Polarons and bipolarons in doped polythiophene: A theoretical investigation

0038-1098/87 $3.00 + .OO Pergamon Journals Ltd.

Solid State Communications,Vo1.63,No.7, pp.577-580, 1987. Printed in Great Britain.

POLARONS

AND BIPOLARONS

IN DOPED POLYTHIOPHENE: INVESTIGATION

A THEORETICAL

J. L. BrCdas* Laboratorie de Chimie Theorique Appliquee, Centre de Recherches sur les Materiaux Avances, Facultes Universitaires Notre-Dame de la Paix, B-5000 Namur (Belgium)

F. Wudl

and A. J. Heeger

Institute for Polymers and Organic Solids, University of California, Santa Barbara, California

93 106

(Received 27 February 1987 by A. A. Maradudin)

We present the results of tight-binding band structure calculations performed in the framework of the adiabatic Su-Schrieffer-Heeger Hamiltonian. We discuss the formation of polaron and bipolaron defects. The polaron wavefunction is analyzed with respect to ESR hyperfine splitting data recently reported for doped solutions of poly(3hexylthiophene).

An important aspect with regard to application opportunities in the field of conducting polymers is the possibility of obtaining conducting polymer solutions from which conventional processing techniques can be exploited. Such solutions were first discovered a few years ago by Frommer and co-workers in the case of poly(p-phenylene sulfide) but were unfortunately restricted to exotic solvents such as AsFj/AsFs mixtures.r An important finding took place recently when several group&3y4 reported that some polythiophene derivatives are soluble in common organic solvents such as tetrahydrofuran or chloroform. The derivatives leading to soluble conducting polymers are thiophenes with rather large alkyl chains (e.g. butyl or hexyl grounds) substituted at the 3 positions, as is shown in Fig. 1. More recently, water soluble polythiophene derivates have also been reported.5 Conducting polymer solutions are interesting from a fundamental point of view as well, since they allow one to investigate the electronic properties of the doped polymers not only as a function of doping level but also as a function of polymer concentration. It is indeed possible to go from the dilute limit, where the chains can be considered as isolated, up to high concentrations where interchain interactions become important. Nowak et al. have recently reported the results of optical absorption and ESR studies on solutions of poly(3hexylthiophene) doped with (NO+PFg-).6 They found that the electronic properties are essentially identical to those in the solid state. In particular, spinless bipolarons are the lowest energy charge storage configuration on single poly(3hexylthiophene) macromolecules in solution. Polarons are formed either as a result of the presence of an odd number of charges on a single polymer chain or as a result of interchain inter%tions at higher-polymer concentrations. From the ESR hvnerfine snlittinr! due to the interaction between the x radical klectron’ on tKe thiophene ring and the adjacent proton, it was possible to estimate that the maximum spin density within a polaron is on the order of 0.2.6

/--

Fig. 1.

Sketch of the geometric hexylthiophene)

structure

of poly(3-

ln this Communication, we calculate the wavefunctions and the energetics of formation of polarons and bipolarons on polythiophene chains and compare our theoretical results mainlv with the exoerimental data collected on solutions of polyc3-hexylthiophene). We note that Valence Effective Hamiltonian IVEH) band-structure calculations performed on polythiophene and its alkyl derivatives indicate that the influence of the alkyl chain, which is essential with respect to the solubility properties, is negligible for what concerns the electronic properties.7 The theoretical model we consider to study polaron and bipolaron formation in polythiophene is identical to the one previously used with great success in the case of poly(p-phenylene)* and polypyrrole.~ It is based on the so-called Su-SchriefferHeeger adiabatic Hamiltonianl” and corresponds to a simple Hiickel model where the compressibility (energy) of the o framework is explicitly taken into account. In this model, the p transfer integrals are expressed as a function of the bond length (r) as: p(r) = A exp[ - r/B].

*Chercheur Qualifie of the Belgian National Fund for Scientific Research (FNRS) 577

578

POLARONS AND BIPOLARONS IN DOPED POLYTHIOPHENE

Vol. 63, No. 7

The energy of the o framework is: f(r) = C (r - r0 + B) p(r). The parameters A, B. and C have been optimized on a neutral polythiophene in order to reproduce the 2.0 - 2.2 eV experimental bandgap,gy*O the = 2.5 eV bandwidth for the highest occupied band,13 and the geometry as optimized by ab initio Hartree-Fock calculations.13 Such a parameterization effectively accounts for some of the Coulomb correlation terms which are not otherwise included explicitly in the model. The parameters we obtain, considering a sulfur on-site integral of -5.0 eV, are quite similar to those optimized for poly(p-phenylene) and polypyxTole: A = 35.0 eV; B = 0.531~ and C = 5.0 i-l. For the neutral chain, the highest occupied level is calculated to be located at -0.47 eV and the lowest unoccupied level at 1.68 eV. The bandgap is thus 2.15 eV, in excellent agreement with the 2.1 eV one-dimensional bandgap experimentally estimated from Resonance Raman Scattering experiments. l2 The lattice deformations which can take place upon oxidation of (i.e. electron removal from) a polythiophene chain are modeled by allowing the bond lengths (and thus the transfer integrals) to vary over a number N of thiophene rings in the following way: rn,n+l

= rO,,,+l

+ c( tanh[n/l]tanh[(

4N - n) /I].

Here, fin ,,=I corresponds to the undistorted bond length between aiom n and atom n+l; n is the site location from one end of the defect and (4N - n) is the separation from the other end (the factor of 4 originating from the fact that there are four carbon atoms in one ring along the backbone of the polymer chain); cx scales the deformation which depends on the type of bond; and 1 modulates the amplitude of the deformation and indicates the abruptness of the defect edges. Maximum possible deformations are taken in accordance with previously optimized ab initio values for highly doped polythiophene.13 The lattice deformations locally convert the backbone geometry from aromatic-like to quinoid-like. The energetics of polaron and bipolaron formation along a polythiophene chain are studied by removing one electron and two electrons, respectively, and optimizing the N and 1 values that lead to the lowest total energies for the ionized systems. In the case of a single oxidation process, polaron formation is energetically favorable as soon as the increase in K + o (total) energy due to lattice deformation around the polaron is more than compensated by a lowering in ionization energy. This difference in energy corresponds to the polaron binding energy. As one electron is extracted from a polythiophene chain, we obtain the formation of a polaron whose binding energy is calculated to be 0.20 eV in our model. As in the case of poly(p-phenylene)8 and we find that the polaron lattice deformation polypyrrole,9 extends mostly over four rings (N = 4) and is quite strong (I= 5). The presence of a polaron results in the appearance of two localized electronic states within the gap. These states are located 0.34 eV above the valence band edge (due to a local upward shift of the highest occupied electronic level) and 0.38 eV below the conduction band edge (due to a local downward shift of the lowest occupied electronic level) as is illustrated in Fig. 2a. Polaron states in the gap can account for the observation of three optical absorptions below the interband absorption, involving electronic transitions from the valance band to the lower polaron level, between the polaron levels, and from the valence band to the upper polaron leve1.14,15

(a)

Fig. 2.

(b)

Band structure of a polythiophene chain in the presence of (a) a polaron and (b) a bipolaron.

In our model, these transitions are predicted to occur at 0.34 eV, 1.43 eV and 1.77 eV. Up to now, spectroscopic evidence for polarons in polythiophene compounds has been reported only in the case of very lightly doped poly(3methythiophene) by Harbeke et al..16 These authors observe three subgap transitions peaking roughly at 0.4 eV, 1.2-1.3 eV, and 1.6 eV. These values are in good agreement with the calculated values but imply that the polaron states are located about 0.1 eV further away from the band edges with respect to what we calculate, at least in poly(3-methylthioph&e). The wave function (spin/charge density) associated with the occupied polaron level is schematically depicted in Fig. 3. The l&alized character of the polaron elkctrhnic state is illustrated by the fact that the spin/charge has a density probability of 80.4% within the four rings of the geometric defect. Due to symmetry reasons, the occupied polaron level has no contributions from the sulfur x atomic orbital but has contributions fron? all carbon atoms. The wavefunction for the polaron in polythiophene is thus significantly different from that for the soliton in trans-polyacetyelene.lo The maximum spin density is on the order of 0.08 and occurs on carbon atoms which are located four sites away from the middle of the defect, a behavior similar to that found for the polaron in tfans-polyacetylene.17 The calculated maximum spin density amounts, however, to only about 40% of the 0.2 maximum spin density estimated from the ESR hyperfine splitting in lightly doped poly(3-hexylthiophene) solutions.6 The reason for this discrepancy can arise from two very different sources. On the one hand, it can be argued that Coulomb correlation effects, which have been mostly neglected in our approach, might lead to an enhancement of spin densities on given sites and a decrease of spin densities (possibly producing negative densities) on the other sites. This situation is experimentally

Fig. 3.

Spin/charge densities calculated from the optimal polaron wavefunction (N =4, a=5). The numbers represent the spin and/or charge densities at the respective carbon atoms.

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POLARONS AND BIPOLARONS IN DOPED POLYTHIOPHENE

observed in tram-polyacetylene.t*~lY However, an analysis of the photoinduced absorption experiments for solid polythiophene12 and of the optical absorption experiments for dissolved poly(3-hexylthiophene)e indicates that Coulomb effects are expected to be rather weak in polythiophene compounds. 01 the other hand, an increase in spin densities might be expected if it turns out that the polaron wavefunction for the polymer h solution is actually more localized than the one we have obtained for a straight long chain. We have therefore calculated the evolution of the spin densities for polarons having a smaller extension of the associated geometric defect. We have first considered the polythiophene chain to remain straight and forced the geometric defect to extend only over three or two rings. (This means that the N value is set equal to 3 or 2, everything else being otherwise normally optimized.) In these instances, we obtain that the maximum spin density actually decreases as the N value goes down. The maximum density is about 0.07 for N = 3 and 0.06 for N = 2. In both cases, the optical 1 value is equal to 5. These results can be understood by realizing that, as the geometric defect becomes less extended, it provokes a smaller disruption of the chain overall electronic structure. This can be illustrated by the fact that the polaron levels are located less than 0.1 eV from the band edges in the N = 2 case. Therefore, the maximum spin densities decrease since the polaron wavefunctions become less localized: in the N = 2 case, the density probability for the spin within the four middle rings (the two defect rings plus one’rine on each side) is 68.6%, i.e. about 12% smaller than in the fi=4 case. ’ We have then considered that the polaron occupies a chain segment which is disconnected from the rest of the chain. Such a situation may occur due to twists in the chain conformation in solution. For chain segments, over which the polaron extends, taken equal to 4, 3, and 2 rings, the maximum spin density evolves to 0.11, 0.13, and 0.19, respectively. Within our simple theoretical approach, agreement with the maximum spin densities experimentally observed in poly(3-hexylthiophene) solutions is thus obtained only if the observed polaron is a non-instrinsic defect which extends over a chain segment which contains two rings and has no electronic overlap with the rest of the chain. This is qualitatively consistent with the fact that the hyperline splitting is observed from defects in QQ&&! (i.e. not doped) chains in solution. More experimental data are needed in order to explore the validity of this possibility. We have also studied the most stable electronic configuration when two electrons are removed from a polythiophene chain. The results indicate the formation of a bipolaron, i.e. a localized dication associated with a very strong lattice distortion.14,15 With respect to two vertical ionization processes, me gain in total energy by forming the

579

bipolaron is 0.66 eV. Therefore, formation of a bipolaron is thermodynamically favored with respect to that of two polarons by (0.66 - [2 X 0.201) eV, i.e. 0.26 eV. This result is in full agreement with both solid-state and solution experimental data which demonstrate that bipolarons are the lowest charge-storage configuration in polythiophene compounds. Polarons can be present either, as we pointed out before, as a consequence of an odd number of charges on a single polymer chain or as a consequence of a diffusion-limited recombination step as has been proposed in the case of polypyrrole.20 (Another interesting aspect will be to rationalize the polaron population increase in solution as polymer concentrations (and thus interchain interactions) are made larger.6) The bipolaron optimally extends over about four rings and the 1 value is optimized to be equal to 1, indicating that the deformations towards a quinoid geometric structure are more pronounced within the bipolaron than the polaron. Two empty bipolaron-related localized electronic levels appear in the gap and are located 0.50 eV and 1.60 eV above the valence band edge, as depicted in Fig. 2b. The location of the bipolaron levels are in perfect agreement with the two sub-gap optical absorptions which are observed at 0.50 eV and 1.55 eV in doped solutions of nolv(3hexylthiophene).e Note that for polythiophene in the solid phase, the same absorptions peak at 0.6 eV and 1.45 eV in the case of the doped systemI and at 0.4 eV and 1.25 eV in the case of photoinduced absorption experiments on the neutral system.12 In summary, our tight-binding band structure calculations on polythiophene show that upon oxidation, bipolarons are the lowest charge-storage configuration, in agreement with experiment. An analysis of the optimal polaron wavefunction indicates that the maximum spin density is about 0.08, to be compared with an experimental estimate of 0.2 in doped solutions of poly(3hexylthiophene). This discrepancy can arise from the neglect of most Coulomb correlation effects in the theoretical approach or from the fact that the polaron extends over chain segments which are about two rings long and disconnected from the rest of the chain (due to twists in the chain conformation in solution). We express our gratitude to J. M. Andre and B. Themans for fruitful discussions. We gratefully acknowledge that the collaborative work between Namur and UCSB is supported by NATO Scientific Affairs Division through Research Grant No. 407/84. We are indebted to the Belgian National Fund for Scientific Research (FNRS), IBM Belgium, and the Facultes Universitaires Notre-Dame de la Paix for the use of the Namur Scientific Computing Facility (SCF).

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