Oxidative coupling and polymerization of pyrroles

Electrochimica Acta 50 (2005) 4936–4955

Oxidative coupling and polymerization of pyrroles Part I. The electrochemical oxidation of 2,4-dimethyl-3-ethylpyrrole in acetonitrile Gregers Hendrik Hansen a,1 , Rikke Mørck Henriksen b , Fadhil S. Kamounah a,b , Torben Lund a , Ole Hammerich b,∗,1 b

a Department of Life Sciences and Chemistry, Roskilde University, DK-4000 Roskilde, Denmark Department of Chemistry, The H.C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

Received 30 November 2004; received in revised form 7 February 2005; accepted 7 February 2005 Available online 28 June 2005

Abstract The electrochemical oxidation of 2,4-dimethyl-3-ethylpyrrole in acetonitrile has been studied using cyclic voltammetry, constant current coulometry, preparative electrolyses and ab initio calculations. The product analysis after the preparative electrolyses was carried out by HPLC combined with UV–vis and electrospray ionization MS detection. The aim of the work was to address some of the unresolved problems in the oxidative oligomerization and polymerization of alkylpyrroles. The title compound was chosen as a model for studies of pyrroles that are more basic than the solvent-supporting electrolyte system and for that reason are forced to serve as the base accepting the protons released during the coupling steps. The voltammograms obtained by cyclic voltammetry at a substrate concentration of 2 mM and voltage scan rates between 0.02 and 2 V s−1 showed a characteristic trace-crossing phenomenon that could be demonstrated by digital simulation to be related to that fact that the deprotonations of the initially formed dimer dication are slow with second order rate constants in the range 103 –104 M−1 s−1 . The relative stability of the different tautomers of the protonated pyrrole monomer and the corresponding 2,2 -dimer was determined by ab initio calculations at the RHF 6-31G(d) level. The studies also included investigations of the effects resulting from addition of a non-nucleophilic base, 2,6-di-tertbutylpyridine, to the voltammetry solutions. The major product observed after preparative electrolyses was a trimer the structure of which is proposed to include a central 2H-pyrrole unit. Since 2H-pyrroles are stronger bases than the corresponding 1H-pyrroles, the trimer is effectively protected against further oxidation by protonation. Two other trimers were observed as minor or trace products as well as a 1H,2H-dimer and several tetramers, also in trace amounts. In addition to the dimer, the trimers and the tetramers, a number of other minor products could be detected. These could all be traced back to the nucleophilic attack by residual water on the radical cations or dications of the 2,2 -dimer and the trimers. The results obtained by constant current coulometry are in agreement with the formation of a 2H-pyrrole based trimer as the major product. © 2005 Elsevier Ltd. All rights reserved. Keywords: Alkylpyrroles; Oligomers/polymers; Electrochemical oxidation; Ab initio calculations; LC–UV–vis–MS

1. Introduction The interest in conducting polymers is steadily growing driven by the unique electronic properties of these materials [1–5]. The reactions leading from a suitable monomer to the conducting polymer include a series of oxidative coupling ∗ 1

Corresponding author. Tel.: +45 35321801; fax: +45 35320322. E-mail address: [email protected] (O. Hammerich). ISE member.

0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2005.02.076

steps and this has stimulated the application of electrochemical techniques not only for studies of the properties of the polymeric materials, but also for studies of the details of the polymerization process [6–11]. Special attention has been paid to the electropolymerization of pyrrole and pyrrole derivatives [6,11–13] and the interest in the kinetic and mechanism details of the coupling steps has lead to numerous studies of the electrochemical oxidation of pyrrole [14–24], substituted pyrroles [25–34], and a number of pyrrole dimers and oligomers [35–40]. Evident

G.H. Hansen et al. / Electrochimica Acta 50 (2005) 4936–4955

Scheme 1.

from these studies is that the kinetics and mechanism details as well as the properties of the materials resulting from the oxidation are highly dependent on both the nature and number of substituents on the pyrrole ring system and the reaction conditions, not least the basicity of the solvent-supporting electrolyte system. The generally accepted notation for electropolymerization of pyrroles is illustrated in Scheme 1 assuming, as it is commonly done, that the coupling processes involve preferably the 2,5-positions; in most cases, however, without proof. Usually, also the number of monomeric units, n, in the chain is not reported. Also, although it is inherent to oxidative coupling processes that two protons are released for each new covalent bond formed, the base accepting the protons is most often not specified. Thus, it appears that in spite of the interest in the oxidative couplings of, for instance, pyrroles, a number of questions important for the understanding of the details of these processes are still not fully answered. In order to gain more insight into the reaction details of processes of the type shown in Scheme 1, we have initiated a series of investigations of the oxidation of alkylpyrroles with the aim to obtain a better understanding of the kinetics and mechanisms, including the acid–base reactions associated with the coupling process, and also to characterize intermediates formed during the oligomerization and polymerization processes. In this paper, we report on the electrochemical oxidation of 2,4-dimethyl-3-ethylpyrrole (24dm3ep), commonly known as kryptopyrrole. In this compound, only the 5-position is free for classical oxidative coupling of the type where the new bond is being formed between two carbon centers and for that reason we initially expected that the electrochemical oxidation of this particular pyrrole would result only in simple oxidation products derived from the 2,2 -dimer, 4,4 -diethyl-3,5,3 ,5 tetramethyl-1H,1 H- [2,2 ]bipyrrolyl. This, as we shall see, was a rather na¨ıve expectation (please notice that coupling through the 5-position leads to a 2,2 -dimer). However, 24dm3ep still proved to be a good model compound for studies of the effects of the acid–base properties of the solvent system.

2. Experimental 2.1. Chemicals 2,4-Dimethyl-3-ethylpyrrole (Aldrich), 2,6-di-tert-butylpyridine (Aldrich, 97%), lithium trifluoromethanesulfonate,

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LiCF3 SO3 (Aldrich, 99.995%), tetrabutylammonium hexafluorophosphate, Bu4 NPF6 (Aldrich, 98%), formic acid, HCOOH (Acros Organics, 99%), acetonitrile, MeCN (LabScan, HPLC grade) and methanol, MeOH (LAB-SCAN, Analytical Science, 99.9%) were all used as received. The water was purified at a Milli-Q Water Purification System. 2.2. Cyclic voltammetry The voltammetry cell was a cylindrical tube (50 mL) fitted with a sidearm, through which the substrate was added, and a B29 joint to accommodate a plastic electrode holder equipped with a nitrogen inlet. Circular, planar platinum working electrodes were made from 2 mm wire sealed into soft glass and polished to mirror quality. Freshly prepared electrodes were conditioned by use in CV experiments of the type described in this paper until highly reproducible results were obtained. After this pretreatment the electrodes were cleaned only by wiping first with paper cloth moistened with acetone or MeCN and then with a dry piece of paper cloth. The counter electrode was a platinum wire and the reference electrode consisted of a silver wire immersed in MeCN/Bu4 NPF6 (0.1 M) and separated from the measurement compartment by a porous ceramic plug [41]. Freshly prepared reference electrodes were allowed to equilibrate by standing until the potential had reached a constant value. The electrochemical equipment was either an ECO Autolab system, including the PSTAT10 potentiostat, without iR-compensation, or composed by a PAR model 173/176 potentiostat driven by a PAR model 175 universal programmer. The PAR 175 programmer was activated by the trigger system described earlier [42] and the experimental data were recorded on a Nicolet model 310 oscilloscope. The function generator and the oscilloscope were interfaced to an HP Vectra personal computer equipped with an HP Basic language processor card. Programs for instrument control and data handling were written in HP Basic 3.0. The measurements typically included 10 mL of a solution that was 2 mM in substrate. Peak potentials (Ep ) were, as a rule, determined as an average of three measurements. The standard deviations were typically less than ±2 mV. The ferrocene/ferrocenium redox couple served as an external reference. The formal potential (Eo ) measured as the midpoint potential (Epox − Epred )/2, of this redox couple is equal to +0.295 V versus the Ag/Ag+ reference electrode used in the voltammetry experiments. 2.3. Constant current coulometry The amount of charge required for the total consumption of substrate was determined by constant current coulometry [41,43], in most cases at a current of 25 mA using 0.1 mmol of substrate dissolved in approximately 50 mL of MeCN/Bu4 NPF6 (0.1 M). Dissolved oxygen was removed by purging with nitrogen saturated with MeCN for at least 15 min and a stream of nitrogen was maintained over the

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solution surface during the experiment. A two-compartment cell with the compartments separated by a horizontal sintered glass disk was used for these experiments. A layer of neutral alumina (1–2 mm thick) covered the sinter to reduce seepage between the compartments. The anode was a platinum gauze electrode and the cathode a platinum wire. The solution in the anode compartment was magnetically stirred during electrolysis. The decay in substrate concentration was monitored through recordings of the voltammetric oxidation peak current due to the substrate at 1-min intervals using the same working and reference electrodes as described above. 2.4. Preparative electrolyses and the identification of products Oxidations at a constant current (i = 25 mA) at the 0.2–0.3 mmol scale were carried out in a three-compartment H-type cell with a platinum gauze electrode as the anode and a carbon rod as the cathode. The solvent was MeCN and the supporting electrolyte was LiCF3 SO3 (0.025 M), the latter used in order to avoid detection problems caused by the presence of tetraalkylammonium salts during the analysis by electrospray ionization mass spectrometry (ESI/MS) [44,45] (see below). Dissolved oxygen was removed by purging with argon for at least 15 min and a stream of argon was maintained over the solution surface during the experiment. The solution in the anode compartment was stirred magnetically during the electrolysis. The oxidations were followed by analyzing small samples (100 ␮L), withdrawn from the anode chamber at regular intervals, by help of the LC–UV–vis–MS system described below. The effect of the presence of a nonnucleophilic base during the electrolysis was investigated in a series of experiments in which an excess of 2,6-di-tertbutylpyridine (200 ␮L, 0.89 mmol) was added to the anode compartment of the cell. The LC–UV–vis–MS instrument used for analysis of the electrolysis products consisted of an HPLC system (TSP Spectra System) equipped with an auto sampler (AS3000), a gradient pump (P4000) and a vacuum degasser. The column was a 50 mm Xterra MS RP C18 (Waters) with an inner diameter of 2.1 mm and a particle size of 2.5 ␮m. The solvent gradient program used for the separation is shown in Table 1. The UV–vis detector was of the diode array type (UV 6000 LP) with a 5 cm flow cell. UV–vis absorptions were recorded Table 1 HPLC gradient program Time (min)

Solvent Aa (%)

Solvent Bb (%)

0 4 14 19 24 35

100 100 25 25 100 100

0 0 75 75 0 0

The eluent flow was 0.2 mL min−1 . a A: MeOH/H O/HCOOH = 20/79/1. 2 b B: MeOH.

between 190 and 800 nm. The mass detector was an LCQDeca ion-trap instrument (Thermo-Finnigan) equipped with an ESI interface run in the positive mode. The ion trap was run in the data dependent MS/MS scanning mode. The chromatographic and mass spectrometric analysis was controlled by the LCQ Xcalibur 1.2 software. The first scan event was obtained in the m/z interval 50–500 followed by a second scan event in which a MS2 spectrum was obtained of either one of the ions selected among the parent mass list or the ion from the first scan event with the highest intensity. The parent mass list included m/z = 124.1, 245.2, 366.3 and 487.4 corresponding to the protonated forms of the monomer, dimer, trimer and tetramer of 24dm3ep, respectively. The reject mass list included m/z = 192.3 corresponding to the protonated form of 2,6-di-tert-butylpyridine. The isolation m/z width was equal to 2, the normalized collision energy was 28% and activation time 30 ms. 2.5. Molecular orbital calculations Molecular orbital calculations at the ab initio level were carried out at dedicated work stations, or a cluster of personal computers, using the Gaussian 98 package [46]. 2.6. Digital simulation Voltammograms were simulated by help of the DigiSim software [47]. 3. Results and discussion 3.1. Cyclic voltammetry without a deliberately added base Voltammograms for the oxidation of a 2 mM solution of 24dm3ep in MeCN at a voltage scan rate (ν) of 0.2 V s−1 , and with the direction of the scan being reversed at +0.93 V, are shown in Fig. 1. A peak (O1 ) corresponding to the oxidation of the substrate is observed +0.715 V. A reverse current corresponding to this peak could not be observed during the backward going scan, even at ν = 1000 V s−1 , indicating that the radical cation initially formed at O1 undergoes a fast follow-up reaction. This is in good agreement with earlier observations that radical cations of simple alkylpyrroles dimerize rapidly [30,35]. For instance, the second order rate constant for the dimerization of the radical cation of 1,2,5-trimethylpyrrole has been reported to be of the order 108 M−1 s−1 [30]. By comparison of the height of O1 with the height of the oxidation peak recorded for a 2 mM solution of ferrocene under the same conditions it is seen that the stoichiometry for the oxidation of 24dm3ep at the time scale of the experiment is close to that for a 1 F process (assuming similar diffusion coefficients for 24dm3ep and ferrocene). During the backward scan a small reduction peak (R2 ) is observed at +0.054 V, the anodic counterpart of which (O2 )

G.H. Hansen et al. / Electrochimica Acta 50 (2005) 4936–4955

Fig. 1. Cyclic voltammograms for the oxidation of (a) 24dm3ep (2 mM) in MeCN/Bu4 NPF6 (0.1 M) recorded at ν = 0.2 V s−1 (first scan, solid line; second scan, dashes) and (b) ferrocene (2 mM) under the same conditions (dots).

is observed at +0.151 V during the second scan in the positive direction. The peak system was observed at scan rates between approximately 0.02 and 2 V s−1 and thus must be caused by an intermediate. In agreement with previous work [35,37–39], we attribute O2 /R2 to the reversible one-electron transfer involving the dimer and the dimer radical cation. • (These two species are labeled Pyr–Pyr and Pyr–Pyr + , respectively, in the schemes to follow. The starting material, 24dm3ep, is labeled PyrH in the schemes and this notation is used also in other places where it is convenient.) Further oxidation of the dimer radical cation to the dication (+ Pyr–Pyr+ in the schemes) is observed at +0.560 V (O3 ). A reduction current corresponding to O3 was not observed indicating that + Pyr–Pyr+ reacts further under the conditions of the experiment. A noteworthy feature of the voltammogram is the so-called trace-crossing observed in the potential region where the dimer is being oxidized. This phenomenon is more clearly illustrated in Fig. 2 in which the current axis has been expanded. It is seen that the current trace resulting from the backward scan crosses that for the forward scan twice at potentials close to the Eo -values for oxidation of the dimer to the radical cation and the dication, respectively. The extent to which the trace-crossing appears is highly dependent on both the substrate concentration and the voltage scan rate and the phenomenon is, for instance, much less pronounced at a substrate concentration of 1 mM or at a voltage scan rate of 2 V s−1 . Trace-crossings always contain important information about the kinetics and mechanism of the electrochemical process and have been reported in a number of cases [19,48–53], including the electrochemical oxidation of pyrroles [19] and thiophenes [52]. However, before addressing the kinetic and mechanism features that result in trace-crossing in the present case, we shall first present further results obtained by voltammetry and coulometry and also discuss some aspects of the

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Fig. 2. The low potential part of the voltammogram in Fig. 1 with the current axis being expanded (first scan, solid line; second scan, dashes).

acid–base reactions inherent to the oxidative coupling of pyrroles. When the voltage scan was extended to +1.2 V a second, rather small oxidation peak (O4 ), was observed at +1.022 V as seen in Fig. 3. Neither in this case we were able to observe the corresponding reduction peak. Peak O4 was observed only in the same range of voltage scan rates as that required for the observation of O2 /R2 and O3 , that is at ν between approximately 0.02 and 2 V s−1 . As an illustration the voltammogram recorded at ν = 2 V s−1 is shown in Fig. 4, and it is seen that O4 , as well as O2 /R2 and O3 , are less developed at this scan rate. Oxidation peaks similar to O4 have been observed also for other alkylpyrroles and have been attributed to the oxidation of the monoprotonated dimer [30,35] (labeled Pyr–HPyr+ in the schemes). There is no indication of the fate of the radical dication resulting from oxidation of the monoprotonated dimer at O4 .

Fig. 3. Cyclic voltammograms for the oxidation of 24dm3ep (2 mM) in MeCN/Bu4 NPF6 (0.1 M) recorded at a ν = 0.2 V s−1 (first scan, solid line; second scan, dashes) with the direction of the scan being reverse at +1.2 V.

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Scheme 2.

Scheme 3.

Fig. 4. Cyclic voltammograms for the oxidation of 24dm3ep (2 mM) in MeCN containing Bu4 NPF6 (0.1 M) recorded at a ν = 2 V s−1 (first scan, solid line; second scan, dashes) with the direction of the scan being reversed at +1.6 V.

3.2. The basicity of simple alkylpyrroles Generally, the coupling of simple aromatic compounds by electrochemical oxidation is formulated without specific notion of the base accepting the protons liberated after the initial bond formation [54] as illustrated in Scheme 2. This, however, is not necessarily an adequate description when the substrate is an alkylpyrrole. For this latter class of compounds the pKa -values (referring to aqueous solutions) for the protonated forms are typically between −4 (unsubstituted pyrrole) and 4 (2,3,4-trialkylpyrroles) depending on the degree of substitution and position of the substituents [55]. For the substrate in question, 24dm3ep, the pKa -value has

been reported to be 3.75 [56]. In comparison, the pKa of protonated MeCN is close to −10 [57]. As a consequence of this rather large difference in pKa -values the equilibrium shown in Scheme 3 is strongly displaced to the left. Although the pKa -values reported above refer to aqueous solutions this conclusion is without doubt valid also under the conditions of the present study. It is seen in Scheme 3 that we assume that protonation of 24dm3ep takes place preferentially in the 5-position. This assumption is based on experimental results reported for a series of 2,3,4-trisubstituted pyrroles [56,58,59] and on data obtained by ab initio calculations (see Table A.1 in Appendix A). The acidity of protonated pyrrole dimers and oligomers relevant to the present study has to the best of our knowledge not been determined. However, considering the similarities of the structures of the monomer and the 2,2 -dimer it seems reasonable to expect that also the two equilibria shown in Scheme 4 are strongly displaced to the left. In other words, the protons either stay at the coupling positions and/or are transferred to other positions or to other pyrroles during the electrochemical oxidation of pyrroles in aprotic solvents, such as MeCN. An analogous problem related to the relative basicity of substituted pyrroles and water has been addressed briefly earlier [32].

Scheme 4.

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ing oxidation under conditions where another, stronger base has not been added. 3.4. The first steps of the mechanism for oxidation of 24dm3ep and the origin of the trace-crossing phenomenon

Fig. 5. The height (ip ) of O1 recorded by voltammetry at 1-min intervals during constant current coulometry (i = 25 mA) of 24dm3ep (0.1 mmol) in MeCN containing Bu4 NPF6 (0.1 M) as supporting electrolyte.

3.3. Constant current coulometry without a deliberately added base Information about the charge involved in the electrochemical oxidation of 24dm3ep at a time scale comparable to that for a preparative electrolysis was obtained by constant current coulometry [41,43]. In a typical experiment, an amount of 24dm3ep corresponding to 0.1 mmol was subjected to oxidation at a constant current of 25 mA. The decrease in the substrate concentration with time was monitored by recording the height of the oxidation peak O1 by voltammetry at 1-min intervals. A plot of the peak height as a function of time is shown in Fig. 5. It is seen that the decrease in substrate concentration is essentially linear in time for the first approximately 4 min. Extrapolation to the time where the peak height would have reached zero results in t ∼ = 4.5 min, which at the conditions of the experiment corresponds to approximately 0.7 F. This is somewhat less than would have been expected considering that the height of O1 (Fig. 1) corresponds roughly to 1 F. This apparent discrepancy has its origin in the difference in time scale between the two types of experiment. We will return to this point later (see Section 3.10). Addition of an excess of a non-nucleophilic base, 2,6-ditert-butylpyridine (pKa = 5) [60], to the solution remaining after coulometry had a marked effect on the height of O1 recorded at t = 5 min. It is seen that the height of O1 after the addition of the base has increased to an extent that corresponds to regeneration of approximately half of the original amount of the starting material according to Scheme 5. This is a clear indication that 24dm3ep partly serves as a base dur-

With reference to the discussion above the reaction steps leading to the 2,2 -dimer and its further oxidation may be outlined as in Scheme 6. Here, it should be emphasized that the scheme does not provide a complete description of the total oxidation reaction as it includes only the reaction steps being discussed so far, but these are sufficient to allow us now to address the origin of the trace-crossing phenomena shown in Fig. 2. Initially, it is convenient to consider two kinetically limiting cases of Scheme 6 under the thermodynamic constraints that the dimer, Pyr–Pyr, and the dimer radical cation, • Pyr–Pyr + , are both easier to oxidize than the starting material, PyrH. (i) The first limiting case corresponds to the situation where deprotonation of the dication, + PyrH–HPyr+ , is too slow to take place at the voltammetry time scale. In that case, the stoichiometry of the reaction at the voltammetry time scale is given by Eq. (1) corresponding to 1 F process: 2PyrH − 2e− → + PyrH–HPyr +

(1)

(ii) The second case corresponds to the situation where the deprotonation of + PyrH–HPyr+ and Pyr–HPyr+ are both fast and irreversible at the voltammetry time scale. The reaction now proceeds to + Pyr–Pyr+ , via Pyr–Pyr and • Pyr–Pyr + , and the stoichiometry is given by Eq. (2a), again corresponding to a 1 F process. In this case, the situation where PyrH does not participate as a base, would instead lead to the stoichiometry given by Eq. (2b) corresponding to a 2 F process. The abbreviation Base in Eq. (2b) symbolizes a non-nucleophilic base that is stronger than PyrH. In other words, when PyrH is the base to accept the protons released during the coupling process the height of O1 is reduced to approximately half the size of that that would have been observed in the absence of this complexity: 4PyrH − 4e− → + Pyr–Pyr + + 2 PyrH2 +

(2a)

2PyrH + 2Base − 4e− → + Pyr–Pyr + + 2BaseH+ (2b) Neither of these two limiting kinetic cases allow for the observation of the oxidation peak O4 in Fig. 3. In the first

Scheme 5.

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Scheme 6.

case, Pyr–HPyr+ is not formed and in the second is has only a transient (steady state) existence. Thus, in order for the oxidation of Pyr–HPyr+ to be observed as a well-defined peak it is required that the rate of its formation as well as the rate of its disappearance is comparable to the time scale of the voltammetry experiment. Considering that the voltage scan rate applied for the experiment reproduced in Figs. 1 and 2 was only 0.2 V s−1 it can be concluded that rate of formation and the rate of disappearance of Pyr–HPyr+ are both relatively slow processes. The stoichiometry of this case of mixed kinetics is between 0.67 and 1 F, dependent on the relative rates of the two proton transfer reactions, which is in

fair agreement with the observation made from Fig. 1. Slow deprotonations have been observed during the electrochemical oxidation of other pyrroles [30] as well as thiophenes [61,62] and thiophene–pyrrole oligomers [63]. In order to investigate whether the voltammograms in Figs. 1 and 2 are indeed compatible with the reaction sequence given in Scheme 6, a series of digital simulations were carried out. However, simulations of voltammograms corresponding to a reaction sequence as complex as that in Scheme 6 are not straightforward. In addition to the steps given in the scheme, the simulation must include also three solution electron transfer reactions (see Appendix B),

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Fig. 6. (A) Experimental voltammogram from Fig. 1 (solid line) and the voltammogram simulated for the mechanism given in Scheme 6 with the parameters given in Appendix B (dash dot). (B) First scan (dash dot) and second scan (dash dot dot) of a voltammogram simulated for the mechanism given in Scheme 6 with the parameters given in Appendix B.

altogether resulting in three electrochemical steps and seven solution steps, and, importantly, most of the kinetic and thermodynamic parameters related to these steps are unknown. The unknown parameters were obtained by fitting the simulated voltammograms to the experimental ones. The details of the simulation and fitting procedures are given in Appendix B. The results are shown in Fig. 6A and B. Comparison of the simulated voltammograms with the experimental one (Fig. 6A), shows that a simulation based on the mechanism in Scheme 6 can indeed reproduce the essential features of the experimental voltammogram, including the trace-crossing. It is beyond the scope of this paper to discuss in details the magnitudes of all the parameters resulting from the simulation, but we do wish to point out a few important features. First, it should be noticed that the simulations were all based on the assumption that the three electrode reactions may be treated as reversible processes at low voltage scan

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rates. By this we are not implying anything about the real values of the heterogeneous electron transfer rate constants for 24dm3ep and the 2,2 -dimer, only that a scheme including only reversible electron transfers is perfectly compatible with the experimental voltammograms obtained at low voltage scan rates, including the trace-crossing phenomenon. Determination of kinetic and thermodynamic parameters by fitting voltammograms resulting from the simulation of a reaction as complex as that in Scheme 6 to experimental voltammograms is a risky approach and the results should be examined carefully. However, the simulations showed that the trace-crossing phenomenon could only be accurately reproduced for values of the two proton transfer rate constants, k2+,m and k+,m , in a very narrow range and also, that these values were only little dependent on the values of the remaining simulation parameters. The values of the two sets of rate and equilibrium constants for the proton transfer reactions were k2+,m = 6 × 103 M−1 s−1 , K2+,m = 7 and k+,m = 4 × 103 M−1 s−1 , K+,m = 0.15, and we find it satisfying that k2+,m and K2+,m are both found to be larger than k+,m and K+,m , respectively, as also intuitively expected. The values of the two proton transfer rate constants compare favorably with those already reported for alkylpyrroles [56,64]. For instance, the value reported [56] for the protonation of 24dm3ep with H3 O+ , 5.7 × 103 M−1 s−1 , is of the same order of magnitude as those resulting from this study. Less important, but still gratifying, is it to notice that the second order rate constant for dimerization of the 24dm3ep radical cation, kdim , resulting from the fitting is 5 × 108 M−1 s−1 , in good agreement with the report [30] that the rate constant for dimerization of the 1,2,5-trimethylpyrrole radical cation is of the order 108 M−1 s−1 . Finally, we wish to point out that the value of kp resulting from the simulation, 5 × 107 s−1 , should be taken only as an indication of the reactivity of the dimer dication since the follow-up reaction is not specified. 3.5. Further considerations concerning the acid–base properties of the pyrrole system It is inherent to the coupling process that the deprotonation of the mono- and diprotonated dimers, Pyr–HPyr+ and + PyrH–HPyr+ , respectively, involves protons that are born in the 2,2 -positions. However, the mono- and the diprotonated dimers exist in no less than 5 and 15 tautomeric forms, respectively, and as a consequence of this the back reactions of the two proton transfer reactions in Scheme 6 do not result exclusively in the two tautomers shown in the scheme, but rather in a mixture of tautomers the relative concentrations of which are being governed by the kinetics and thermodynamics of the complete set of proton transfer equilibria. Results from ab initio calculations indicate that the most stable form of the monoprotonated dimer, for instance, is that where the proton is situated in the 5-position (see Table A.2 in Appendix A), and thus a more complete description of the proton transfer reactions associated with the oxidation of 24dm3ep would have to include also equilibria of the type shown in Scheme 7.

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Scheme 7.

Here, abbreviations, such as Pyr–HPyr+ , symbolize a tautomer in which the proton is bound to one of the coupling sites, whereas abbreviations, such as Pyr–PyrH+ , symbolize a tautomer in which the proton is bound to a non-coupling site. Also, once formed the 2,2 -dimer, Pyr–Pyr, may in principle participate in the reaction as a base as illustrated by just one example in Scheme 8. However, the voltammograms resulting from digital simulations in which additional proton transfer reactions of the type shown in Schemes 7 and 8 were included were nearly identical to those shown in Fig. 6A and B and also, the values of the kinetic and thermodynamic parameters that relate to Scheme 6 were essentially unaffected by the inclusion of a more detailed proton transfer scheme. This is likely to be related partly to the fact that Pyr–Pyr once formed is oxidized rapidly to the radical cation and dication and the reactions that involve Pyr–Pyr as a base cannot compete with the electron transfer reactions. 3.6. Cyclic voltammetry in the presence of 2,6-di-tert-butylpyridine

gram. Thus, in order to investigate the effect of the basicity of the solvent system on the oxidation process, a series of measurements were carried out in the presence of an excess of the non-nucleophilic base, 2,6-di-tert-butylpyridine. In addition to being non-nucleophilic 2,6-di-tert-butylpyridine is also rather difficult to oxidize (Ep = 2.4 V) and is for that reason expected not to interfere with the electron transfer processes related to the pyrrole system. A typical voltammogram for the oxidation of 24dm3ep in MeCN containing an excess of 2,6-di-tert-butylpyridine is shown in Fig. 7. By comparison with Fig. 1 it is clearly seen that the result of adding the base is (a) that the height of the peak for oxidation of the substrate, O1 , has increased, (b) that the peak owing to the oxidation of the monoprotonated dimer, O4 , has essentially disappeared, (c) that the trace-crossing phenomenon has disappeared and (d) that the peaks corresponding to the dimer, R2 /O2 and O3 , have disappeared. All these observations are in agreement with the effects expected as the result of an increase of the rates of deprotonation of + PyrH–HPyr+ and

The fact that 24dm3ep is forced to serve also as a base during the oxidation process predicts that addition of another base, stronger than the parent pyrrole, to the voltammetry solution would have a noticeable influence on the voltammo-

Scheme 8.

Fig. 7. Cyclic voltammograms recorded at ν = 0.2 V s−1 for the oxidation of (a) 24dm3ep (2 mM) in MeCN/Bu4 NPF6 (0.1 M) and an excess of 2,6-ditert-butylpyridine (10 mM) (first scan, solid line; second scan, dashes) and (b) ferrocene (2 mM) in the absence of 2,6-di-tert-butylpyridine (dots).

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Scheme 9.

Pyr–HPyr+ caused by the addition of the non-nucleophilic base. In other words, the kinetic behavior of the system has now approached that corresponding to the limiting case (ii) discussed above in which the reaction proceeds rapidly to the dimer dication, + Pyr–Pyr+ with the additional complexity that + Pyr–Pyr+ reacts further under the conditions. Still the height of O1 does not correspond to that of 2 F process. The origin of this apparent discrepancy is related to the fact that the final product is not the dimer dication as discussed later (see Section 3.8 below). At this point, it is relevant to address the question of whether the addition of base to the solution may result in deprotonation of the initially formed radical cation [26] according to Scheme 9. However, as it will become apparent later, we did not observe products such as hydrazines [65], side-chain substituted products [66] or other products that may originate from radicals of the type shown in Scheme 9. Thus, it appears that the proton transfer from the radical cation to 2,6-di-tert-butylpyridine is not sufficiently fast to compete with the rapid dimerization of the radical cations. 3.7. Constant current coulometry in the presence of 2,6-di-tert-butylpyridine The results obtained by cyclic voltammetry in the presence of 2,6-di-tert-butylpyridine are paralleled by the results obtained by constant current coulometry. The results presented in the same manner as in Fig. 5, are shown in Fig. 8. In spite of the fact the decay in substrate concentration is not perfectly linear, the extrapolation of the data to ip = 0 shows that exhaustive oxidation of the substrate in the presence of base requires an amount of charge corresponding to approximately 1.3 F. We will return to this result when the final products of the reaction have been presented (see Section 3.10) 3.8. Preparative electrolyses and the analysis of the product mixtures by LC–UV–vis–ESI/MS As already emphasized, the reaction sequence given in Scheme 6 is not a complete description of the oxidation of 24dm3ep and, in particular, the scheme does not give information about the products of the oxidation, that is the fate of the dimer.

Fig. 8. The peak height (ip ) of O1 recorded by voltammetry at 1-min intervals during constant current coulometry (25 mA) of 24dm3ep (0.1 mmol) in MeCN/Bu4 NPF6 (0.1 M) and an excess of 2,6-di-tert-butylpyridine (0.445 mmol).

In order to identify the products we have carried out a number of preparative electrolyses at the 0.2–0.3 mmol level, but in spite of numerous attempts it has not been possible, so far, to unambiguously identify all the products. However, valuable insight into the compositions of the product mixtures were obtained from a series of experiments in which samples were withdrawn from the electrolysis cell with regular, predetermined time intervals and then analyzed by HPLC coupled to UV–vis and ESI/MS [67–69]. The latter is a powerful analytical technique, but it should be remembered that ESI/MS is in it self an oxidative technique and therefore care should be taken to insure that the products detected are indeed the result of the electrochemical oxidation and not of the electrospray ionization. However, in general we found a good match between the chromatograms resulting from the UV–vis detector and the ESI/MS detector, which indicates that additional products do not arise to a significant degree as a result of the ionization technique. In order to avoid over-oxidation, the electrolyses were, as a rule, not run to completion and for that reason the product mixtures contain 24dm3ep in various concentrations. A typical set of results is shown in Figs. 9 and 10 for oxidations carried out in the absence (Fig. 9) and the presence

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Fig. 9. (A) LC–UV–vis and (B) LC–ESI/MS chromatograms of a solution resulting from the electrochemical oxidation of 24dm3ep (0.22 mmol) in MeCN/LiCF3 SO3 (0.025 M). The distribution of the m/z values is shown in (C). The material conversion corresponds to 0.47 F.

Fig. 10. (A) LC–UV–vis and (B) LC–ESI/MS chromatograms of a solution resulting from electrochemical oxidation of 24dm3ep (0.22 mmol) in MeCN/LiCF3 SO3 (0.025 M) with an excess of 2,6-di-tert-butylpyridine (0.89 mmol) added. The distribution of the m/z values is shown in (C). The material conversion corresponds to 0.77 F.

(Fig. 10) of 2,6-di-tert-butylpyridine. The figures labeled A and B show the chromatograms obtained using the UV–vis and ESI/MS detectors, respectively, and the figures labeled C show the same data as those in the figures labeled B, but displayed as a function of m/z. Reference to the peaks in the chromatograms is made below as “Figure no./retention time”, for example 9A/2.92. The mass-to-charge ratios,

m/z, correspond in all cases to the monoprotonated species. The presence of the starting material (m/z = 124) is reflected by the peaks at 9A/2.92, 9B/3.03, 10A/2.78 and 10B/2.90. Also, of course, the product mixtures contained 2,6-di-tert-butylpyridine (m/z = 192) in the cases where the oxidations were conducted in the presence of an excess of

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this compound, as seen at 10A/10.12 and 10B/10.21. In brief, the following results were obtained: (1) The ESI/MS spectra showed that the major product, observed at 9A/16.17, 9B/16.21, 10A/16.27 and 10B/16.29, was a trimer (m/z = 366) and not one or more simple oxidation products derived from the dimer as initially expected. In addition to this compound, two other trimers were observed, a minor component at 9A/15.62, 9B/15.72, 10A/15.70 and 10B/15.81 and a trace component at 10A/15.43 and 10B/15.53, the latter only when the electrolysis was conducted in the presence of 2,6-ditert-butylpyridine. (2) The reaction mixtures showed the presence of a dimer (m/z = 245) in trace amounts at 9A/12.55, 9B/12.65, 10A/12.58 and 10B/12.67. This is also surprising considering that the 2,2 -dimer according to Figs. 1 and 2 is converted to a reactive dication at the potential necessary to drive the oxidation of the starting pyrrole. (3) It is seen that the reaction mixtures contained even tetramers (m/z = 487) although only in trace amounts. (4) The reaction mixtures contained, in addition to the dimer, the trimers and the tetramers, also a number of other oxidation products, seen in particular at retention times in the range 11–16 min. These observations are discussed in some detail below. 3.8.1. The monomer and oxidation products derived from the monomer The peaks located at 9A/2.92, 9B/3.03, 10A/2.78 and 10B/2.90 are caused by protonated 24dm3ep (m/z = 124) as mentioned already. The UV–vis spectrum is shown in Fig. 11A and the MS2 spectrum in Fig. 11B. There are two reasons to dwell on these spectra. First, it is important to notice that the UV–vis spectrum shows the maximum intensity at 256 nm, which should be compared with the published data for 24dm3ep, λmax (EtOH) = 200–214 nm [70–72] and for protonated 24dm3ep, λmax (EtOH) = 261 nm [70]. Thus, there seems no doubt that the spectrum reproduced in Fig. 11A is that for the protonated pyrrole reflecting that the solvent mixture used for the HPLC part of the experiment, MeOH/H2 O/HCOOH, is sufficiently acidic to keep the pyrrole on the protonated form. We have no reason to believe that this should not be the case also for the pyrrole products observed in this study. Second, it is of interest to notice that the MS2 spectrum, in addition to the peak for the protonated pyrrole observed at m/z = 124, shows only one other major peak, at m/z = 96, corresponding to the loss of 28 mass units. This turns out to be specific for an ethyl substituted pyrrole and is not seen, for instance, for pyrroles substituted with methyl groups only [73]. The loss of 28 mass units is attributed to the loss of C2 H4 (ethylene). This is at variance with the electron impact MS spectrum of 24dm3ep, in which the predominant fragmentation is the loss of 15 mass units corresponding to loss of a methyl group [74].

Fig. 11. (A) UV–vis (9A/2.92, 10A/2.78) and (B) MS2 spectrum (9B/3.03, 10B/2.90) of 24dm3ep.

Only one oxidation product (m/z = 140, not marked in Figs. 9 and 10) containing a single pyrrole unit was detected, and only in trace amounts. A control experiment demonstrated, however, that this compound was present in the starting material as an impurity, presumably caused by autooxidation. The value of m/z = 140 corresponds to the uptake of one oxygen atom. We have not been able to detect monomeric products that appear to result from the electrochemical oxidation of 24dm3ep indicating that the rapid dimerization of the radical cations competes effectively with, for instance, deprotonation or nucleophilic attack by residual water or MeCN. 3.8.2. Dimers and oxidation products derived from the dimers The UV–vis and MS2 spectra of the dimer (m/z = 245) are shown in Fig. 12A and B, respectively. These spectra are not in agreement with the spectral data that we would expect for the 2,2 -dimer, Pyr–Pyr. First, we would expect that λmax for the protonated dimer would exceed that for the protonated monomer (λmax = 256 nm) by more than the 17 nm observed. The literature data given above for the monomer, and other data [55], shows that protonation results in a shift of λmax to longer wavelengths by at least

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Scheme 10.

2H-pyrroles are, as a rule, less stable but more basic than the corresponding 1H-analogues. For instance, the pKa of protonated 2,2,3,5-tetramethyl-2H-pyrrole has been reported to be 8.40 [79], whereas the values for the structurally related 2,3,5-trimethyl-1H-pyrrole and 2,3,4,5-tetramethyl1H-pyrrole are 2.0 and 3.7, respectively [55]. As a consequence of this the 2H-pyrroles compete effectively with the 1H-pyrroles as bases during the oxidation and the 2Hpyrroles are for that reason better protected against further oxidation than their 1H-analogous. We believe this to be the major factor behind the unexpected presence of a dimer in the reaction mixture. However, there is no doubt that the 2,2 -dimer, of course, is the major product resulting from dimerization of the radical cations, but this species is

Fig. 12. (A) UV–vis (9A/12.55, 10A/12.58) and (B) MS2 spectrum (9B/12.65, 10B/12.67) of a dimer resulting from the electrochemical oxidation 24dm3ep. The structural assignment is given in the text (the absorbance observed in the UV–vis spectrum at λmax = 388 nm appears to be caused by another compound (m/z = 275) that has a retention time comparable to that for the compound with m/z = 245).

40 nm. This together with the prediction, based on the known information about λmax for pyrrole dimers with a structure similar to Pyr–Pyr [75,76], that λmax for Pyr–Pyr is likely to be in the range 260–275 nm makes it unlikely that the protonated form of Pyr–Pyr would have a λmax of only 273 nm. Thus, a value of λmax = 273 nm seems to indicate that the two pyrrole units of the dimer are non-conjugated. Second, we would expect that the MS2 spectra of the monomer (Fig. 11B) and the dimer would show some resemblance, which is not the case. The MS2 spectrum for the monomer Fig. 11B) shows the loss of 28 mass units as the predominant fragmentation route, whereas the characteristic peaks in Fig. 12 B correspond to loss of 17, 29 and 123 mass units, respectively. With this information at hand we propose that the dimer observed is 4,3 -diethyl-3,5,2 ,4 -tetramethyl-1H,2H -[2,2 ]bipyrrolyl (Scheme 10) resulting from the unsymmetrical dimerization of two radical cations. (Since the assignments of structures are, so far, only tentative we shall not discuss the fragmentation patterns further.) The 2H-pyrrole (pyrrolenine) ring system is a well-known structural element in pyrrole chemistry [77,78].

Fig. 13. (A) UV–vis spectrum (10A/15.43) and (B) MS2 spectrum (10B/15.53) of Trimer-I resulting from the electrochemical oxidation of 24dm3ep in the presence of 2,6-di-tert-butylpyridine. The structural assignment is given in the text.

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Fig. 14. (A) UV–vis spectrum (9A/15.62, 10A/15.70) and (B) MS2 spectrum (9B/15.72, 10B/15.81) of Trimer-II resulting from the electrochemical oxidation of 24dm3ep. The structural assignment is given in the text.

Fig. 15. (A) UV–vis spectrum (9A/16.17, 10A/16.27) and (B) MS2 spectrum (9B/16.21, 10B/16.29) of Trimer-III resulting from the electrochemical oxidation of 24dm3ep. The structural assignment is given in the text.

further oxidized as, for instance, evidenced by the voltammetry results reported above. Thus, we would expect to find also simple oxidation products derived from the 2,2 -dimer in the reaction mixture. A careful analysis of the MS-data reveals the presence of a number of such products. Significant amounts of components with m/z = 259 (dimer + O − 2H), 261 (dimer + O) and 277 (dimer + 2O) were detected together with traces of components with m/z = 273 (dimer + 2O − 4H) and 275 (dimer + 2O − 2H). Common to these is that they all appear to be the result of nucleophilic attack by residual water on the dimer radical cation or dication. The observation

of such products under nominally non-aqueous conditions might have consequences for the design of better media for electropolymerizations. This aspect will be discussed in forthcoming publications resulting from our pyrrole studies. 3.8.3. Trimers and oxidation products derived from the trimers The UV–vis and MS2 spectra of the three trimers (m/z = 366) are shown in Fig. 13 (Trimer-I, the trace observed at 10A/15.43 and 10B/15.53, only in the presence of base), 14 (Trimer-II, the minor component observed at 9A/15.62, 9B/15.72, 10A/15.70 and 10B/15.81) and 15 (Trimer-III, the

Scheme 11.

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major product observed at 9A/16.17, 9B/16.21, 10A/16.27 and 10B/16.29), respectively, here ordered according to increasing retention time. From Fig. 13A it is seen that λmax for Trimer-I equals 389 nm, which we have found is typical for a protonated pyr-

role containing the 2,2 -dimer as a structural unit [73]. In addition, it is seen that Trimer-I has also an absorption maximum around 270 nm, typical, as we have seen above, for a compound having a single pyrrole unit. Thus, it appears that Trimer-I contains a dimer unit and monomer unit separated

Scheme 12.

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possibly by an alkyl bridge. This assignment is supported by the ESI/MS data, which include two important fragment peaks, m/z = 230 and 137 corresponding to a dimer that has lost a methyl group (m/z = 230) and a monomer that has taken up a methyl group (m/z = 137). The only possible structure compatible with these data is shown in Scheme 11. The trimer labeled Trimer-II has the largest value of λmax (400 nm) of the three (Fig. 14A and B). This value is close to the values observed for the protonated, fully conjugated trimers of, for instance, 2,5-dimethylpyrrole and 1,2,5trimethylpyrrole [80]. The MS2 spectrum shows only one intensive peak at m/z = 243 corresponding to the loss of one pyrrole unit. We take this fragmentation pattern as an indication that the protonated form of this trimer has a rather weak bond linking two pyrrole units. The tentative assignment of the structure is given in Scheme 11. Trimer-II is the only one of the three trimers proposed that has a fully conjugated (although not planar) ␲-system and is the most stable of the likely trimers derived from 24dm3ep (see Table A.3 in Appendix A). Owing to the extended ␲-system it might be expected that this particular trimer would be further oxidized during the course of the reaction, in particular when the oxidations were carried out in the presence of 2,6-ditert-butylpyridine. As a matter of fact, we observe that the concentration of Trimer-II with time passes through a maximum and the compound is essentially gone towards the end of the electrolysis. The spectral data for Trimer-III is shown in Fig. 15A and B, respectively. This trimer has a rather low value of λmax (376 nm) indicating, as for Trimer-I, that the three pyrrole units are not part of the same conjugated ␲-system. Of particular importance is the fragmentation pattern reproduced in Fig. 15B, which shows peaks corresponding to the loss of 17, 29 and 123 mass units, respectively, or, in other words, the same fragmentation pattern as observed for the dimer. Thus, we propose that Trimer-III has same basic structure except for the extra 1H-pyrrole unit attached to the 2H-pyrrole as shown in Scheme 11. The presence of the central 2H-pyrrole unit also in this case explains the effective protection by protonation towards further oxidation of this trimer. As it was the case for the 2,2 -dimer, the reaction mixture also contained products resulting from further oxidation

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of the trimers, in particular, Trimer-II. Dominant are two products observed as a double peak at retention time close to 14 min and both with m/z = 414 (not labeled in the figures). These products have essentially the same λmax and fragmentation pattern and are, apparently, two stereoisomers. However, the data are not sufficient to allow for even a tentative structural assignment. 3.8.4. Tetramers It is seen from Figs. 9C and 10C that the product mixtures contain one or more tetramers (m/z = 487) in minor amounts. Close inspection of the ESI/MS fragmentation data reveals that the product mixtures contain, at least, four tetramers, which have structural features in common with either TrimerII or Trimer-III. We have not been able to detect a tetramer with a structure similar to Trimer-I. However, the tetramers constitute only a small fraction of the product mixture and further discussion of the data seems for that reason not justified. 3.9. The over-all reaction sequence With the above information at hand we propose the route from the starting material to the products shown in Scheme 12A and B. For the sake of clarity we have omitted the details of proton transfer reactions, which have been replaced by the usual notation “–H+ ” meaning transfer of a proton to a pyrrole species or an added base. The data that may be obtained by studies of 24dm3ep only do not allow for conclusions regarding the mechanism of formation of the trimers (and tetramers), but for obvious reasons the trimers can only result from a reaction between the 2,2 dimer, Pyr–Pyr, and the monomer, PyrH. The two routes indicated at Scheme 12B include coupling reactions (upwards) and reactions including deprotonation of + Pyr–Pyr+ followed by electrophilic attack at the monomer (downwards). TrimerIII may in principle result from any of these two routes, and possibly also Trimer-II, whereas Trimer-I can only be formed via the deprotonation route. The observation that + Pyr–Pyr+ is unstable even at the time scale of slow scan cyclic voltammetry (Figs. 1 and 2) is in support of the deprotonation route as a major pathway to the final products. Work is now in progress aiming at the synthesis of the 2,2 -dimer, which is

Scheme 13.

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crucial for further studies of the unusual formation of trimers from a trialkylsubstituted pyrrole. 3.10. Stoichiometry We will now return to the questions of stoichiometry left unanswered in some of the sections above. At the time scale of slow scan cyclic voltammetry the oxidation of 24dm3ep seems to be adequately described by Scheme 6 as shown above. At the longer time scale typical for coulometry and preparative electrolyses it is necessary to include also the formation of, at least, Trimer-III. In that case, we have the over-all reactions shown in Scheme 13, in the absence and presence of 2,6-di-tert-butylpyridine, respectively. Here, it is assumed that the 2H-pyrrole unit is even a stronger base than 2,6-di-tert-butylpyridine (pKa = 5) [60]. The stoichiometry predicted by these two reaction schemes agree well with those reported above, 0.7 and 1.3 F, although Scheme 13 is an oversimplification of the real system.

The nucleophilic attack by residual water on the radical cations or dications of the 24dm3ep dimers and trimers competes to some extent with further coupling reactions, except in the case of the initial dimerization of the two substrate radical cations. This observation indicates that strictly nonaqueous conditions may be advantageous for the preparation of oligo- and polypyrroles.

Acknowledgments We wish to express our gratitude to Roskilde University for a scholarship to GHH and to Professors Gustav Bojesen (Copenhagen), Kjeld Schaumburg (Copenhagen and Roskilde) and Poul Erik Hansen (Roskilde) for their kind interest in this work. Professor Stephan P.A. Sauer (Copenhagen) is acknowledged for giving us access to a computer cluster. Appendix A

4. Conclusions

A.1. Results from ab initio calculations

The oxidation of 24dm3ep by cyclic voltammetry conforms to the pattern that has emerged from studies of other alkylpyrroles. The trace-crossing phenomenon observed during slow scan cyclic voltammetry is shown to result from slow deprotonation of the dimer dication initially formed by coupling of two 24dm3ep radical cations. When a base stronger than 24dm3ep is not added to the MeCN solutions the deprotonation reactions involve 24dm3ep as the base. The combination of HPLC with UV–vis and ESI/MS detection is a powerful technique for studies of the initial stages of the oxidation of pyrroles. The observation that the major product observed after preparative electrolyses of 24dm3ep is a trimer illustrates that alkyl substitution is not sufficient to hinder coupling through positions already occupied by alkyl substituents.

During our studies of the oxidative coupling of alkylpyrroles we were occasionally confronted with the need of physical–chemical parameters that were experimentally inaccessible or, at the least, impossible to determine without unreasonable efforts. In such cases, it was decided instead to resort to molecular orbital calculations. One such problem concerns the site of protonation of pyrrole monomers and dimers. Preliminary calculations at the semi-empirical level (AM1) demonstrated that this level of sophistication was insufficient to provide us with reliable data. For instance, from AM1 calculations it would be predicted that pyrrole itself is protonated preferentially in the 3-position whereas it is observed experimentally that the 2-position is the preferred site [81]. Instead, we have found that ab initio calculations at the RHF 6-31G(d) level, as a rule, are sufficient

Table A.1 Energies of the tautomers of protonated 24dm3ep resulting from RHF 6-31G(d) ab initio calculations Site of protonation

Conditions

E

ZPEa

E (corr)b

E (therm)c

1 2 3 4 5 (=PyrH2 + )

Vacuum Vacuum Vacuum Vacuum Vacuum

−365.305513 −365.337945 −365.332475 −365.323948 −365.350543

0.223523 0.222801 0.222235 0.222667 0.222103

−365.081990 −365.115144 −365.110240 −365.101281 −365.128440

−365.116538 −365.150920 −365.144713 −365.135971 −365.163579

1 2 3 4 5 (=PyrH2 + )

PCMd PCMd PCMd PCMd PCMd

−365.373645 −365.404676 −365.396423 −365.389854 −365.417478

0.223367 0.222281 0.222089 0.222550 0.221913

−365.150278 −365.182395 −365.174334 −365.167304 −365.195565

−365.184806 −365.216543 −365.208777 −365.202030 −365.230885

Energies are given in units of Hartrees per particle. Values for the lower energy tautomer are given in bold typescript. a Zero point correction; scaling factors were not applied. b Sum of electronic and zero point energies. c Sum of electronic and thermal free energies. d Solvation by the Polarizable Continuum Model (PCM) with the value of the dielectric constant equal to that of neat MeCN (36.64).

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Table A.2 Energies of the tautomers of protonated 4,4 -diethyl-3,5,3 ,5 -tetramethyl-1H,1 H- [2,2 ]bipyrrolyl resulting from RHF 6-31G(d) ab initio calculations Site of protonation

E

ZPEa

E (corr)b

E (thermo)c

1 2 (=Pyr–HPyr+ ) 3 4 5 (=Pyr–PyrH+ )

−729.1238079 −729.1575722 −729.1673455 −729.1470986 −729.1752349

0.410751 0.409393 0.410290 0.409638 0.411133

−728.713056 −728.748179 −728.757056 −728.737460 −728.764102

−728.762559 −728.797928 −728.805067 −728.786562 −728.813191

The anti conformation of the [2,2 ]bipyrrolyl system is assumed in all cases. Energies are given in units of Hartrees per particle. Values for the lower energy tautomer are given in bold typescript. a Zero point correction; scaling factors were not applied. b Sum of electronic and zero point energies. c Sum of electronic and thermal free energies. Table A.3 Energies of the most likely trimers derived from the 2,2 -dimer and the monomer of 24dm3ep resulting from RHF 6-31G ab initio calculations Coupling pattern

E

ZPEa

E (corr)b

E (therm)c

2,2 ,1 ,1 2,2 ,1 ,2 (=Trimer-II) 2,2 ,2 ,1 2,2 ,2 ,2 2,2 ,3 ,1 2,2 ,3 ,2 2,2 ,4 ,1 2,2 ,4 ,2 2,2 ,5 ,1 2,2 ,5 ,2 (=Trimer-III)

−1092.0905639 −1092.1318934 −1092.0845738 −1092.099199 −1092.0944807 −1092.107092 −1092.0858515 −1092.1017548 −1092.0910662 −1092.1033256

0.586108 0.586537 0.586315 0.586227 0.586506 0.586996 0.586331 0.586692 0.587161 0.587048

−1091.504456 −1091.545356 −1091.498259 −1091.512972 −1091.507975 −1091.520096 −1091.499521 −1091.515059 −1091.503906 −1091.516278

−1091.565375 −1091.607148 −1091.557754 −1091.573925 −1091.568483 −1091.581226 −1091.559908 −1091.576020 −1091.564026 −1091.578090

The anti conformation of the [2,2 ]bipyrrolyl system is assumed in all cases. Energies are given in units of Hartrees per particle. a Zero point correction; scaling factors were not applied. b Sum of electronic and zero point energies. c Sum of electronic and thermal free energies.

for predicting the relative stability of protonated pyrroles and pyrrole dimers. A.2. The energies of the tautomers of the protonated monomer and the protonated 2,2 -dimer The results from calculations aimed at determining the site of protonation of the starting material, 24dm3ep, and the 2,2 -dimer are given in Tables A.1 and A.2, respectively. From Table A.1 it is seen that the calculation predicts, in agreement with the experimental observation that 24dm3ep is protonated preferentially in the 5-position [56,58,59]. Also, it is seen that this conclusion does not require that solvation is taken into account. Solvation is for that reason omitted in the more computer heavy calculations of the relative energies of the tautomers of the protonated 2,2 -dimer (Table A.2). A.3. The relative stabilities of the most likely trimers The less expensive RHF 6-31G basis set was used for these calculations (Table A.3). Appendix B B.1. Details of the digital simulations The DigiSim software used for simulations requires the input of a number of experimental parameters in real values.

In the present case, the effective electrode area (0.042 cm2 ), the uncompensated solution resistance (600 ) and the double layer capacitance (4.4 × 10−7 F) were all determined by manual fitting of simulated voltammograms to that obtained for the oxidation of a 2 mM solution of ferrocene in the MeCN/Bu4 NPF6 solution. Using the shorthand notation of Scheme 6, the following reactions were included in the simulation of voltammograms for the 24dm3ep system (Scheme B.1). The fitting procedure included only the voltammogram obtained at ν = 0.2 V s−1 (reproduced in Fig. 1). Voltammograms obtained at higher or lower voltage scan rates were not included since the chemical reactions that are the origin of the trace-crossing phenomenon do only manifest themselves kinetically in a rather narrow range around ν = 0.2 V s−1 . Voltammograms obtained outside this range are structurally only little different from that for a simple irreversible dimerization process and are thus of no help in the determination of the crucial proton transfer rate constants. The assumptions made were the following: (i) The electrode reactions (B.1, B.2 and B.3) are all assumed to be reversible with ks being arbitrarily set to the simulation default value 1 × 104 cm s−1 . (ii) The diffusion coefficients, D, are assumed to be the same for all species with D being set equal to the simulation default value 1 × 10−5 cm2 s−1 . (iii) The rate constants for solution electron transfers with large driving forces were assumed to be close to that for

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References [1] [2] [3] [4] [5]

[6] [7] [8] [9]

[10]

Scheme B.1.

[11] [12] [13]

diffusion controlled reactions. These reactions include the • comproportionation of the dimer radical cation, Pyr–Pyr + , that is backward reaction (B.4), and the electron transfer • between the monomer radical cation, PyrH + , and the dimer, Pyr–Pyr (B.5). The rate constants were arbitrarily set to 2 × 1010 M−1 s−1 . This value together with the equilibrium constants for the two reactions, calculated from the differences of the formal potentials (see below), defines the two remaining rate constants. The initial guess of the formal potentials, Eo (1), Eo (2) and Eo (3), was based on readings from experimental voltammograms such as that in Fig. 1, the value of Eo (1) being determined as the midpoint potential and the values of Eo (2) and Eo (3) being determined from the potential of the oxidation peaks corrected for the kinetic shifts caused by the follow-up reactions. The initial values of kp and kdim for that purpose were arbitrary set to 105 s−1 and 108 M−1 s−1 , respectively. The initial value of the rate constant for forward reaction (B.6) was arbitrary set to 107 M−1 s−1 . First guesses of the values of the two rate constants, k+,m and k2+,m , and the corresponding equilibrium constants, K+,m and K2+,m were determined by trial-and-error simulations. During the fitting of the simulated voltammograms to the experimental ones it happened occasionally that the fitting procedure led to chemically unrealistic values of rate or equilibrium constants. In such cases, the values were readjusted manually before the fitting procedure was resumed. The fitting procedure terminated with the following values of the most important parameters, Eo (1) = 0.732 V, Eo (2) = 0.092 V, Eo (3) = 0.779 V, kdim = 5 × 108 M−1 s−1 , Kdim = 2.5 × 1013 M−1 , k2+,m = 6.1 × 103 M−1 s−1 , K2+,m = 7.0, k+,m = 4.1 × 103 M−1 s−1 , K+,m = 0.15, kp = 5 × 107 s−1 and Kp = 1 × 1020 . The large values of Kdim and Kp have no physical–chemical meaning and should be taken only as an indication that these processes are essentially irreversible.

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