Novel blue emitters based on π- conjugated block copolymers

Novel blue emitters based on π- conjugated block copolymers

Materials Science and Engineering C 29 (2009) 372–376 Contents lists available at ScienceDirect Materials Science and Engineering C j o u r n a l h ...

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Materials Science and Engineering C 29 (2009) 372–376

Contents lists available at ScienceDirect

Materials Science and Engineering C j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / m s e c

Novel blue emitters based on π-conjugated block copolymers L.O. Péres a, S.H. Wang b, J. Wéry c, G. Froyer c, E. Faulques c,⁎ a b c

Universidade Federal de São Paulo - Campus Diadema, Rua Prof. Artur Riedel, 275, Cep 09972-270 - Jd Eldorado - Diadema - SP, Brazil Departamento de Engenharia Metalurgica e de Materiais, Escola Politécnica, Universidade de São Paulo, Av. Prof. Mello Moraes 2463, 05508-900 Sao Paulo, SP, Brazil Institut des Matériaux Jean Rouxel, 2 Rue de la Houssinière, BP 32229, 44322 Nantes Cedex 03, France

a r t i c l e

i n f o

Article history: Received 28 April 2008 Received in revised form 17 July 2008 Accepted 19 July 2008 Available online 29 July 2008 Keywords: Conjugated polymers Fluorene Copolymers Vibrational spectroscopy Photoluminescence Suzuki reaction

a b s t r a c t A series of new phenyl-based conjugated copolymers has been synthesized and investigated by vibrational and photoluminescence spectroscopy (PL). The materials are: poly(1,4-phenylene-alt-3,6-pyridazine) (COP-PIR), poly(9,9-dioctylfluorene)-co-quaterphenylene (COP-PPP) and poly[(1,4-phenylene-alt-3,6-pyridazine)-co(1,4-phenylene-alt-9,9-dioctylfluorene)] (COP-PIR-FLUOR), with 3.5% of fluorene. COP-PPP and COP-PIRFLUOR have high fluorescence quantum yields in solution. Infrared and Raman spectra were used to check the chemical structure of the compounds. The copolymers exhibit blue emission ranging from 2.8 to 3.6 eV when excited at Eexc = 4.13 eV. Stokes-shift values were estimated on pristine samples in their condensed state from steady-state PL-emission and PL-excitation spectra. They suggest a difference in the torsional angle between the molecular configuration of the polymer blocks at the absorption and PL transitions and also in the photoexcitation diffusion. Additionally, the time-resolved PL of these materials has been investigated by using 100 fs laser pulses at Eexc = 4.64 eV and a streak camera. Results show very fast biexponential kinetics for the two fluorene-based polymers with decay times below 300 ps indicating both intramolecular, fast radiative recombination and migration of photogenerated electron–hole pairs. By contrast, the PL of COP-PIR is less intense and longer lived, indicating that excitons are confined to the chains in this polymer. © 2008 Elsevier B.V. All rights reserved.

1. Introduction In the past few years, there has been increasing interest in novel πconjugated polymers demonstrating light-emitting and/or photoconductive properties. Conjugated polymers, suitable for use in active layers of organic light emitting diodes (OLEDs), photovoltaic cells, electrochromic displays, or biological sensors should be tailored to exhibit long-term chemical/electrical stability and to combine microstructure control, light efficiency, and processability [1–3]. Copolymers containing aromatic or heteroaromatic rings, such as phenyl, biphenyl, quaterphenyl, fluorenyl, thiophene, pyridyl, might fulfill these requirements [4,5]. As a consequence, many oligomer systems were also studied in order to better understand the transport and optical phenomena in long polymeric chains. These model systems have been investigated using a variety of spectroscopic techniques [6–8] and can be useful to better understand molecular interactions in biological systems. Therefore, the search for novel polymers based on a πconjugated framework which could demonstrate OLEDs and sensing properties constitutes a very attractive challenge for chemists and physicists. Basically, the aim is to synthesize with good yields complex ⁎ Corresponding author. E-mail addresses: [email protected] (L.O. Péres), [email protected] (S.H. Wang), [email protected] (E. Faulques). 0928-4931/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msec.2008.07.022

copolymers with blocks made of luminescent chromophores so as to combine light efficiency, processability and long-term stability. The materials, whenever possible, should be harmless for the environment and should comply with energy sustainability. In this context, Péres et al. have recently reported the synthesis of new conjugated copolymers containing pyridazine, fluorene, and quaterphenyl groups, which exhibit interesting emissive properties [9,10]. Two copolymers comprising the pyridazine group have been prepared: poly(1,4-phenylene-alt-3,6-pyridazine) (COP-PIR), and poly[(1,4-phenylene-alt-3,6-pyridazine)-co-(1,4-phenylene-alt-9,9-dioctylfluorene)] (COP-PIR-FLUOR). Another copolymer [10], poly(9,9-dioctylfluorene)-coquaterphenylene (COP-PPP), is based on fluorene and an oligophenylene, quaterphenyl, obtained by reacting 9,9-dioctylfluorene-2,7-diboronic acid and 4,4′-dibromo-p-quaterphenyl (Fig. 1). The three compounds have different emitting characteristics in the blue range and have the advantage of being soluble. COP-PIR-FLUOR and COP-PPP possess high fluorescence quantum yield [9] and may be good candidates for OLEDs or optoelectronic devices. COP-PPP has been partially characterized for optical properties by infrared and UV visible absorption spectroscopy, Raman scattering, and (timeresolved) photoluminescence (PL) [10]. In this paper, we report additional vibrational and PL studies on these copolymers, which include transient experiments in order to provide a wider comparative view of the optical properties of these systems.

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2. Experimental All spectroscopic experiments described in this paper were done at air and at room temperature on pristine samples. The copolymers were provided in the form of powder or thin white brittle platelets (COP-PPP), reddish-brown paste more or less solid (COP-PIR-FLUOR), or as reddish viscous liquid (COP-PIR). These materials were therefore investigated in their as-grown solid (COP-PPP, COP-PIR-FLUOR) or viscous state (COP-PIR). Fourier-transform infrared (FTIR) and Fouriertransform Raman spectra were acquired on VERTEX 70 BRUKER and BRUKER RFS100 instruments, respectively, with a 4 cm− 1 spectral resolution. FTIR measurements of the copolymers were made with an attenuated total reflectance (ATR) apparatus. Continuous-wave photoluminescence spectra (cw PL) were recorded using a JOBIN-YVON Fluorolog fluorimeter. Ultrafast photoluminescence experiments were carried out with the regenerative amplified femtosecond laser system installed in Nantes (Hurricane X, SPECTRA-PHYSICS) delivering 100 fs pulses at 1 kHz, and 800 nm. The setup is equipped with a confocal optical system. The samples were excited at λexc = 267 nm (4.64 eV) by harmonic generation of the Ti:Sapphire laser line in a SHG/THG box with output pump power less than 0.19 µJ/pulse. The transient PL was spectrally dispersed into an ORIEL MS260i imaging spectrograph (150 grooves/mm, f = 1/4) designed to minimize stray light with high spectral resolution. Spectral calibration was performed by entering weak signals at 267 nm and 534 nm in the spectrometer during acquisition through an EKSPLA filter No bc3. These laser lines could also be removed by using an EKSPLA filter No bc4. The time-resolved emission spectra were detected with a high dynamic range HAMAMATSU C7700 streak camera of temporal resolution 5 ps. 3. Results and discussion 3.1. Infrared spectroscopy Fig. 2 compares the FTIR spectra of the alternating copolymer COPPPP and the molecules used for its synthesis. In spectrum (b) the bands at 1320 and 1350 cm− 1 are characteristic of the B–O bonds in the boron linkage in the 9,9-dioctylfluorene-2,7-diboronic acid. These bands disappear in the spectrum (a) of COP-PPP which is evidence of

Fig. 2. Infrared absorption spectra of (a) poly(9,9-dioctylfluorene)-co-quaterphenylene (COP-PPP), (b) 9,9-dioctylfluorene-2,7-diboronic acid, and (c) 4,4′-dibromo-pquaterphenyl.

the copolymer formation, since the boron-containing groups are eliminated during the polycondensation reaction. Furthermore, the two bands of 4,4-dibromo-p-quaterphenyl at 1464 and 814 cm− 1 in spectrum (c) can be ascribed to the aromatic CfC stretching and aromatic C–H out of plane rocking, respectively. They are both observed in spectrum (a) together with aromatic and aliphatic C–H stretching absorptions at 3029 cm− 1 and 2850–2930 cm− 1. The IR spectra thus confirm that COP-PPP contains quaterphenyl and fluorene blocks as depicted by the chemical formula of Fig. 1. The FTIR spectra of the three alternating copolymers are compared in Fig. 3. From inspection of these spectra and those of the starting molecules, we can conclude that lines located around 688, 758, 795 cm− 1 stem from the quaterphenyl sequences while the bands at 694, 822, 1012, 1410 cm− 1 could be signatures of fluorenyl groups. The absorptions at ~ 1448–1464 cm− 1 for all compounds are due to the aromatic CfC stretching vibration. Lines at ~ 1270 cm− 1 and 1726 cm− 1

Fig. 1. Structure of the copolymers poly(1,4-phenylene-alt-3,6-pyridazine) (COP-PIR) (1), poly[(1,4-phenylene-alt-3,6-pyridazine)-co-(1,4-phenylene-alt-9,9-dioctylfluorene)] (COP-PIR-FLUOR) (2), and poly(9,9-dioctylfluorene)-co-quaterphenylene (COP-PPP) (3).

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expected, characteristic oligophenylene vibrations dominate the spectra. In all spectra the lines observed at ~1222,1278 and 1600 cm− 1 can be unambiguously ascribed to in plane bending of the C–H, C–C inter-ring stretch and benzene ring fundamental vibrations, respectively [11,12]. The high-frequency bands between 2849 and 3062 cm− 1 can be ascribed as in IR spectroscopy to aliphatic and aromatic C–H stretching modes. Comparison of copolymer Raman spectra with literature data on pyridazine [13,14] and with Raman spectra of the starting molecules (see Fig. 5) allows us to assign bands at 1063, 1124,1293,1581, 3072 cm− 1 (COP-PIR) and bands at 591, 617, 1040, 1121, 1412, 1442, 3040 cm− 1 (COPPIR-FLUOR) to vibrations of the pyridazine rings involving, in particular, N–C and NfN stretchings. Lines at 1448–1455 cm− 1 and at 1726 cm− 1 are clearly revealed for COP-PIR both in IR and Raman spectra. The former could be possibly ascribed to vibrations of CfC bonds in the rings [15] while the latter is typical of CfO groups. For all compounds, we assign other bands occurring between 1000 and 1135 cm− 1 to mixtures of alternating CfC–C bond stretchings and C–H bending modes [11,16]. Fig. 3. Infrared ATR spectra of (a) poly(1,4-phenylene-alt-3,6-pyridazine) (COP-PIR), (b) poly[(1,4-phenylene-alt-3,6-pyridazine)-co-(1,4-phenylene-alt-9,9-dioctylfluorene)] (COP-PIR-FLUOR), and (c) poly(9,9-dioctylfluorene)-co-quaterphenylene (COP-PPP).

are found in the IR spectrum of COP-PIR. They are characteristic of a C–O–C stretch mixed with a CfO bending and of carbonyl stretching, respectively. These two lines might therefore be a fingerprint of ester groups OfC–O–C whose occurrence in the COP-PIR spectra might be linked to partial oxidation of this polymer. Lines in the region of 3000 cm− 1 are characteristic of aliphatic and aromatic C–H absorptions. 3.2. Raman spectroscopy The atomic structure of the copolymers was also checked by using Fourier-transform Raman spectroscopy. This vibrational technique uses a laser excitation wavelength at 1064 nm which avoids overwhelming signals of fluorescence that can appear by exciting in the visible range. In this way, Raman lines of photoluminescent compounds can be fully revealed. The Raman spectra of the copolymers are displayed in Fig. 4. As

3.3. Steady-state photoluminescence Fig. 6 shows the cw PL spectra recorded for λexc = 300 nm (4.13 eV) in Nantes from the three copolymers. These results strongly corroborate those obtained by Péres and Wang on chloroform solutions (Refs. [9–10]). Here, the spectra were obtained from the condensed state of the polymers, and not in solvent solutions. For all compounds, a welldefined vibronic structure occurs on the emission spectrum. The vibronic peak shapes were determined by fitting the PL spectra to Voigt functions. They are located at 356, 374, 397, 422, 443 nm for COP-PIR-FLUOR, at 329, 348, 370, 388, 413 nm for COP-PIR, and at 421, 443, 472, 508, and 551 nm for COP-PPP. Within our experimental uncertainty in spectral resolution/calibration, the energy difference between consecutive vibronic peaks agrees with the energy of the aromatic and inter-ring vibrational lines of COP-PPP (1125, 1416, 1540, 1468 cm− 1) and COP-PIR-FLUOR (1354, 1591, 1463, 1147 cm− 1); i.e. corresponding to spacings in the range of 0.14–0.21 eV. The PL-excitation (PLE) spectra of the copolymers are presented in Fig. 7. They are characteristic of the actual π–π⁎ absorption

Fig. 4. Fourier-transform Raman spectra of (a) poly(1,4-phenylene-alt-3,6-pyridazine) (COP-PIR), (b) poly[(1,4-phenylene-alt-3,6-pyridazine)-co-(1,4-phenylene-alt-9,9dioctylfluorene)] (COP-PIR-FLUOR), and (c) poly(9,9-dioctylfluorene)-co-quaterphenylene (COP-PPP).

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Fig. 5. Fourier-transform Raman spectra of (a) 9,9-dioctylfluorene-2,7-diboronic acid, and (b) 4,4′-dibromo-p-quaterphenyl.

bandshapes in the condensed state of the materials. For instance, PLE bandshapes and features of COP-PIR-FLUOR match well with those found in the absorption spectrum taken in solution [9]: two peaks at 304 and 330 nm are clearly observed. For COP-PIR and COP-PPP, the maximum PLE intensities in the condensed state are found at 300, and 371–411 nm, respectively. They are red-shifted with respect to the maximum absorptions in solvent (275 and 344 nm) [9,10]. From absorption and PL spectra, it is possible to evaluate the Stokes shifts of the polymers. The Stokes shift corresponds to the energy difference, hereafter referred to as Es between (i) the equilibrium ground state and the Franck–Condon (FC) excited state and (ii) the equilibrium excited state and the FC ground state. It arises from the energy lost by the systems in the excited state through non-radiative processes such as thermalization. This quantity is useful for evaluating molecular configuration, photoexcitation diffusion, and resonant energy transfer processes in luminescence. The energy of 0–0 (zero-phonon) electronic transitions, which take place between the zeroth vibronic level in the (ground) excited state and the zeroth vibronic level in the (excited) ground state, is used to determine Es. In general, the highest-energy emissive peak of the vibronic progression in cw PL spectra can be ascribed to the 0←0 electronic transition. Normally, the 0←0 peak in emission should be the most intense. We attempted to locate the positions of the zero-phonon or one-phonon (0→1, 1←0) electronic transitions for the present compounds. For instance, the PL-emission

Fig. 6. Steady-state photoluminescence emission spectra of: (a) poly(9,9-dioctylfluorene)-co-quaterphenylene (COP-PPP), (b) poly[(1,4-phenylene-alt-3,6-pyridazine)-co(1,4-phenylene-alt-9,9-dioctylfluorene)] (COP-PIR-FLUOR), and (c) poly(1,4-phenylene-alt3,6-pyridazine) (COP-PIR). Excitation: 300 nm.

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Fig. 7. Steady-state photoluminescence excitation spectra of (a) COP-PPP, (b) COP-PIRFLUOR, and (c) COP-PIR, recorded at emission wavelengths of 375, 380, and 443 nm, respectively. A baseline has been subtracted from spectrum (a).

spectrum of COP-PPP shows that the relative intensity of the highestenergy peak at 421 nm is weaker compared to the other transition peaks. This can be explained by the fact that this spectral feature lies within the self-absorption overlap region. Therefore, this peak could be ascribed to the 0←0 transition, while the most intense one at 443 nm may stem from the 1←0 transition. Weaker self-absorption for COP-PIR-FLUOR enables us to locate the zero-phonon peak at 356 nm. We give Es values which are based on gross estimates of the 0→0 electronic transition energy in the π–π⁎ absorption bands. We find Es ~ 0.080 eV in COP-PPP (assuming the 0→0 transition occurs at ~411 nm instead of ~371 nm, see Fig. 7), ~0.32 eV for COP-PIR-FLUOR and 0.36 eV for COP-PIR. These values are large enough to suggest that the copolymers may undergo substantial change in the torsional angle of chain blocks or aromatic rings upon light excitation [17–20] favored by additional degrees of freedom in the viscous state. Additionally, the Stokes shift in these materials could be related to possible intrachain exciton migration as in oligothiophenes [21], a property which could bear relevance for possible application of the copolymers in OLEDs. Finally, it can be noticed that the steady-state fluorescence of the two pyridazine-based copolymers is strongly blue-shifted by about 100 nm with respect to COP-PPP. The presence of quaterphenyl groups in COP-PPP likely promotes the occurrence of PL in the blue region of the spectrum while pyridazine groups in COP-PIR-FLUOR and COP-PIR would favor an emission in the near UV range.

Fig. 8. Time-integrated transient photoluminescence of the copolymers (1 ns): (a) COPPPP, (b) COP-PIR-FLUOR, and (c) COP-PIR. Excitation: 267 nm.

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nential, longer-lived PL in COP-PIR (τ1 =732 ps) likely originates from the radiative decay of localized excitons that are unable to diffuse. Exciton trapping on the ester groups detected with ATR spectroscopy can contribute to much smaller exciton mobility in this material. 4. Conclusions

Fig. 9. Spectrally-integrated transient photoluminescence decays of the copolymers: (a) COP-PIR, (b) COP-PPP, and (c) COP-PIR-FLUOR. The solid lines are fits to the curves. Excitation: 267 nm.

3.4. Time-resolved photoluminescence The results obtained in time-resolved PL spectroscopy with a sweep range of 1 ns are shown in Fig. 8. The transient spectra of COPPPP and COP-PIR are similar to those recorded in cw PL by Péres and Wang on solutions [9,10]. In COP-PIR-FLUOR there is a collapse of the vibronic features observed at 356 and 374 nm in the cw PL spectrum. Modification of the geometrical chain conformation in the excited state, exciton-vibration coupling, presence of radiative traps below the lowest excitonic level, or exciton migration in the copolymer could be invoked as possible explanations of this observation. The PL decays are presented in Fig. 9 for all compounds. The fluorescence is quenched within a few hundred picoseconds in COPPIR-FLUOR and COP-PPP (only 1% and 3% of the signal remains at t = 950 ps, respectively), while it persists monoexponentially at least over 5 ns in COP-PIR (26% of the signal remains at t = 950 ps). We assume that photobleaching or bi-exciton collisions can be neglected in our experiments. We have simulated the PL decays by taking into account the contribution of the apparatus function given by the Gaussian temporal dependence G(t) of the laser pulse. We found that implementing either monoexponential or biexponential decays in the following rate equations can best fit the PL kinetics [10]: dn1 ðt Þ n1 ðt Þ ¼ Gðt Þ− dt τ1 dn2 ðt Þ n1 ðt Þ n2 ðt Þ ¼ − dt τ1 τ2 where n1 and n2 are the excited state populations of levels 1 and 2, respectively, and τ1, τ2 their decay times. In this case, the observed signal is reproduced with the expression: Sðt Þ ¼ A1 n1 ðt Þ þ A2 n2 ðt Þ with A1 and A2 being the amplitude of each exponential contribution. The modelling of decays confirms that the decay times τ of the photogenerated species are very short in COP-PPP (τ1 =91 ps, τ2 =323 ps) and COP-PIR-FLUOR (τ1 =78 ps, τ2 =235 ps) when using the 267 nm laser excitation. This may indicate fast quenching due to intrachain exciton migration. Indeed, one can anticipate that the exciton transfer is much faster in intrachain processes than that in interchain ones. This agrees, for instance, with the fact that τ decreases in oligofluorenes when chain length increases [22]. At the initial stage of the emission process intrachain excitons populating the higher energy level 1 migrate toward defects and fastly relax with lifetime τ1 on the lower energy state 2. At longer time the relaxed excitons on level 2 are less mobile, and consequently survive longer with a slower time constant τ2 [23]. In contrast, the monoexpo-

The vibrational and photoluminescence properties of a series of novel π-conjugated copolymers comprising a pyridazine ring, an electron donor group for the two of them, have been characterized. Infrared and Raman techniques proved to be appropriate tools for probing the chemical structure of the as-prepared compounds. Vibrational spectroscopy confirms that the Suzuki reaction is an efficient synthesis route for preparing new alternating copolymers from pquaterphenyl, pyridazine and alkyl-fluorene derivatives. The copolymers COP-PPP and COP-PIR-FLUOR present strong fluorescence with emission lifetimes and yield comparable to the prototype of photoluminescent polymers, poly-p-phenylene vinylene. Despite weaker photoluminescence yield, the novel COP-PIR material is a good model compound for determining the emissive characteristics of the πconjugated sequences of this series. The excellent solubility and easy processability of these block copolymers, combined to their interesting optical properties in the blue range of the visible spectrum, make them potential candidates for integration as active layers in polymer LEDs and biological sensors based on luminescence recognition. Acknowledgments This research was supported by the Brazilian agencies National Council for Scientific and Technological Development (CNPq) and State of São Paulo Research Foundation (FAPESP). The transient photoluminescence studies of this work were performed on a setup funded in the frame of the French “Contrat de Plan Etat-Région” 2000– 2006. We thank the referees for valuable comments. References [1] J.A. Burroughes, C.A. Jones, R.H. Friend, Nature 335 (1988) 137 London. [2] S. Tasch, C. Brandstätter, F. Meghadi, G. Leising, G. Froyer, L. Athouël, Adv. Mater. 9 (1997) 33. [3] L. Torsi, N. Cioffi, C. Di Franco, L. Sabbatini, P.G. Zamboni, T. Bleche-Zacheo, SolidState Electron. 45 (2001) 1479. [4] T. Kobayashi (Ed.), Relaxation of Polymers, World Scientific, Singapore, 1993. [5] E. Mulazzi, R. Perego, H. Aarab, L. Mihut, S. Lefrant, E. Faulques, J. Wéry, Phys. Rev. B 70 (2004) 155206. [6] Zhigang Li, Hong Meng (Eds.), Organic Light-emitting Materials and Devices, Taylor and Francis CRC Press, 2006. [7] Z.V. Vardeny, X. Wei, in: T.A. Skotheim, R.L. Elsenbaumer, J.R. Reynolds (Eds.), Handbook of Conducting Polymers II, Marcel Dekker, New York, 1997. [8] E.M. Conwell, in: R. Farchioni, G. Grosso (Eds.), Organic Electronic Materials, Springer, Berlin, 2001. [9] L.O. Péres, S.H. Wang, Proceedings of the 6th International Symposium on Natural Polymers and Composites ISNAPOL2007, April 22–25 2007, Gramado, Brazil. [10] L.O. Péres, N. Errien, E. Faulques, H. Athalin, S. Lefrant, F. Massuyeau, J. Wéry, G. Froyer, S.H. Wang, Polymer 48 (2007) 98. [11] S. Lefrant, E. Faulques, S. Krichene, G. Sagon, Polym. Commun. 24 (1983) 361. [12] G. Heimel, D. Somitsch, P. Knoll, E. Zojer, J. Chem. Phys. 116 (2002) 10921. [13] M. Muniz-Miranda, N. Neto, G. Sbrana, J. Phys. Chem. 92 (1988) 954. [14] S. Breda, I.D. Reva, L. Lapinski, M.J. Nowak, R. Fausto, J. Mol. Struct. 786 (2006) 193. [15] E. Faulques, A. Leblanc, P. Molinié, M. Decoster, F. Conan, J.E. Guerchais, J. Sala-Pala, Spectrochim. Acta, Part A 51 (1995) 805. [16] E. Mulazzi, S. Lefrant, E. Perrin, E. Faulques, Phys. Rev. B 35 (1987) 3028. [17] G. Bongiovanni, A. Mura, A. Piaggi, C. Botta, S. Destri, R. Tubino, Solid State Commun. 97 (1996) 903. [18] S. Guha, W. Graupner, R. Resel, M. Chandrasekhar, R. Glaser, G. Leising, Phys. Rev. Lett. 82 (1999) 3625. [19] S. Karabunarliev, E.R. Bittner, M. Baumgarten, J. Chem. Phys. 114 (2001) 5863. [20] K. Ohno, J. Kimura, Y. Yamakita, Chem. Phys. Lett. 342 (2001) 207. [21] K. Kanemoto, T. Sudo, I. Akai, H. Hashimoto, T. Karasawa, Y. Aso, T. Otsubo, Phys. Rev. B 73 (2006) 235203. [22] C. Chi, C. Im, G. Wegner, J. Chem. Phys. 124 (2006) 024907. [23] M. Anni, G. Gigli, R. Cingolani, Y. Galvao Gobato, A. Vercik, A. Marletta, F.G.E. Guimaraes, R.M. Faria, Brazil. J. Phys. 34 (2004) 659.