Conjugated and fluorescent polymer based on dansyl-substituted pyrrole prepared by electrochemical polymerization in acetonitrile containing boron trifluoride diethyl etherate

Electrochimica Acta 122 (2014) 50–56

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Conjugated and fluorescent polymer based on dansyl-substituted pyrrole prepared by electrochemical polymerization in acetonitrile containing boron trifluoride diethyl etherate Andresa K.A. Almeida a , Jéssica M.M. Dias b , Ana Julia C. Silva a , Diego P. Santos b , Marcelo Navarro a,b , Josealdo Tonholo a , Marília O.F. Goulart a,1 , Adriana S. Ribeiro a,∗ a b

Instituto de Química e Biotecnologia,Universidade Federal de Alagoas, Campus A. C. Simões, Tabuleiro do Martins, 57072-970 Maceió, AL, Brazil Departamento de Química Fundamental, CCEN, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil

a r t i c l e

i n f o

Article history: Received 28 June 2013 Received in revised form 7 October 2013 Accepted 8 October 2013 Available online 17 October 2013 Keywords: Conjugated polymer Fluorescence Electropolymerization Dansyl BFEE

a b s t r a c t A fluorescent pyrrole derivative bearing a dansyl substituent was prepared by a simple synthetic route and electropolymerized onto Indium Tin Oxide (ITO) electrodes. The presence of the dansyl group in the monomer precursor prevents the electropolymerization in usual systems, such as (C4 H9 )4 NBF4 in acetonitrile (CH3 CN). For this reason, it was added 20% boron trifluoride diethyl etherate (BFEE) to this system, to achieve electropolymerization. The resulting poly[3-(N-pyrrolyl)propyl dansylglycinate] (PPyPDG) films displayed electrochromic behavior. Their color varied from greenish-yellow, in the neutral state, to greyish-green, in the oxidized state; moreover PPyPDG is a good green light emitter material. Therefore, PPyPDG films might be potentially applicable in displays and optoelectronic devices. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, a great deal of interest has been focused on the synthesis of novel ␲-conjugated polymers, because they display intriguing features such as electrical conductivity, electroluminescence, third-order non-linear optical properties and chemical sensing [1]. Their potential applications include their use as materials for electrochromic devices [2,3], organic light emitting diodes (OLEDs) [4], organic solar cells (OSCs) [5], organic field effect transistors (OFETs) [6], and energy storage [7,8]. All these applications usually require the modification of the monomer structure, to tune the properties of the polymers with respect to desired applications [9]. Hence, creating new design and strategies to synthesize new conjugated polymers constitutes a rapidly expanding area: it provides a wealth of possibilities, leading to interesting materials and electro-optical devices with enhanced performance. Furthermore, this approach has created a strong change in point of view regarding the molecular engineering of the electronic properties of materials derived from conjugated systems and hence on the structural control of their band gap [9,10].

∗ Corresponding author. Tel.: +55 82 3214 1393; fax: +55 82 3214 1389. E-mail addresses: [email protected], [email protected] (A.S. Ribeiro). 1 ISE member. 0013-4686/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.electacta.2013.10.008

Among conjugated polymers, polythiophenes and polypyrroles are particularly important, because they exhibit good electric conductivity and chemical stability in ambient atmosphere, besides their structural versatility, which allows tailoring of their electronic and electrochemical properties by the manipulation of the monomer structure [11–13]. These modifications in the main chain of the conjugated polymer generally occurs by the changing of the appending moiety [14,15], or by preparation of fused rings [16–18] or either by copolymerization [19,20]. Different functional groups, such as electron donating and/or electron withdrawing, n-dopable, or fluorescent substituents [21–24], can be attached to the system. However, substitution of the electron withdrawing groups on the precursor usually lead to a monomer with higher oxidation potential, culminating in poor film quality [25]. One way to prepare good-quality conjugated polymer films bearing electron withdrawing substituents involves replacement of common organic media with a strong Lewis acid, such as boron trifluoride diethyl etherate (BFEE) [13,25]. BFEE solution has been widely used as catalyst to electrochemically polymerize aromatic monomers, such as polythiophene and its derivatives, polyselenophene, oligopyrene, and so on [13,26,27], however the mechanism of interaction between BFEE and the aromatic ring and/or the effects of different substituents present in the monomer precursor are still poorly discussed in the literature.

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Scheme 1. Synthetic route to obtain PyPDG.

Our group has synthesized and characterized a series of fluorescent materials based on 1-(dimethylamino)-naphthalene5-sulfonyl, also known as dansyl, derivatives [28–30]. The dansyl fluorophore contains both electron donating and electron withdrawing substituents in its molecular structure: the dimethylamino moiety acts as an electron donor, whereas the naphthalene sulfonyl group acts as an acceptor. This fluorophore exhibits intense absorption bands in the near UV region as well as strong fluorescence in the visible region with high emission quantum yields [31]. These characteristics, together with the synthetic versatility of the sulfonyl group, aroused considerable interest in attaching the dansyl group to the pyrrole ring, to obtain a new fluorescent conjugated polymer. Based on these considerations, in this paper, a dansyl-based pyrrole precursor was synthesized and electrochemically polymerized using a mixed electrolyte containing (C4 H9 )4 NBF4 /CH3 CN and 20% BFEE (by volume). New insights about energetically favorable interactions between the active sites of this pyrrole derivative and BFEE during electropolymerization process were presented and discussed with basis in theoretical calculations and electrochemical results. Also, the electrochemical, morphological, UV–vis-NIR spectroscopy and fluorescence properties of the as-prepared polymer films deposited onto ITO electrodes were investigated.

2. Experimental

2.2. Synthesis Scheme 1 illustrates the synthetic route used to obtain 3-(Npyrrolyl)propyl dansylglycinate (PyPDG). 1-(3-Iodopropyl)pyrrole (0.66 g, 2.82 mmol) and 1,8-bis(dimethylamino)naphthalene (proton-sponge® , 0.44 g, 2.09 mmol) were added to a solution of dansylglycine (0.63 g, 2.05 mmol) in 15 mL of dry CH3 CN. The reaction mixture was stirred at 50 ◦ C for 1.5 h; a white precipitate was generated and removed by filtration. CH3 CN (15 mL) was added to the solution, which was then stirred; the precipitate was formed again and removed by filtration. The filtration step was repeated until no more precipitate was detected. The solvent present in the remaining solution was evaporated in a rotatory evaporator; the crude product was chromatographed on silica using CH2 Cl2 as eluent, to give 0.50 g (59% yield) of the compound as a pale yellow solid. M.p. 84.9–85.5; 1 H NMR (400 MHz, methanol-d4 , ı): 8.56 (d, J = 8.6 Hz, 1H), 8.37 (d, J = 8.6 Hz, 1H), 8.18 (dd, J = 7.3 and 1.2 Hz, 1H), 7.62–7.54 (m, 2H), 7.27 (dd, J = 7.5 and 1.2 Hz, 1H), 6.57 (m, 2H), 5.99 (m, 2H), 3.80–3.70 (m, 6H), 2.87 (s, 6H), 1.92–1.78 (m, 2H); FTIR (KBr): 3287 (s,  (N–H)), 3098 (w,  (C–H␣ pyrrole)), 2928 (m, as (C–H)), 2776 (m, as (C–H)), 1752 (s,  (C=O)), 1576 (w, as (C=C)), 1325 (w, ␦ (N–H)), 1227 (m, ␦ (C–H, naphthalene)), 1160 (m,  (C–O)), 789 (m, ␦out-of-plane (C–H, naphthalene), 721 (s, ␦out-of-plane (C–H␣ pyrrole)) cm−1 . Anal. calcd for C21 H25 N3 O4 S: C 60.70, H 6.06, N 10.11, O 15.42, S 7.72; found: C 63.05, H 6.27, N 9.09, O 14.05, S 7.54.

2.1. Materials and instrumentation All the chemical reagents for synthesis were purchased from Sigma-Aldrich or Acros and used as received. Anhydrous acetonitrile 99.8% (CH3 CN <0.001% water, Sigma-Aldrich), tetrabutylammonium tetrafluoroborate ((C4 H9 )4 NBF4 , Aldrich) and lithium perchlorate (LiClO4 , Aldrich) were used as received, boron trifluoride diethyl etherate (BFEE, Sigma-Aldrich) was freshly distilled before use. The 1 H NMR spectrum of 3-(N-pyrrolyl)propyl dansylglycinate (PyPDG) was recorded on a Bruker spectrometer operating at a frequency of 400 MHz. The FTIR spectrum was acquired on a Bruker IFS66 spectrophotometer using KBr pellets. The elemental analysis determinations were performed on a Carlo Erba EA 1110 CHNS equipment. Melting points were determined on a Micro Química MQAPF 301 melting point apparatus and are uncorrected. Scanning Electron Microscopy (SEM) analysis was conducted on a JEOL JSM 6340F microscope using secondary electrons (SE) mode. UV–vis-NIR spectroelectrochemistry was carried out on a Hewlett-Packard 8453A diode array spectrometer. The CIE (Commission Internationale de l’Eclairage) chromaticity diagram and color coordinates [32] of the polymer films were obtained using a Spectraluxs Software v.2.0 Beta [33]. Fluorescence spectra were registered at room temperature using a Fluorolog Horiba Jobin Yvon fluorometer.

Fig. 1. Cyclic voltammograms on ITO registered during the attempts to electrochemically polymerize PyPDG using (C4 H9 )4 NBF4 /CH3 CN solution ( ); dansylglycine solution in the same electrolyte (----) and PyPDG (-. -. -) or dansylglycine (. . .. ) in 0.1 mol L−1 (C4 H9 )4 NBF4 /CH3 CN with 20% BFEE (by volume),  = 0.02 V s−1 .

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2.3. Electrochemistry Poly[3-(N-pyrrolyl)propyl dansylglycinate] (PPyPDG) films were deposited onto ITO electrodes (1.0 cm2 , Rs ≤ 10  cm; Delta Technologies) in a single compartment cell using an Autolab PGSTAT30 galvanostat/potentiostat. In order to prevent the migration of water into the experimental system, a home-built non-aqueous Ag/Ag+ (CH3 CN) reference electrode (+0.298 V vs. normal hydrogen electrode; Analion), isolated from the working solution by a Vycor® frit, was used in all the experiments. A Pt foil was used as the counter electrode. PyPDG was employed at a concentration of 0.02 mol L−1 in a supporting electrolyte consisting of 0.10 mol L−1 (C4 H9 )4 NBF4 in CH3 CN, or in a mixed electrolyte system of (C4 H9 )4 NBF4 /CH3 CN with 20% BFEE (by volume). Deposited films were washed several times with CH3 CN to remove unreacted PyPDG monomer and excess electrolyte. Electrochemical studies of the polymer films deposited on ITO were carried out in a solution of LiClO4 (0.10 mol L−1 ) in CH3 CN, by varying the potential from −1.80 to 0.50 V vs. Ag/Ag+ . Cyclic voltammograms of the PPyPDG films were acquired using LiClO4 rather than the (C4 H9 )4 NBF4 electrolyte, because the former generated better electrochemical response [8]. 2.4. Computational methods The quantum calculations were performed using the Gaussian 09 program [34]. Ground state structures for PyPDG and its interaction with BFEE were evaluated using the density functional theory (DFT) level of the three-parameter compound functional of Becke (B3LYP) [35] and the 6-31 + G(d,p) basis set was used for all atoms. The frontier orbitals were plotted using the Chemcraft package [36]. 3. Results and Discussion 3.1. PyPDG Electrochemical polymerization Initial attempts to electropolymerize PyPDG onto ITO surface employed a (C4 H9 )4 NBF4 /CH3 CN solution as electrolyte. A series of cyclic voltammograms using the potential range of 0.00 ≤ E ≤ 1.70 V vs. Ag/Ag+ , with E increasing in steps of 0.10 V, displayed an irreversible wave at 0.85 V, but the formation of the electroactive film deposited onto ITO was not evidenced. Furthermore, it was not possible to detect the nucleation loop [37] or any other reduction process in the reverse scan in the investigated potential range. Therefore, we attributed this irreversible wave (Fig. 1, full line) to the tertiary amine (present in the dansyl moiety) oxidation, since the cyclic voltammogram of its precursor dansylglycine, in the same supporting electrolyte, revealed a similar behavior (Fig. 1, dashed line). Our group has discussed results concerning the electrochemical responses of dansylglycine in an earlier paper [28]. When BFEE (20%) was added to the (C4 H9 )4 NBF4 /CH3 CN electrolyte system, PyPDG oxidation initiated at about 0.90 V (Fig. 1, dash-dotted line), which was accompanied by polymerization, as confirmed by (i) the presence of the nucleation loop in the reverse scan, (ii) the presence of a cathodic wave at ca. 0.18 V vs. Ag/Ag+ , which is associated with PPyPDG reduction, and (iii) the increase in the current densities of the redox pair in the 0.15–0.60 V region (Fig. 2), implying that the amount of PPyPDG deposited on the electrode is increasing. Layers of different thickness were obtained by varying the number of the performed voltammetric cycles, in order to produce films with deposition charge (Qdep ) in the range of 15 and 75 mC cm−2 . In the presence of BFEE the irreversible waves attributed to the tertiary amine oxidation, for both PyPDG and dansylglycine, were

Fig. 2. Cyclic voltammograms of PyPDG in 0.1 mol L−1 (C4 H9 )4 NBF4 /CH3 CN with 20% BFEE (by volume) mixed electrolyte,  = 0.02 V s−1 .

suppressed (Fig. 1, dash-dotted line and dotted line, respectively). It is known from the literature that BFEE interacts with the aromatic ring by the formation of ␲-complexes that suppress the resonance stability of the aromatic ring thus facilitating further reactions [38]. In the present case, it is possible to suggest that BFEE and the free electrons of the nitrogen in the tertiary amine of the dansyl moiety form a Lewis acid/base adduct, allowing, thus, the selective pyrrole ring activation toward polymerization. To better understand this behavior, it is necessary to compare the effects of electropolymerization conditions for pyrrole itself in (C4 H9 )4 NBF4 /CH3 CN and its interaction with BFEE. According to the cyclic voltammograms shown in Fig. 3, it is possible to observe a shift in the oxidation potential of the pyrrole to more anodic region upon BFEE addition to the electrolyte system. This behavior is opposite for thiophene and its derivatives, as well as for fused rings. Compared with thiophene, pyrrole has lower aromaticity and is unstable in Lewis acid medium. Hence, it is not possible to

Fig. 3. Cyclic voltammograms of pyrrole in (C4 H9 )4 NBF4 /CH3 CN ( ) and in the same electrolyte with addition of 20% BFEE (by volume) (----),  = 0.02 V s−1 .

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Fig. 4. DFT-calculated HOMO-1, HOMO and LUMO of the ground state structures of PyPDG (a), PyPDG interacting with BFEE at the pyrrole ring (b) and PyPDG-BFEE complex formation by interaction between the tertiary amine of PyPDG and BF3 (c). Isodensity value 0.01 a.u.

obtain polypyrrole in BFEE solution through electrochemical polymerization because BFEE is an initiator of cationic polymerization; consequently, ring-opening reactions will occur, generating only nonconjugated polymers [13]. To get a clarifying view of the process, theoretical calculations were performed. 3.2. Theoretical calculations Density functional theory (DFT) electronic structure methods have been extensively employed in the interpretation, assignment and explanation of oxidation/reduction potentials observed in electrochemical studies [20,39]. Fig. 4 shows the frontier orbitals for PyPDG (Fig. 4a) and for the interaction between PyPDG and BFEE (PyPDG-BFEE). Considering PyPDG-BFEE, two different possibilities of interaction sites of the PyPDG and BFEE were investigated: in the aromatic ring of the pyrrole (Fig. 4b) or in the tertiary amine of the dansyl moiety (Fig. 4c). The frontier molecular orbitals play an important role to understand the polymerization process of the PyPDG in both systems (with or without BFEE). The HOMO energy level is associated with the molecule ability of losing its electrons, while the LUMO energy level corresponds to the electron affinity potential and reflects the ability of to receive electrons. According to Fig. 4a, the PyPDG HOMO and LUMO orbitals are mainly located in the tertiary amine region. Therefore, oxidation and reduction processes occur in this region of the molecule, preventing pyrrole ring activation (electron removal) toward electropolymerization. The HOMO-1 orbital presents a feature of pyrrole ring activation, showing that excitations involving these electrons could promote polymerization. However, this would require much higher energy, which would oxidize other electroactive sites or even degrade the molecule. Fig. 4b shows that BFEE interaction via the pyrrole ring does not alter the initial PyPDG configuration, in terms of frontier orbitals; in other words, BFEE interaction only with the pyrrole ring would still hamper polymerization. When we considered the situation in which BFEE interacts with the tertiary amine present in the dansyl

moiety, we verified that inclusion of the BF3 orbitals into the PyPDG molecule modifies the electronic configuration in such a way that HOMO is located in the pyrrole ring (Fig. 4c). This configuration would facilitate electron removal from this region, initiating polymerization. Effective formation of new molecular orbitals in that region proves formation of the complex PyPDG-BFEE via interaction between the tertiary amine and BF3 . 3.3. Morphological characterization of the PPyPDG film Fig. 5 depicts the SEM micrograph of the electrodeposited PPyPDG film with Qdep = 15 mC cm−2 . This film is homogeneous and

Fig. 5. SEM images (mode SE) of PyPDG film deposited onto ITO with Qdep = 15 mC cm−2 using (C4 H9 )4 NBF4 /CH3 CN 0.10 mol L−1 with addition of 20% BFEE (by volume).

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Fig. 6. Cyclic voltammogram of the PPyPDG film deposited onto ITO with Qdep = 56 mC cm−2 , recorded in LiClO4 /CH3 CN 0.10 mol L−1 with  = 0.02 V s−1 .

presents the typical morphology of polypyrrole and/or polypyrrole derivatives deposited on inert substrates; i.e., it has globular morphology resembling a cauliflower [40–42]. SEM images of films deposited with different Qdep show similar morphology. 3.4. Spectroelectrochemical properties of PPyPDG films Considering the anodic region, the cyclic voltammogram of the PPyPDG film displayed an anodic wave with and anodic peak potential (Epa) at 0.39 V and a cathodic wave with cathodic peak potential (Epc) at 0.32 V vs. Ag/Ag+ (Fig. 6). This redox couple may correspond to the polymer p-doping. The difference (Ep) of 0.07 V between the anodic and cathodic peak potentials is within the range of commonly observed values for conducting polymers and may be explained by kinetic limitations like ion diffusion or interfacial charge transfer processes, including slow heterogeneous electron transfer, effects of structural reorganization processes within the polymer film, and electronic charging of a sum of two interfacial exchanges, namely the electrode/polymer and the polymer solution interfaces [43,44]. At the cathodic region, it is possible to note two irreversible waves at −1.20 V and −1.62 V, that can be associated with polymer n-doping [22,45,46] and electroreduction of the carbonyl from the ester linkage of the dansylglycine moiety at ca. −1.50 V, giving carboxylate anions that can react and form a series of different products [47]. Furthermore, cyclic voltammetry can be used to estimate the relative position of the HOMO and LUMO energy levels of the conjugated polymer, EHOMO and ELUMO , respectively [48,49]. Thus, the HOMO and LUMO energy levels as well as the electrochemical band gap energy (Eg ec ) were calculated from the onset oxidation potential (Eonset , ox ) and the onset reduction potential (Eonset , red ) of the of the PPyPDG films as being EHOMO = −4.55 eV, ELUMO = −3.49 eV, and Eg ec = 1.06 eV. The behavior of PPyPDG films upon doping and undoping was monitored by UV–vis-NIR spectroscopy in a solution containing LiClO4 0.10 mol L−1 in CH3 CN. The changes in the absorbance spectra of the film were plotted as a function of the potential applied to the electrode during cyclic voltammetry and are presented in Fig. 7. All the films investigated presented similar spectroelectrochemical behavior, independently of the Qdep , just with slight variation in the absorbance values.

Fig. 7. Spectroelectrochemical characterization of the PPyPDG film deposited onto ITO with Qdep = 37 mC cm−2 , recorded in LiClO4 /CH3 CN 0.10 mol L−1 showing absorbance as a function of the applied potential (0.00 ≤ E ≤ 0.50 V vs. Ag/Ag+ ).

The absorption spectrum of the film in the neutral state (E = 0.00 V) exhibited a band with maximum at 338 nm (UV region), which indicates an optical band gap energy of 2.65 eV (calculated from the onset of the ␲–␲* transition, onset = 468 nm). Comparison of the optical band gap energy (Eg op ) and electrochemical band gap energy (Eg ec ) values obtained of the PPyPDG film showed that the Eg ec , calculated from the Eonset , ox and the Eonset , red in the cyclic voltammogram of the PPyPDG film, is clearly lower than the Eg op , which was determined from the absorption edges of UV–vis-NIR spectra in the film. The effect of the discrepancy between Eg ec and Eg op was also reported by other authors [48,50]. According to Ma et al. [51] apart from experimental uncertainties, differences between Eg ec and Eg op reflect the fact that free ions are created in the electrochemical experiment in which Eg ec is calculated, considering the difference between HOMO (oxidized state) and LUMO (reduced state). On the other hand Eg op is determined from the absorbance spectrum of the film in the neutral state. So, these differences in the experimental procedure used to calculate Eg can cause the discrepancy between the values of Eg ec and Eg op . Rising potentials decreased the peak intensity at 338 nm and shifted the absorbance to lower wavelengths. It is also detected an increase in the absorbance at about 520 nm (broad band), corresponding to the formation of the polaron state, as well as a broad band in the NIR region above 800 nm, assigned to the formation of bipolarons [52]. Although a visible region spectrum gives an objective measure of color absorption, it provides little insight into the impact on the human eye of the subjective perception of hue, saturation and relative luminance. The quantification of color stimulus through the measurement of the CIE chromaticity coordinates, which is based on the tristimulus values of a color, provides a numerical description of color and allows that spectral changes over the entire visible region to be plotted as a single color trajectory on a single graph [53]. Despite the low chromatic contrast (%T) in the visible region (<20%), the variation in the color of the PPyPDG film from greenishyellow (CIE color coordinates x: 0.301, y: 0.173), in the neutral state (E = 0.00 V), to greyish-green (CIE color coordinates x: 0.363, y: 0.234), in the oxidized state (E = 0.50 V), is perceptible. These results suggest that the PPyPDG films are potentially applicable as an electrochromic material.

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for kindly provide the Spectralux® software; CTI (Centro de Tecnologia da Informac¸ão Renato Archer, Campinas-SP) and LNLS (National Synchrotron Light Laboratory, Campinas-SP) for the use of scanning electron microscope; and INCT/INAMI/CNPq, INAMI/CAPES/Nanobiotechnology, and Braskem Co. (Brazil) for the partnership in the field of scientific and technological development. References

Fig. 8. Emission spectra of the PPyPDG solubilized in NMP. Inset: photoluminescence of the monomer in the solid state (a) and of the PPyPDG solution (b) exposed to 366 nm UV light.

3.5. PPyPDG fluorescence properties The PPyPDG films electrochemically synthesized were solubilized in N-methylpyrrolidone (NMP) and the fluorescence spectrum of PyPDG solution in NMP was recorded (Fig. 8). The polymer solution is fluorescent and presented an emission band at 483 nm, which corresponds to light green color. The inset of Fig. 8 evidenced the photoluminescence properties of the monomer PyPDG in the solid state and of the soluble polymer PPyPDG upon exposure to UV light with a wavelength of 366 nm. 4. Conclusions The use of the Lewis acid BFEE in the electrolyte system constitutes a strategy to improve the electrodeposition of PPyPDG films and to fine-tune their electrochemical and optical properties. It was observed through cyclic voltammograms that PyPDG behaved differently in solutions without and with BFEE, with anodic peaks attributed to the oxidation of the tertiary amine of the dansyl moiety and to pyrrole ring oxidation, respectively. These alternative processes were discussed with basis in theoretical calculations that corroborated the electrochemical results. Cyclic voltammograms of the PPyPDG films revealed a redox pair in the anodic region, related to the polymer doping/undoping process, and two irreversible waves at the cathodic region, attributed to polymer n-doping and to reduction of the carbonyl from the ester linkage of the dansylglycine moiety. Furthermore, PPyPDG films exhibited electrochromic behavior and fluorescence when solubilized in NMP. These features make this material a potential candidate for application as active layer in optoelectronic devices, such as displays and electrochromic devices. Acknowledgments The authors wish to thank the research funding agencies CNPq, CAPES, FINEP (FUNTEL and CTENERG Programs), and FAPEAL for financial support and for fellowships granted to AKAA, AJCS (CAPES), and SMFF (CNPq). The authors are particularly thankful to Professor Petrus Santa Cruz (Universidade Federal de Pernambuco)

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