case considered here is an example of reductive cleavage of halogen in derivatives analogous to those investigated recently in detail (see Andrieux et al., 1997; Antonello and Maran, 1999; Save´ ant, 1994)

3. Results

2. Kinetics The following consecutive ECE–ECE reaction sequence is considered kA, hA

kfBC

on the subject can be found (e.g. Speiser, 1996; Bott, 1997; Bott et al., 1996; Alden and Compton, 1997a,b; Ja¨ eger and Rudolph, 1997; Bieniasz and Speiser, 1998; Gosser, 1993). The ESTYM – PDE simulation software applied here was tested and compared with other commercially available programs namely EASI-CVSIM, ELSIM (Bieniasz, 2002) and DIGISIM (BAS; Bott et al., 1996). The ECE/DISP example proposed by Speiser (1996) as a test for simulation software proved the suitability of the program used.

kC, hC

kD, h D

kfEF

kF, hF

A “ B“C “ D “ E“F “ G

(1)

where kA =k1, kC =k2, kD =k3, kF =k4 are the heterogeneous rate constants (cm s − 1) and kfBC =kf1, kfEF = kf2 are the chemical rate constants (s − 1). The numerical treatment of the kinetic sequence was described in Sanecki and Kaczmarski (1999). Further information

An ECE–ECE reductive process of cleavage of SF bond in m-benzenedisulfonyldifluoride m-C6H4-(SO2F)2 (m-BDF), investigated and modeled in Save´ ant (1994) was selected as an example to be presented. It involves two separate two-electron stages (Andrieux et al., 1997). Each two-electron stage consists of one-electron step followed by another one and separated by the chemical step: ArSO2F+ e=ArSO2F’−

Fig. 1. (A) The experimental voltammetric curve (thick black line) and the simulated ones (black lines) for electroreduction of m-BDF in 0.3 M TBAP in DMF. The estimation was made for the curve at scan rate w =2.007 V s − 1. I1 – I4 are the simulated currents for the respective electron transfer; Iexp and I are the total currents, experimental and simulated, respectively. The estimated parameters were taken from (Sanecki and Kaczmarski, 1999, 2001): k1 =4.75 ×10 − 22 92.2 × 10 − 24 cm s − 1, Ep1,cons = −1.187 V, k2 = 6.41 ×10 − 21 99.72 × 10 − 21 cm s − 1, Ep2,cons = − 1.189 V, h1 =0.8258 9 0.00005, h2 =0.8422 9 0.03, k3 =9.00 ×10 − 21 9 1.0 ×10 − 23 cm s − 1, Ep3,cons = − 1.953 V, k4 = 1.99×10 − 17 91.0 × 10 − 19 cm s − 1, Ep4,cons = −1.957 V, h3 =0.5001 9 0.00006, h4 = 0.4726 9 0.00004. Other parameters: D= 5.08× 10 − 6 cm2 s − 1, kf1 =14 500 s − 1, kf2 =6500 s − 1, electrode surface 0.0150 9 0.00035 cm2. (A (T)) Consecutive electroreduction of m − BDF as shown in Fig. 1A transformed into the reduction of individual species mode (the substrate and each intermediate at c= 1 × 10 − 6 mol cm − 3 are reduced separately). The currents I1, I2, I3, … were calculated one by one for single individual species and than added up as indicated in the plots. The top plot is the sum of the all four currents for A, C, D and F components electroreduction. The top plot is an idealized and simplified form of simulation of A + C +D + F mixture reduction. The concentration of each component was assumed to be 1 ×10 − 6 mol cm − 3 concentration. All input kinetic parameters are as in Fig. 1. The output peak potentials for individual species are: Ep1,ind = −1.187 V, Ep2,ind = −1.080 V, Ep3,ind = − 1.953 V, Ep4,ind = − 1.661 V.

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Fig. 2. A comparison of the three ways of transforming CV curve from consecutive electroreduction mode into the individual electroreduction mode: idealized and simplified way (1) (one component approach): (1) each of electroactive intermediates A, C, D, F present in the solution alone: cA = 1× 10 − 6 mol cm − 3 or cB = 1 ×10 − 6 mol cm − 3, etc. Each current I1, I2, I3, I4, … was calculated for each species and the resulting currents appropriately added up. The simple way was applied to transform the consecutive electroreduction of iodobenzenes (Sanecki, 2001). Ways (2), (3) (all components together approach) are less elegant on display (plot) but more close to real reduction. Interdependence of concentrations of all components is included into considerations. (2) All electroactive intermediates A, C, D and F are present together in the solution at the start of reduction in concentration e.g. 1 × 10 − 6 mol cm − 3. Concentration of the rest of components B, E and G is assumed to be zero. (3) all substrates and intermediacies A – G are present in the starting solution in concentration e.g. 1 × 10 − 6 mol cm − 3. In all above cases, the reaction Eq. (1) is considered. kf1

ArSO2F’− “ ArSO2’ +F− ArSO2’ +e=ArSO− 2

(2) e

The sequence (Eq. (2)) corresponds to the part A “

kf1

e

e

kf2

e

B“ C“ D and again to the part D “ E “ F “ G of Eq. (1). The electroreduction proceeding according to Eq. (2) is analogous to that observed for halo-derivatives (CX bond) (Save´ ant, 1994) and CS bond (Andrieux et al., 1994). The transformation procedure becomes simple provided the mechanism of the process has been recognized and simulated correctly. On the basis of data from Save´ ant (1994), it can be shown how to transform the consecutive reduction mode (CR mode) into a multicomponent system reduction mode (MSR mode) without recalculating any parameters. To do it and to evaluate Ep,ind values for individual electroactive species taken separately (or as a mixture of noninteracting depolarizes) in, say, 1 mM concentrations, one can make use of their estimated kinetic parameters and use them in the simulation procedure. It can be done in

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three ways. In the first one, each of the four electrochemical steps of Eq. (1) (A – B, C–D, D–E, F–G) is treated as a simple separate one-electron reaction and the resulting currents are added up. Fig. 1A (T) was obtained in this way. This is the simplest way and it has been applied to transform modeled CV curves for reduction of iodobenzenes (Sanecki, 2001). The discussed problem should now be treated in a more precise and comprehensive manner with interdependence of concentrations of all components included into considerations. The initial CV curve can be translated into the situation where only the electroactive intermediates A, C, D and F are initially present in the solution and jointly undergo reduction (the second way of transformation). The third way is to consider the case where all substrates and intermediates A –G are initially present. The electrochemical responses for the three ways of transformation are compared in Fig. 2. The only difference between the three ways of transformation is the concentration of species at t =0 and, as the consequence of it, the differences at t \ 0. Further explanation on the concentration differences is included in caption of Fig. 1. Despite of the fact that the first approach describes evidently idealized situation, it gives the most elegant and the easiest picture to read (Fig. 1A (T), top curve). It corresponds to the sum of elementary electroreductions where no consecutive process exists (i.e. a product of any step is not a substrate for any other one). The transformation procedure can be applied to the kf1 e e simpler A “ B“ C “ D case as well as to more complicated ones. Advantages of the proposed transformation from CR mode to MSR mode are the following: “ the reduction in multicomponent system that is impossible to record in an experiment can be presented; “ the subtle structure of two-electron processes can be shown (see and compare the experimental curve of Fig. 1A with top curve of Fig. 1A (T)); “ the order of appearance of resolved peaks becomes consistent with the decreasing values of their respective kinetic parameters (ki, hi ) (Fig. 1A); the positions of four peaks Ep,i (i = 1, 2, 3, 4), determined by both ki and hi values, remain in agreement with common sense and with the reduction of individual substances A, C, D and F one at a time (see further discussion). The shape of the CV curves obtained in MSR mode is not the same as the original ones in Fig. 1; furthermore, the fact that the peak potentials for the second and fourth reactions are completely different from the original (i.e. consecutive) values is easy to understand although, at the first sight, hard to accept. However, we cannot assume that the picture for both electroreductions (i.e. CR and MSR) should be the same. For MSR, the sequence (Eq. (1)) with their kinetic parame-

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ters values must be rewritten into the simplified form (without chemical steps): e

e

e

e

A“ B, C “ D, D “ E, F “ G

(3)

The essential difference in the respective electroreductions is caused by different concentrations of species. In the multistep charge transfer, only the initial substrate is present in a solution before experiment (csubstrate \0, cintermediates =0). For multi-component systems, all species are the substrates and they are present from the very start (csubstrate \0, cintermediates \0). Note that the positions of calculated subpeaks I1, I2, I3, and I4 in CR mode and MSR mode are governed by different factors. For the MSR case only, the numerical values of ki, hi are decisive: the higher parameter the earlier reduction (the concentration of all species is assumed to be

the same). The position of four peaks Ep,i (i = 1, 2, 3, 4), determined by both ki and hi values, are consistent with expectations. For the CR case, the equal start rule is not fulfilled since the more reactive species are reduced after the less reactive one. For the consecutive sequence, the appearance of a more reactive component (for k2 \ k1) is possible after reduction of the less reactive one and the Faraday current (i.e. peak) of the more reactive substrate is the one that follows the Faraday current of the less reactive intermediate. The slower process is the parent for the faster one. The concentration of species is decisive here, not the reactivity of species (values of ki and hi ) (cf. Fig. 1A). The position of the simulated sub-peaks along E-axis (Fig. 1A) does not reflect the real power of kinetic parameters of the second electron

Fig. 3. (A) Concentration vs. potential (or time) dependences calculated for four systems presented in Fig. 1A and Fig. 2. The systems correspond to CR mode of Fig. 1A and to three plots (1) – (3) of Fig. 2 related to MSR mode, respectively. (B) The space concentration plots for A –G species calculated for the systems corresponding to that presented in Fig. 3A for CR mode and to three cases of MSR mode, respectively.

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transfer. The values of kf1 and kf2, if not extremely low, do not change positions of peaks (see Fig. 4) or subpeaks, but only their height. The evaluated peak potentials for individual electroactive species A, C, D, and F are different in CR and MSR modes. The subscripts ‘cons’ and ‘ind’ will

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distinguish the appropriate values, respectively. Generally, the peak potentials for the first electron transfer are the same, i.e. Ep,1,cons = Ep,1,ind since in both cases, the electroreduction of ‘free’ A takes place. In MSR mode, the difference between Ep,2,cons and Ep,2,ind depends on the ratio of rate constants k2/k1 (if h1 $ h2).

Fig. 3. (Continued)

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Fig. 3. (Continued)

For k2 k1, the peak corresponding to the second electron transfer appear at a lower cathodic potential than that of the first one (as in Fig. 1A (T)); for k2 k1, the positions are reversed. On the other hand, for k1 \ k2 and k3 \k4, Ep,cons =Ep,ind.

Since in MSR mode, individual species are present in solution from the very beginning, the values of kf1 and kf2 do not influence either the position nor the height of the peaks (see Fig. 4) and subpeaks. It should be noted that the same computer file sup-

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for both modes are presented in Fig. 3A and B, respectively. In the case of a mixture of any species, it is enough to introduce the concentration of each species into the algorithm and to compare the result with experimental curve. The curve fitting procedure should be similar to that applied for consecutive reactions and based on a series of curves rather than on a single one. A series of curves for a mixture of depolarizers can be created by successive additions of known volumes of standard solution. It is worth noting that by applying this procedure, the problems discussed in Bard and Faulkner (1980) with establishing the base line for the next wave are avoided. This is one of the advantages of the complex systematic modeling with all chemical species taken simultaneously into account (seven species in our case). Furthermore, the same modeling procedure can easily be extended to molecules containing more then two identical reducible centers. Some problems of multistep charge transfers and multicomponent systems as well as the reduction of molecules containing two or more reducible centers were raised by Bard and Faulkner (1980) as inconvenient or not yet solved. This includes the setting of the baseline for the second wave in a two-component system or in a multistep reduction as well as the problem of CV peak positions for intermediates in the multistep reduction process. The similar problem of complex curves coming from multicomponent mixtures and from consecutive processes in normal pulse polarography was discussed in a previous work (Sanecki and Lechowicz, 1997).

References Fig. 4. The influence of kf1 and kf2 on simulated CV response of electroreduction process from Fig. 1A.

ports both CR and MSR modes; it is enough to put in merely a proper initial concentration of species (listed in caption of Fig. 2). The case (1) just requires a reduction of the number of differential equations. Note that in each resolved two-electron stage, the second electron transfer peak is followed by the first-electron transfer peak (Fig. 1A (T)), while in the parent consecutive electroreduction process, with resolved one-electron peaks, the situation is just the opposite (Fig. 1A). This seems to be a significant difference between CR and MSR modes. The cases with the second electrochemical step being faster than the first one are often met in organic electrochemistry (Nicholson and Shain, 1965; Andrieux et al., 1979). To make the picture more complete, the simulated concentration dependences c=f(t) as well as c=f(x)

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