Synthetic Metals, 51 (1992) 203-209
Poly(alkylthiophenes)" chain conformation and thermochromism D. A. dos Santos, D. S. Galvfio and B. Laks Universidade Estadual de Campinas, Departamento de Fisica Aplicada, 13081 Campinas, SP (Brazil)
M. C. dos Santos Universidade Federal de Pernambuco, Departamento de Quimica Fundamental, 50739 Recife, PE (Brazil)
Abstract The role of conformational disorder in the electronic structure of alkyl-substituted polythiophene is investigated. Thermally-induced twisting of thiophene rings out of the main conjugation plane is assumed. AM1 geometry optimizations were carried out to obtain the molecular torsion potential curves for substituted bithiophenes. Total torsion potentials acting on inter-ring rotations are assumed to come from two contributions, the molecular potential and a phenomenological 'solid state potential' that accounts for inter-chain interactions. It is found that the molecular potential for rotations does not depend on the length of the alkyl group but only on the regiochemistry of substitution. A long, disordered thiophene chain is built to be representative of a classical probability distribution of torsion angles. The electronic structure associated with valence and conduction u bands is calculated within VEH pseudopotential theory and the NFC technique. The dependence of the optical gap on temperature is obtained and is in agreement with experiment.
An important step towards processible conjugated polymers has been attained with the synthesis of soluble polymeric systems. Poly(alkylthiophenes), the soluble forms of polythiophene, are among the best examples of such materials. Chemical or electrochemical synthesis using alkylthiophene substituted in the fl position as the starting reagent results in long, high-molecular-weight chains where thiophenes are mostly coupled in a head-to-tail configuration of side groups, with 10-20% of head-to-head connected rings . Regiochemically-well-defined, all head-to-head-coupled polymers result when the synthesis starts from the head-to-head substituted dialkyl-bithiophene. Thermochromism and solvatochromism have been observed in poly(alkylthiophenes) with head-to-tail coupling of side groups  (and not in the regiochemically-well-defined polymers ). Many electronic and structure-related properties, such as optical absorption and X-ray spectra, show reversible changes upon heating and cooling cycles . 0379-6779/92/$5.00
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These observations have been interpreted in terms of a reversible loss of conjugation due to out-of-plane twisting of thiophenes. However, the thermochromic transition does not seem to be a completely reversible phenomenon, since the infrared activity of the polymer shows new features upon heating which are not recovered on cooling . Infrared modes induced by thermal t r e a t m e n t have been attributed to single-chain behavior and were interpreted as local symmetry breaking. The effects of thermally-induced structural disorder on the electronic structure of a single poly(alkylthiophene) chain is investigated in this work. A series of AM1 calculations is carried out to estimate the total energy as a function of torsion angle of dialkyl-bithiophenes . The dependence of torsion energy on the side-chain length and substitution position is studied. A phenomenological 'solid state' potential barrier is introduced to account for interchain interactions. A simple statistical model is formulated to simulate single-chain configurations at a given temperature, where each ring is supposed to twist independently against a torsion barrier resulting from the summation of the molecular and 'solid state' barriers. Electronic structure calculations on disordered chains containing up to 200 thiophenes were performed by the combination of Valence Effective Hamiltonian (VEH) and the Negative Factor Counting (NFC) techniques . We concluded that all calculated properties, unless for the 'solidstate' potential, were independent of side-chain length. On the other hand, the substitution position may drastically affect molecular torsion barriers. Changes in the gap between valence and conduction bands are fully consistent with experimental observations of the thermochromic transition. Thermally-induced disorder on alkyl-substituted polythiophenes is shown to explain the irreversible changes in the infrared spectrum of the polymer upon heating and cooling cycles.
Theory The present work is based on a number of quantum-chemical techniques. Geometry optimizations have been performed within the Austin Method 1 (AM1)  semiempirical technique. Full geometry optimizations were carried out in order to obtain torsion potential curves for substituted bithiophenes. Those curves were fitted to the analytical form: V(O) = A + B cos(0) + C cos(20)
and their dependence on length and substitution position of the alkyl groups was found. A phenomenological solid-state potential has been assumed to account for inter-chain interactions and is given by: V,s(O) = (Hs~/2)[1 - cos(20)]
where H~ is the height of the barrier that depends on the length of the alkyl substituent. Thiophenes are considered to rotate against the potential, Vtota~, given by the sum of both contributions. The probability distribution of torsion angles was taken as the classical distribution, exp(-Vtota](O)/kT). A chain containing up to 200 thiophenes has been simulated to represent a given torsion-angle distribution. We have adopted the Valence Effective Hamiltonian (VEH) method  for the electronic structure calculations. The VEH method has been successful in reproducing the band structure of conjugated systems , and it is also a very convenient approach for our purpose since it is a non-self-consistent technique. The disordered Fock matrix is finally diagonalized using the Negative Factor Counting (NFC) technique .
The optimized ground state geometries of substituted bithiophenes are shown in Fig. 1. These were found for (dihexyl)bithiophene. We have also calculated the ground state geometric structure for ethyl- and butylsubstituted species, as well as for the bithiophene molecule, and obtained tt ]
125.0, , . . . . ~ ~
C (c) .-'"
H. 120"2dS~1226 ":/ ~,. ' ~ H
Fig. 1. AM1 optimized geometries for substituted bithiophenes in three different couplings: (a) head-to-head; (b) head-to-tail; (c) tail-to-tail. The ground state geometry of bithiophene is shown in (d) for comparison.
3.2 • heod-to-head o
48. 72. ANGLE (de gree-)
Fig. 2. Torsion potential curves obtained from AM1 calculations.
essentially the same results. Three distinct couplings have been considered: from (a) to (c) in Fig. 1, respectively, head-to-head, head-to-tail, and tail-to-tail (dialkyl)bithiophene. Bond lengths and bond angles are not affected by the presence of the ligands, in agreement with the MNDO calculations of Th~mans and collaborators . However, the optimum torsion angle between the aromatic rings is drastically affected by the regiochemistry of substitution, as can be seen in Fig. 2. Bithiophene and the tail-to-tail substituted molecule are both planar, with potential barriers of 0.63 kcal and 0.62 kcal, respectively. On the other hand, the head-to-head coupled isomer has a minimum energy twist angle of 90 °, with a barrier against the planar geometry of 2.65 kcal, while for the head-to-tail conformer the corresponding values are 100.6 ° and 0.66 kcal. As the barriers could be sensitive to end effects and to a - ~ interactions t h a t arise in n o n p l a n a r systems, we have performed calculations on trimers and pentamers in all head-to-tail configurations, adopting ethyl groups as ligands. The ground state geometries obtained are fully consistent with previous results: the aromatic rings are twisted at 90 ° to each other and the associated torsion energy is 1.2 kcal for the trimer, namely, 0.6 kcal per couple of rings. We recall that the values obtained for the torsion barriers may not be realistic, even t h o u g h we believe they are qualitatively right. Several theoretical investigations on poly(alkylthiophenes) have been reported in the literature [11-13]. Most adopt the torsion potential curve appropriate for bithiophene as a model for the torsion barrier in the substituted polymer. Our results have shown that torsion barriers very much depend on the regiochemistry of substitution. Thermochromism is
\\\ \ \
/ /\\ /
/ / / x.
Fig. 3. Typical total potential for thiophene rotatiorls, calculated from expressions (1) and (2) (see text): (8) molecular potential; (b) so]id-state potential; (c) total potential.
observed in substituted polythiophenes that are not regiospecific, and that are mostly coupled in the head-to-tail configuration. A nonplanar ground state is predicted for the system. It is experimentally observed to adopt a planar configuration , however. Thus, in the solid-state material the packing energy as well as the energy associated with ~ conjugation should be large enough to compensate the energy barrier against planarity. The height of the solid-state potential is expected to weaken with fl-substitution of side chains (longer side chains leading to weaker inter-chain interactions), tending to reduce the minimum energy required to induce ring rotations. This is in agreement with the experimental observation of a decrease in the thermochromic transition temperature with increasing length of the side chain. We have investigated the effect of assuming a solid-state potential to be added to the molecular torsion curves, following eqn. (2). The torsion potential for rotations around a bond connecting thiophenes would have the form shown in Fig. 3. Angle distributions as a function of temperature have been calculated for solid-state barriers of 1.5 and 2.0 kcal. A random distribution of defects (20%) in the head-to-head coupling has been considered. In Fig. 4 distributions at several temperatures for a fixed solid-state barrier of 1.5 kcal are shown. We were unable to identify a preferred torsion angle at high temperature, as has been suggested . The distribution tends to be uniform instead. A chain composed of 200 thiophenes has been simulated to represent a given distribution. The optical band gap has been computed and the
Fig. 4. Angle distribution D(0) (arbitrary units) for several temperatures. Following 0 = 0, from top to bottom: 50 K, 100 K, 150 K, 200 K, 250 K, 300 K, 350 K, 400 K, 450 K.
results are s h o w n in Table 1. We note t h a t the V E H method underestimates ~ - ~ * band gaps, which is c a l c u l a t e d to be 1.605 eV at zero temperature, while it is experimentally estimated to be a r o u n d 2.0 eV . For the first set of data (Hss = 1.5 kcal), the gap rapidly increases up to 2.231 eV at room t e m p e r a t u r e and then saturates. This represents an increase of 0.6 eV in the optical gap, in a g r e e m e n t with experiment . The correct b e h a v i o r of the band gap as a function of t e m p e r a t u r e is not r e p r o d u c e d however: experiments have reported that, for long alkyl tails, the increase in optical gap starts at room t e m p e r a t u r e and s a t u r a t e s at a b o u t 450 K. It is possible t h a t the solid-state barrier itself is affected by disorder , so that the potential d o e s not keep the same form for all temperatures. We can interpret other experimental data on t h e r m o c h r o m i s m by admitting that the ground state s t r u c t u r e is t r a p p e d in the potential well a r o u n d 0 degrees (Fig. 3), namely, in the planar geometry. Raising the t e m p e r a t u r e allows the rings to r o t a t e and e v e n t u a l l y overcome the barrier at 90 °. These rings are now t r a p p e d in the potential well a r o u n d 180 ° and may not r e t u r n to the original position on cooling. This effect TABLE 1 Optical gaps, in eV, as a function of temperature and solid-state potential Hss (in kcal)
209 m i g h t e x p l a i n i r r e v e r s i b l e c h a n g e s o b s e r v e d in t h e i n f r a r e d s p e c t r u m of t h e s e m a t e r i a l s d u r i n g h e a t i n g - c o o l i n g c y c l e s , s i n c e t h e r i n g s w h i c h w o u l d b e t r a p p e d in l a r g e t o r s i o n a n g l e s s h o u l d g i v e r i s e to specific i n f r a r e d a c t i v i t y , t h o u g h t h e e l e c t r o n i c s p e c t r u m w o u l d n o t c h a n g e . O u r r e s u l t s a l s o s e e m t o b e in a g r e e m e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n t h a t a c r y s t a l l i n e s t a t e is f o u n d in t h e m a t e r i a l c o m p o s e d o f h e a d - t o - t a i l d i m e r s , w h i l e h e a d - t o - h e a d c o u p l e d m o l e c u l e s do n o t c r y s t a l lize a n d f o r m g l a s s e s a t l o w t e m p e r a t u r e . W e see f r o m Fig. 2 t h a t t h e h e a d - t o - h e a d i s o m e r h a s a b a r r i e r a g a i n s t p l a n a r i t y w h i c h is a b o u t f o u r times stronger than the corresponding one for head-to-tail isomer. Steric h i n d r a n c e is t h u s m a x i m i z e d in t h e f o r m e r c a s e a n d s h o u l d w e a k e n intermolecular interactions. Moreover, the regiospecific head-to-head c o u p l e d p o l y ( a l k y l t h i o p h e n e ) d o e s n o t p r e s e n t s o l v a t o c h r o m i s m , w h i c h i m p l i e s a r i g i d b a c k b o n e s t r u c t u r e a n d is c o n s i s t e n t w i t h a h i g h torsion barrier.
Acknowledgements T h i s w o r k h a s b e e n s u p p o r t e d in p a r t b y t h e B r a z i l i a n A g e n c i e s FINEP, CNPq, and FAPESP.
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