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A theoretical study of structural defects in conjugated polymers
ELSEVIER
SyntheticMetals 101(1999) 335-336
A theoretical study of structural defects in conjugated polymers E.Yurtsever’, M.Yurtseverb a Chemistry Dep., KOGUni., 80860 Istanbul, (Turkey) bChemistry Dep., Istanbul Tech.Uni., 80626, Istanbul, (Turkey)
Abstract Accurate ab-initio calculations are performed for pyrrole and thiophene oligomers bonded through c1 and p carbons. The thermodynamical stabilitiy of all possible binding types including the branched forms of tetramers and pentamers are compared. Employing the probabilities obtained from these calculations, a Monte Carlo type growth scheme is applied to predict branching as functions of the chain length and temperature. A high degree of branching for polypyrrole is reported whereas the linear chains dominate the structure of polythiophene. Keywords: Ab initio quantum chemical methods and calculations, polythiophene, polypyrrole 1. Introduction The detailed analysis of the structures of polymers involving 5-member rings still offer challenging problems. The structures depend heavily on the preparation methods and a high degree of insolubility, especially in case of polypyrroles, makes the analysis more difficult. The basic evidence related to the structure comes from XPS, 13C and “N NMR, IR, and Raman spectroscopy as well as electron diffraction and X-ray investigations [ 1,2]. On the other hand quantum chemical calculations can explain the bonding in gas phase however they are restricted to small oligomers. The accepted structures of both polymers are linear chains composed of ct-a linkages however it is also commonly accepted that bonding through /3 carbons is possible and the break-up in the conjugation can lead to branching. In this study we will report our results which combine the quantum mechanical calculations of oligomers and a statistical mechanical approach. The quantum results are carried out in order to assign a set of Boltzmann probabilities of various types of bonding including the 3- and 4-way branching. These probabilities can then be used to generate an ensemble of chains where the average branching can be calculated.
conformations. The least unstable forms are those which consist of solely p-p linkages and the energy differences are usually less than 10 kcal/mol which allow a reasonable degree of branching at room temperatures. Once the relative stability of oligomers with respect to the linear form are calculated, we have observed that they can be fitted to an empirical formula: AE= n,E,+npEp+n,E,+n,pE,p+nppEpp + naapLp + naPp&pg + naappE,gp
(1)
where n denotes the number of monomers of a given type in a specific chain and E is the corresponding energy parameter for that monomer type. In Fig.1 we present the correlation between the quantum mechanically calculated energy differences to those obtained from Eq, 1 for pyrrole and thiophene oligomers.
,P 12 s g 9 ‘: 6
. d
E 3
8.
l .
. 0.
.
.
l
3
2. Branching Ratio All possible bonding types of pyrrole and thiophene oligomers up to tetramers are calculated. In case of pentamers only the tilly linear form of CL-ctlinkages and the 4-way branched form are calculated. The minimum basis sets which give reasonable geometric parameters especially in terms of twist angles are 43 1G for pyrrole and 6-3 lG(d) for thiophene. Detailed reports for all pyrrole calculations are given previously [3-51. Among all oligomer sizes, CI-CIlinearly bonded ones are the lowest energy
CIK”1.1.d.t.bil”los Fig.1: The correlation between ab-initio stability of various isomers of pyrrole and thiophene oligomers and Eq. 1. It is clear that the above partitioning of the energy presents an accurate representation of the relative stability of various isomers. Based on this empirical formula, we proceed to define a growth
0379-6779/99/$- seefront matter0 1999 Elsevier ScienceS.A. All rights reserved. PII: SO379-6779(98)01343-5
336
E. Yurtsever,
M. Yurtsever
I Synthetic
model [5,6]. Assuming that a chain of m monomer unit is already formed, the growth probabilities to each available site is calculated from: Pj = exp (-A% / kT)
(2)
where AEj is the energy required to add a monomer to the site j and it is obtained from Eq.1. The monomers are treated as nonvibrating planar structures. Torsional angles between successive units are 145’ and 158’ for pyrrole and thiophene respectively. During the growth process if the added monomer is very close to another ring of the chain, it is discarded and a new site is tried. Once a reasonably large ensemble of such grown chains is formed, the average branching is calculated as functions of the chain length and the temperature. We observe that in order to get reasonably converged averages, a sample size of 5000 chains is sufficient for chain lengths up to 100 units. In Fig.2 we present the branching ratio as functions of the chain length at 280K and 300 K for both polypyrrole and polythiophene. 0.26
,P
1
1
c_____--c--
0.20
E
Metals
IO1 (1999)
33.5-336
3. Ring Closure Hydrogenation is among the structural defects thought to occur in conjugated polymers [7]. Due to the weakening of the double bonds upon oxidation, an accidental hydrogenation of the polymer backbone may be observed. Here we report a similar defect which is also due to weak double bonds. If two nonbonded rings lie very close to each other , there is a possibility of the interaction of R-bonds which results in a weakening of the double bonds and the formation of a weak bond between these two rings. We observe that this process is thermodynamically possible under certain conditions even though the likelihood is not very high. We have carried out ab-initio calculations on bipolaron formation in various isomers of pyrrole oligomers in order to understand the effects of oxidation on defects . The tetramers consisting of J3-p linkages form kinks in the structure causing the two nonbonded rings to appraoch each other. Upon removal of two electrons from such systems, the weakened n:bonds form a new d bond and connects two monomers. For neutral oligomers p-pp-pj3-p linear tetramer is 12 kcaVmo1 less stable than the most stable CY-clcl-oraa form which is low enough to support the occurrence of ring formations.
8. ,_--
0.14
# #'
P Ii5
0.10 -_--
0.05
-----
______--
0.00 0
20
40
60
Lenglh
80
100
N
Fig.2. Variation of the branching ratio with the chain length. The upper curves are for polypyrrole and the dotted ones correspond to 300K. It is seen that the branching starts at very short chains and is relatively independent of the chain length. At room temperature polypyrrole has 20% and polythiophene has 5% branching. These results are consistent with the experimental observations [3] and the relative solubility of both poymers. The temperature slightly affects the branching ratio as expected. No phase transitions are detected with respect to the temperature. End-to-end distances follow power-law behavior with respect to the monomer number if very short chains are discarded. The Fig.3 also shows the lack of the phase transition.
0
20
40
60
80
100
LenathN Fig.3. Variation of end-to-end distance with chain length
Fig.4. The optimized geometry of the neutral and oxidized pPPPP-P whole.
4. References. [l] H.S.Nalwa (ed) , Handbook of Organic Conduc&e Molecules and Polymers, John Wiley and Sons, 1997 [2] T.A.Skotheim, R.L.Elsenbaumer, C.R.Reynolds (eds), Handbook of Conducting Polymers, Marcel Dekker, (1998) [3] M.Yurtsever, E.Yurtsever, Tr.J.Chem. 22 (1998) 87 [4] M.Yurtsever, E.Yurtsever, Synth.Met. (In press) [S]E.Yurtsever, O.Esenttirk, H.&Pamuk, M.Yurtsever, Synth.Met. (In press) [6] O.Esenttirk H.b.Pamuk, E.Yurtsever, Tr.J.Chem. 21 (1997) 327 [7] M.G.Kanatzidis, Chem.Eng.News (1990) 36
SyntheticMetals 101(1999) 335-336
A theoretical study of structural defects in conjugated polymers E.Yurtsever’, M.Yurtseverb a Chemistry Dep., KOGUni., 80860 Istanbul, (Turkey) bChemistry Dep., Istanbul Tech.Uni., 80626, Istanbul, (Turkey)
Abstract Accurate ab-initio calculations are performed for pyrrole and thiophene oligomers bonded through c1 and p carbons. The thermodynamical stabilitiy of all possible binding types including the branched forms of tetramers and pentamers are compared. Employing the probabilities obtained from these calculations, a Monte Carlo type growth scheme is applied to predict branching as functions of the chain length and temperature. A high degree of branching for polypyrrole is reported whereas the linear chains dominate the structure of polythiophene. Keywords: Ab initio quantum chemical methods and calculations, polythiophene, polypyrrole 1. Introduction The detailed analysis of the structures of polymers involving 5-member rings still offer challenging problems. The structures depend heavily on the preparation methods and a high degree of insolubility, especially in case of polypyrroles, makes the analysis more difficult. The basic evidence related to the structure comes from XPS, 13C and “N NMR, IR, and Raman spectroscopy as well as electron diffraction and X-ray investigations [ 1,2]. On the other hand quantum chemical calculations can explain the bonding in gas phase however they are restricted to small oligomers. The accepted structures of both polymers are linear chains composed of ct-a linkages however it is also commonly accepted that bonding through /3 carbons is possible and the break-up in the conjugation can lead to branching. In this study we will report our results which combine the quantum mechanical calculations of oligomers and a statistical mechanical approach. The quantum results are carried out in order to assign a set of Boltzmann probabilities of various types of bonding including the 3- and 4-way branching. These probabilities can then be used to generate an ensemble of chains where the average branching can be calculated.
conformations. The least unstable forms are those which consist of solely p-p linkages and the energy differences are usually less than 10 kcal/mol which allow a reasonable degree of branching at room temperatures. Once the relative stability of oligomers with respect to the linear form are calculated, we have observed that they can be fitted to an empirical formula: AE= n,E,+npEp+n,E,+n,pE,p+nppEpp + naapLp + naPp&pg + naappE,gp
(1)
where n denotes the number of monomers of a given type in a specific chain and E is the corresponding energy parameter for that monomer type. In Fig.1 we present the correlation between the quantum mechanically calculated energy differences to those obtained from Eq, 1 for pyrrole and thiophene oligomers.
,P 12 s g 9 ‘: 6
. d
E 3
8.
l .
. 0.
.
.
l
3
2. Branching Ratio All possible bonding types of pyrrole and thiophene oligomers up to tetramers are calculated. In case of pentamers only the tilly linear form of CL-ctlinkages and the 4-way branched form are calculated. The minimum basis sets which give reasonable geometric parameters especially in terms of twist angles are 43 1G for pyrrole and 6-3 lG(d) for thiophene. Detailed reports for all pyrrole calculations are given previously [3-51. Among all oligomer sizes, CI-CIlinearly bonded ones are the lowest energy
CIK”1.1.d.t.bil”los Fig.1: The correlation between ab-initio stability of various isomers of pyrrole and thiophene oligomers and Eq. 1. It is clear that the above partitioning of the energy presents an accurate representation of the relative stability of various isomers. Based on this empirical formula, we proceed to define a growth
0379-6779/99/$- seefront matter0 1999 Elsevier ScienceS.A. All rights reserved. PII: SO379-6779(98)01343-5
336
E. Yurtsever,
M. Yurtsever
I Synthetic
model [5,6]. Assuming that a chain of m monomer unit is already formed, the growth probabilities to each available site is calculated from: Pj = exp (-A% / kT)
(2)
where AEj is the energy required to add a monomer to the site j and it is obtained from Eq.1. The monomers are treated as nonvibrating planar structures. Torsional angles between successive units are 145’ and 158’ for pyrrole and thiophene respectively. During the growth process if the added monomer is very close to another ring of the chain, it is discarded and a new site is tried. Once a reasonably large ensemble of such grown chains is formed, the average branching is calculated as functions of the chain length and the temperature. We observe that in order to get reasonably converged averages, a sample size of 5000 chains is sufficient for chain lengths up to 100 units. In Fig.2 we present the branching ratio as functions of the chain length at 280K and 300 K for both polypyrrole and polythiophene. 0.26
,P
1
1
c_____--c--
0.20
E
Metals
IO1 (1999)
33.5-336
3. Ring Closure Hydrogenation is among the structural defects thought to occur in conjugated polymers [7]. Due to the weakening of the double bonds upon oxidation, an accidental hydrogenation of the polymer backbone may be observed. Here we report a similar defect which is also due to weak double bonds. If two nonbonded rings lie very close to each other , there is a possibility of the interaction of R-bonds which results in a weakening of the double bonds and the formation of a weak bond between these two rings. We observe that this process is thermodynamically possible under certain conditions even though the likelihood is not very high. We have carried out ab-initio calculations on bipolaron formation in various isomers of pyrrole oligomers in order to understand the effects of oxidation on defects . The tetramers consisting of J3-p linkages form kinks in the structure causing the two nonbonded rings to appraoch each other. Upon removal of two electrons from such systems, the weakened n:bonds form a new d bond and connects two monomers. For neutral oligomers p-pp-pj3-p linear tetramer is 12 kcaVmo1 less stable than the most stable CY-clcl-oraa form which is low enough to support the occurrence of ring formations.
8. ,_--
0.14
# #'
P Ii5
0.10 -_--
0.05
-----
______--
0.00 0
20
40
60
Lenglh
80
100
N
Fig.2. Variation of the branching ratio with the chain length. The upper curves are for polypyrrole and the dotted ones correspond to 300K. It is seen that the branching starts at very short chains and is relatively independent of the chain length. At room temperature polypyrrole has 20% and polythiophene has 5% branching. These results are consistent with the experimental observations [3] and the relative solubility of both poymers. The temperature slightly affects the branching ratio as expected. No phase transitions are detected with respect to the temperature. End-to-end distances follow power-law behavior with respect to the monomer number if very short chains are discarded. The Fig.3 also shows the lack of the phase transition.
0
20
40
60
80
100
LenathN Fig.3. Variation of end-to-end distance with chain length
Fig.4. The optimized geometry of the neutral and oxidized pPPPP-P whole.
4. References. [l] H.S.Nalwa (ed) , Handbook of Organic Conduc&e Molecules and Polymers, John Wiley and Sons, 1997 [2] T.A.Skotheim, R.L.Elsenbaumer, C.R.Reynolds (eds), Handbook of Conducting Polymers, Marcel Dekker, (1998) [3] M.Yurtsever, E.Yurtsever, Tr.J.Chem. 22 (1998) 87 [4] M.Yurtsever, E.Yurtsever, Synth.Met. (In press) [S]E.Yurtsever, O.Esenttirk, H.&Pamuk, M.Yurtsever, Synth.Met. (In press) [6] O.Esenttirk H.b.Pamuk, E.Yurtsever, Tr.J.Chem. 21 (1997) 327 [7] M.G.Kanatzidis, Chem.Eng.News (1990) 36