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Effect of Side Chains on Molecular Conformation of AnthraceneEthynylene-Phenylene-Vinylene Oligomers: A Comparative Density Functional Study With and Without Dispersion Interaction Chuanding Dong,† Harald Hoppe,‡ and Wichard J. D. Beenken*,† †

Institut für Physik and Institut für Mikro- und Nanotechnologie, Technische Universität Ilmenau, 98693 Ilmenau, Germany Center for Energy and Environmental Chemistry Jena and Laboratory of Organic and Macromolecular Chemistry, Friedrich Schiller University Jena, 07743 Jena, Germany

‡

ABSTRACT: Using density functional calculations with and without dispersion interaction, we studied the effects of linear octyl and branched 2-ethylhexyl side chains on the oligomer conformation of the conjugated copolymer poly(p-anthraceneethynylene)-alt-poly(p-phenylene-vinylene). With dispersion included, the branched side chains can cause significant bending of the oligomer backbone, while without dispersion they induce mainly torsional disorder. The oligomers with mainly linear side chains keep good planarity when optimized with and without dispersion. Despite their dramatically different conformations, the calculated absorption spectra of the oligomers with various side chain combinations are very similar, indicating that the conformation of the copolymer is not the main reason for the experimentally observed different spectra of ordered and disordered phases.

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the polymer chain. The Egbe group at LIOS15−17 synthesized several poly(p-anthracene-ethynylene)-alt-poly(p-phenylene-vinylene) copolymers (AnE-PVs) with two types of side chains: a straight octyl and its isomer, a branched 2-ethylhexyl. Interestingly, they found that the different substitution positions of these two side chains result in different degrees of order for the polymer conformation in films.15,18 Substituting the 2-ethylhexyl next to the p-anthracene-ethynylene units and the octyl next to vinylene, one obtains a copolymer called AnEPV ba in ref 15. The corresponding AnE-PV-AnE oligomer we call bab. These substitutions seem to result in almost amorphous polymer chains, as inferred from the absorption spectrum. The reverse substitution, that is, the octyl side chains to those phenylene next to the p-anthracene-ethynylene units and 2-ethylhexyl side chains to the phenylenes next to the vinylene unit, called AnE-PV ab in ref 15. AnE-PV-AnE for aba for oligomers seems to exhibit a considerable crystallinity of the polymer. This is deduced from an apparent splitting in the lowenergy subband in the experimental absorption spectra.6,15 These findings make AnE-PV copolymer an interesting model system for studying order−disorder phenomena in conjugated polymers and BHJ. A number of experimental studies have then been devoted to studying effects of order and disorder associated with AnE-PV copolymer system, such as tuning the phase separation and fine-tuning the polymer phase order by tenary blending.6,15,19−22 These studies confirm the enhancement of charge

INTRODUCTION A typical bulk heterojunction (BHJ) of organic solar cell consists of a mesoscopic blend of electron donor (polymer) and acceptor (usually fullerene derivates such as [6,6]-phenylC61-butyric acid methyl ester or PCBM) materials to increase the area of donor−acceptor interface.1 The morphology of the blend has significant impact on the quantum efficiency of the solar cell.2−5 On the one hand, an amorphous phase may be appropriate for intercalation of PCBM,6 but it hinders exciton transport by trap statesboth favoring geminate recombination of electron and hole.2,3 Interestingly, it has been found that an ordered or (semi)crystalline phase of the polymer improves the yield of charge generation.2,4 Herrmann et al. demonstrated that the photoexcitation in the ordered subphases of poly(3hexylthiophene) (P3HT) results in a higher charge generation rate than in the disordered subphases.2 One possible explanation is that the exciton in ordered polymer phases is more delocalized, which reduces the exciton diffusion length and facilitates direct exciton dissociation at the interface as Wang et al. showed for P3HT.7 Other mechanisms such as increasing of conjugation length,4,8 charge carrier stabilization by delocalization,5 intermediate involvement of charge transfer exciton, charge extraction by lower lowest unoccupied molecular orbital (LUMO) and higher highest occupied molecular orbital (HOMO),9−11 have been proposed as well. Moreover, various studies show that the ordered structure increases the charge carrier mobility.12−14 Therefore, it is highly desirable to control the degree of (dis)order of the polymer aggregate to explore the BHJ functionality. An effective measure to this end is substitution of the aliphatic side chains attached to the conjugated backbone of © XXXX American Chemical Society

Received: February 9, 2016 Revised: May 9, 2016

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DOI: 10.1021/acs.jpca.6b01386 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. (a) Illustration of AnE units and PV units, side chain scheme a and b. (b−f) AnE units and PV units with different side chains and the corresponding color maps of the calculated torsional potential energy surfaces.

carrier generation and hole mobility by ordered copolymer phase. The absorption spectrum of the AnE-PV bb copolymer with only 2-ethylhexyl side chains provides the same signatures of an amorphous conformation as the AnE-PV ba copolymer.15,16 However, theoretical exploration of the various conformations of AnE-PV copolymers is still lacking. Knowledge of their conformations on molecular level is not only key to elucidating the order/disorder issue but also fundamental for studying their electronic spectroscopic properties. Recently, the conformations of several donor copolymers have been addressed by density functional theory (DFT) studies. The effects of torsional disorder and stacking structure on electronic properties such as bandstructure, conjugation length, and charge separation have been investigated for thieno[3,4b]thiophene/benzodithiophene polymers (PTB7), 23,24 P3HT,25,26 poly(3-alkylthiophenes) (P3AT),27 oligothiophene,28 and so on. The insights gained by these materials make the conformation study of AnE-PV copolymers rather desirable. To probe the polymer structures in the framework of DFT, it is crucial to include properly van der Waals (dispersion) interactions, since they play an important role not only for interchain aggregation but also for the intrachain, namely, side chain−side chain and side chain−backbone, interactions. In the present work we will focus on the conformation of single AnEPV-AnE oligomers, where our goal is twofold: (i) to understand the role of different (linear and branched) side chains on the conformation of the oligomer, which sheds light into the formation of ordered/disordered polymer phases in BHJ, and in turn the variation of excited electronic states with the various conformation, and (ii) to examine the effect of dispersion interaction on the oligomer’s conformation, namely, how, and

to what extent, the conformation is modified by dispersion. We performed a comparative DFT study of the side chaindecorated AnE-PV-AnE oligomers without and with dispersion interaction. We find that these two methods result in distinctly different structural conformations of the oligomers, where the branched side chains reduce the planarity of the backbone in different ways, namely, torsion or bending. However, the calculated absorption spectra of these oligomers vary little with torsion and only a little bit more significantly with bending of the backbone.

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COMPUTATIONAL DETAILS Torsional Potential Energy Surfaces. In the investigation of oligomer conformation we will first consider the effect of torsion between specific units in the backbone. The atomic configurations of AnE and PV units, as well as the two side chain combinations a and b differing in the number of 2-ethyl branches, are shown in Figure 1a. For isolated AnE units and PV units with different side chains, we scanned the torsional potential energy surface by varying the dihedral torsional angles between the peripheric phenylene sections and the middle section (anthracene for AnE, vinylene for PV). In both the AnE unit and the PV unit, the torsional angles θ1 and θ2 are defined as demonstrated in Figure 1b−f: the angle θ1 denotes the rotation of the left phenylene, in the direction where the top side chain turns into the paper plane, whereas the bottom side chain turns out of the paper plane. For the right phenylene the angle θ2 denotes the rotation in the same direction, that is, the top side chain into the paper plane the bottom side chain out of the paper plane. These two dihedral angles were turned over the range from −180° to 180° with a step width of 10° (see Figure 2). At each step we fixed only the two dihedral angles B


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checked that the variation of the energy with θ1 (θ2) at different values of θ2 (θ1) results in very similar profiles, indicating only a small correlation between θ1 and θ2. This reflects the fact that in the description of B3LYP functional little interaction exists between the side chains. Compared with that of AnE a, the PES of AnE b is evidently less symmetric, and the minimum position of AnE b is shifted to positive θ1 and negative θ2 (see Table 1). For the PV units, the planar configurations are Table 1. Optimal Torsional Angles (θ1, θ2) Optimized by B3LYP/6-31G and Reoptimized by B3LYP+GD3BJ/631G** mol AnEa AnEb PVaa PVab PVbb

Figure 2. The variation of the torsional potential energy of AnE a and PV aa with θ2 when θ1 = 0°, calculated with B3LYP/6-31G and B3LYP+GD3BJ/6-31G**.

and let relax all other degrees of freedom of the molecular structures to acquire the torsional potential energy. The resulting torsional potential energy surface for AnE a and AnE b, as well as for PV aa, PV ab, and PV bb, are shown in Figure 1b−f. Because of the large volume of computation, for the calculation of torsional potential surfaces we used the hybrid exchange-correlation functional B3LYP29 with only a 631G basis set,30 denoted as B3LYP/6-31G. Units and Oligomer (Re)optimization. The structures of the lowest-energy structures of each of AnE a, AnE b and PV aa, PV ab and PV bb units relaxed by B3LYP/6-31G were then reoptimized using the larger basis set 6-31G** 31 and the stateof-the-art Grimme’s D3 dispersion32-corrected B3LYP and Becke−Johnson (BJ) damping33 (B3LYP+GD3BJ/6-31G**) without any constriction. We use D3 version of Grimme’s dispersion, since it has been shown that this gives better results for nonbonded distances. On the basis of the optimal torsional angles acquired by B3LYP/6-31G calculations, the oligomer conformations were constructed and also optimized independently by B3LYP/6-31G** and B3LYP+GD3BJ/6-31G**, which are shown in Figure 3. Electronic Spectra. In the present work the optical absorption spectra of optimized oligomers were given as set of broadened (Gaussian width 0.1 eV) electronic excited-state levels calculated by time-dependent (TD) DFT using B3LYP/ 6-31G** (see Figure 4). All calculations in the present work were performed with the Gaussian09 package.34

B3LYP/6-31G

B3LYP+GD3BJ/6-31G**

minimum

reoptimization

(0°, (10°, (0°, (0°, (20°,

0°) −10°) 0°) 10°) −10°)

(0°, (7°, (15°, (16°, (4°,

0°) −8°) 15°) 19°) 4°)

energetically favored as well. However, there are two features in the PESs of the PV units significantly different from those of the AnE units: (i) the central low-energy area spreads over a larger range of angles, which indicates that in the PV units small torsion around θ1 = 0° and θ2 = 0° are energetically less constricted by π-conjugation than in the AnE units. It is interesting to note that, at the room temperature (thermal energy ∼0.026 eV), the variation of torsions roughly corresponds to θ1 and θ2 ≈ ±20°. (ii) In PV ab and PV bb units the side chains collide for |θ1 − θ2| ≈ 180°, which results in forbidden conformations shown as empty areas in the PES color maps (see Figure 1e,f). By rotating the side chains with respect to the oxo-phenyl bond in the optimization, such collisions can be avoided for PV aa but not for PV ab and PV bb due to entanglement of the side chains. This is supported by the fact that the molecular conformations close to the forbidden area are characterized by heavily deformed side chains and considerably higher potential energies, which is even seen for the PV aa unit with noncolliding octyl side chains as well (see Figure 1d, the red zones in color map of PV aa). To acquire a more accurate description of the conformations of these units, it is desirable to re-examine the important features of the calculated PESs with dispersion interaction and larger basis set, namely, B3LYP+GD3BJ/6-31G**. The reoptmization with B3LYP+GD3BJ/6-31G** was performed for the minima structures in the torsional PESs to check the variation of optimal torsional angles (Table 1), as well as for one section line of the PESs of AnE aa and PV aa with fixed θ1 = 0° to estimate the change of torsional energy barriers (Figure 2). Figure 2 shows that, for both AnE a and the PV aa, the energies calculated with dispersion vary smoothly for θ2 from 0° to ±110°, but they drop abruptly at θ2 = ±120°. The reason is that, with θ1 fixed at 0° (i.e., the left phenylene is coplanar with anthracene) and |θ2| ≥ 120°, spatially the two side chains are so close to each other that the dispersion interaction makes the ends of the side chains approaching each other at the expense of significant bending of the side chains. This effect should induce a significant correlation between θ1 and θ2 in constrast to the case of B3LYP optimization described above. For AnE a, in the ranges 120° ≤ θ2 ≤ 180° and −180° ≤ θ2 ≤ −120°, the minimal energy is at θ2 = ±170°. At θ2 = ±180°, the two side chains distort away from each other to avoid collision,

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RESULTS AND DISCUSSION Torsional Potential of AnE Units and PV Units. For the AnE units we calculated only those where on both phenylene units the same kind of side chain has been substituted, denoted as AnE a or AnE b, which were first experimentally studied by Egbe et al.15 For the PV units, which connect AnE to PV units or two PV units together, the two phenylenes may have same or different side-chain combinations, which is considered as combinations aa, ab, and bb. Figure 1b−f shows the molecular structures of these AnE and PV units and the corresponding color maps for the torsional potential energy surface (PES) calculated using B3LYP/6-31G. The PESs of the AnE units show that conformations close to planarity (i.e., θ1 and θ2 ≈ 0° and ±180°) are energetically preferred due to the effect of a strong π-conjugation. We C


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Figure 3. AnE-PV-AnE oligomers with different side chains optimized with B3LYP/6-31G** and B3LYP+GD3BJ/6-31G**. For each oligomer three views are presented: front view (left upper), side view of the backbone without side chains (left lower), and the view along the backbone (right).

Figure 4. The calculated absorption spectra of the AnE-PV-AnE oligomers shown in Figure 3.

which consequently results in higher energies. For PV aa, a dispersion-induced side-chain bending occurs as well, whereas the resulted lower energy at θ2= ± 120° has similar reasons as in the case of AnE a. Although these nearly planar configurations with two side chains approaching each other (e.g., θ1 = 0° and θ2 = 180°) are energetically closer to or even

more favorable than the configurations with parallel side chains (e.g., θ1 = 0° and θ2 = 0°), such a geometric configuration makes the interdigitation of neighboring chains very difficult and, thus, hinders the formation of the ordered phase (e.g., as shown in Figure 3 of ref 17). Therefore, in the present work we do not take such configurations into consideration. Within the D


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The Journal of Physical Chemistry A range of |θ2| ≤ 110°, the B3LYP+GD3BJ/6-31G** calculations yield larger torsional energy barriers than the B3LYP/6-31G calculations: for AnE a 0.22 versus 0.11 eV and for PV aa 0.56 versus 0.32 eV. The Conformations of AnE-PV-AnE Oligomers. The AnE-PV-AnE oligomer may be used as a model system of the AnE-PV copolymers to explore the order/disorder issue of the latter, which is important for their photovoltaic properties. In analogy to the previous subsections, we indicate the side chain schemes of AnE-PV-AnE oligomers now with the triples of the characters a or b: the first and the last positions represent the substitution on the phenylenes at the AnE units, and the middle one represents that at the PV unit. Again keeping the two AnE units with the same substitution, one gets four combinations: AnE-PV-AnE aaa, aba, bab, and bbb (see Figure 3). The initial structures of these oligomers were constructed by using the optimal torsional angles from the single AnE and PV units (see Table 1) as initial values. In addition, we also built more candidate structures with reversed torsional angles. All candidate structures were then optimized independently with B3LYP/6-31G** and with B3LYP+GD3BJ/6-31G**. Figure 3 presents three views of the lowest-energy structures of AnE-PV-AnE oligomers: the front view, the side view of the backbone without side chains, and the view along the backbone. The left side of Figure 3 shows structures optimized with B3LYP/6-31G** (without dispersion). There, for AnE-PVAnE aaa and aba, the backbones basically maintain a good planarity with the largest relative torsional angle (LRTA) between any two units lower than 23°, whereas the backbones of AnE-PV-AnE bab and bbb are nearly screwed, with an LRTA larger than 54°. Thus, consistent with the B3LYP/6-31G calculations of the AnE and PV units in the previous subsection, these configurations of the oligomers demonstrate a dramatic reduction of the backbone planarity by branched side chains. As low planarity of the copolymer backbones already indicates disordered aggregation, these results explain the branched-side chain-induced disorder observed in XRD experiment.17 Nevertheless, it is still desirable to check the effect of dispersion interaction on the conformation of the oligomers. The right column of Figure 3 shows the oligomers optimized with dispersion (B3LYP+GD3BJ/6-31G**) for the same oligomer structures. The difference brought by dispersion interaction is rather prominent: depending on the type of the side chains, the bending of the backbone is caused to different extents. For the oligomers with no or less branched side chains, such as AnE-PV-AnE aaa and aba, dispersion interaction manifests its effect by tilting the side chains on the middle phenylene toward the octyl side chains on the neighboring phenylenes (see Figure 3), while the backbone is still wellplanar. For AnE-PV-AnE bab and bbb, the bending angle of the backbone evidently increases with the growing number of branched side chains. From the optimized configurations, an obvious observation is that the bending of the backbone is accompanied by the branched side chains’ trend of gathering. As this gathering is not present in any results obtained without dispersion (B3LYP/6-31G or B3LYP/6-31G**), it is reasonable to assume that the dispersion interaction between the 2ethyl branches of the side chains enforces the gathering and consequently bends the backbone. Thus, in the present work it is observed twice that the branched side chains lower the planarity of the oligomer, but with distinctly different distortions of the conformations: the torsion between the units in the backbone resulted from calculations without

dispersion, and the bending of the backbone resulted from inclusion of dispersion. The bending of the backbone is natually not favorable for the formation of π-stacked phases. For long chains, this can even cause coiling of the chain. However, in the aggregation of the copolymer, the interchain dispersion may also play a significant role in the conformation of the chains, which can interplay with the trend of backbone bending in a complex way. Although in the present work we confine ourselves in the conformation of single chains represented by the corresponding oligomers, the effect of interchain dispersion and π-stacking structures will be of our further interest. It is important here to notice that, although the DFT optimization allows for free relaxation of the oligomers, the side chain’s degrees of freedom are not explicitly addressed. Concerning the AnE-PV-AnE oligomer, these degrees of freedom lie in mainly two aspects: the rotation of the side chain around the oxo-phenyl bond and the distribution of the 2-ethyl branches. Given the 10 side chain groups on the backbone, a full exploration of their rotational possibilities would be very challenging. In the test calculations for a series of conformations with rotated side chains, we found that with dispersion effect most side chains endure considerable distortion to each other due to the reduced spatial separation by the rotation. Although some of these conformations have lower energies than the ones shown in Figure 3 right panel, it is very hard to indentify clear trend in structural feature or their effect on the backbone planarity. However, the oligomer planarity can be affected by the distribution of the 2-ethyl branches. For example, in oligomer bbb, when the two 2-ethyl branches on the middle PV unit are located on the other side of the molecular plane, the gathering of the 2-ethyl branches would be weakened, and the backbone bending would be much mitigated. However, such a positioning of the 2-ethyl branches is rather artificial and results in different chirality of the side chains. For these reasons, in the present study we did not deeply probe the side chain’s degrees of freedom. The Absorption Spectra of AnE-PV-AnE Oligomers. The absorption spectra of the AnE-PV-AnE oligomers are highly interesting because they are of fundamental importance for AnE-PV copolymer’s photovoltaic properties as light absorber. Figure 4 presents the calculated absorption spectra (TDDFT, B3LYP/6-31G**) of the oligomer conformations shown in Figure 3. In the left panel, the spectra of the oligomers in the left column of Figure 3, namely, featured by torsional disorder, are almost identical. For all these spectra, the main absorption peaks are ∼1.85 eV and primarily originated from the excitation from HOMO to LUMO. The secondary absorption peaks at ∼2.35 eV are attributed to HOMO−1 to LUMO+1 excitation. Spatially, HOMO and LUMO orbits spread over the backbones, whereas HOMO−1 and LUMO+1 states are almost localized on the anthracene units, which may explain the difference in the oscillator strength of those two main excitations. The spectra of the most twisted oligomers AnE-PV-AnE bab and bbb (Figure 3 left column) are blueshifted by only 0.02 and 0.01 eV from the reference of AnE-PVAnE aaa, which indicates that the torsion of the backbone has only insignificant impact on the electronic spectrum. In the right panel of Figure 4, the spectra of the dispersioncorrected conformations reveal that the spectrum of the bbb oligomer, whose backbone is most strongly bent (Figure 3 right column), differs significantly from the other spectra. Its main excitation at 1.91 eV is almost 0.06 eV blueshifted with respect to that of the AnE-PV-AnE aaa oligomer, and the E


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higher planarity of the polymer resulting from straight side chains as mentioned above.

corresponding oscillator strength is significantly reduced as well. Moreover, the second excitation at 2.19 eV is red-shifted with respect to its counterparts in other spectra and stronger in oscillator strength. Comparing the calculated spectra with the experimental data is difficult because of lacking of vibrational progression and aggregation effects in our calculations. The experimental absorption spectra are ∼0.3 eV blue-shifted in energy position compared to our calculated spectra, and the spectra shapes show little resemblance. An important experimental observation is that the spectra of the amorphous copolymers are blue-shifted and less structured compared with those of ordered phases.15 These differences, however, can be seen as only roughly compatible with the trends shown by the spectrum of the AnE-PV-AnE bbb presented in this study (Figure 4). Thus, we come to the conclusion that the conformation of the single AnE-PV oligomer has no sufficient influence on the electronic states, namely, in terms of a πconjugation “broken” by torsional disorder, to explain the differences between the experimental spectra of AnE-PV ab and ba. This is in good agreement with previous studies concerning the effect of torsions and bendings of on oligothiophenes.35,36 There horizontal bending similar to that found for the AnE-PVAnEbbb oligomer resulted in a redistribution of oscillator strength of the first and second electronic transitions, whereas torsions only results in a spectral shift comparable to that caused by the bending.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 3677 69 3258. Fax: +49 3677 69 3271. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to E. Runge for valuable comments and to D. A. M. Egbe for inspiration. We would also like to show our gratitude to H. Schwanbeck from the computing center of the Technische Univ. Ilmenau for quick and professional IT support. This work was financially supported by the DFG research grant “PhotogenOrder”.

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REFERENCES

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CONCLUSION In the present work, by DFT calculations of dimers and oligomers made of anthracene-ethynylene (AnE) and phenylene-vinylene (PV), we find that isomeric side chains (linear and branched) have a significant influence on the conformation not only by number but also by their specific substitution sites. We find torsional disorder increases with the proportion of branched side chains substituted and that, for equal number of branched and linear side chains, the torsional disorder is larger if the branched side chains are attached to both phenylenes next to the vinylene unit. Both findings are in agreement with experimental XRD data of the corresponding copolymer,17 which indicated an amorphous phase for the latter case. These effects seem to be of mainly steric nature. Nevertheless, inclusion of dispersion interaction dramatically modifies the structural conformation of our model oligomers, since, only when dispersion interaction is included into the calculation, the branched side chains have a strong tendency of gathering, which causes not only additional torsion potential barriers but also a horizontal bending of the conjugated backbone. Since only such a bending of the backbone enables a coiling of a polymer, this could be the most important structural feature for the forming of the amorphous phase of AnE-PV copolymer with branched side chains. Notably, even the most dramatic conformational change has only limited impact on the electronic absorption spectra, as indicated by our TD-DFT calculations. Though the spectral shifts found in our calculationsin particular, those for the bent conformationare not in contradiction to the experimental findings, they cannot resemble the dramatic differences found in the experimental absorption spectra of AnE-PV copolymers with different side chain substitution schemes. We suggest the reason for these experimentally observed differences are not to be searched for in the intrachain effects, as described in this study, but rather in interchain effects, for example, πstacking, caused by aggregation, which of course is favored by a F


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