Chinese Journal of Chemical Physics  2018, Vol. 31 Issue (2): 171-176

#### The article information

Ding-hao Hong, Li Chen, Qing-gang Kong, Hui Cao

First Principles Probing of Photo-Generated Intermolecular Charge Transfer State in Conjugated Oligomers

Chinese Journal of Chemical Physics, 2018, 31(2): 171-176

http://dx.doi.org/10.1063/1674-0068/31/cjcp1707151

### Article history

Accepted on: September 27, 2017
First Principles Probing of Photo-Generated Intermolecular Charge Transfer State in Conjugated Oligomers
Ding-hao Hong, Li Chen, Qing-gang Kong, Hui Cao
Dated: Received on July 27, 2017; Accepted on September 27, 2017
Jiang Su Laboratory of Atmospheric Environment Monitoring and Pollution Control, Collaborative Center of Atmospheric Environment and Equipment Technology, School of Environmental Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
*Author to whom correspondence should be addressed. Hui Cao, E-mail:yccaoh@hotmail.com
Abstract: We perform density functional theory calculations to investigate the polaron pair (charge transfer state) photo-generation in donor-acceptor oligomer methyl-capped (4, 7-benzo[2, 1, 3]thiadiazole-2, 6-(4, 4-bis (2-ethylhexyl)-4H-cyclopenta[1, 2-b; 3, 4-b']dithiophene-4, 7-benzo[2, 1, 3]thiadiazole)(CPDTBT).Results show that effective photo-generation of charge transfer state can happen in CPDTBT dimer when the group 4, 7-benzo[2, 1, 3]thiadiazole (BT) in one monomer deviates against the conjugated plane (onset torsion angle is about 20°).The lower excitation energy (530 nm) can only generate the intramolecular excitonic state, while the higher excitation energy (370 nm) can generate the intermolecular charge transfer state, in good agreement with the experiment.Moreover, the mechanism of charge separation in CPDTBT oligomers is discussed.
Key words: CPDTBT    Charge transfer state    Charge separation
Ⅰ. INTRODUCTION

Charge separation upon photo-excitation in organic semiconductors has attracted much interest due to its broad application prospects in photovoltaic cells [1-3]. Although the charge separation ordinarily happens in the heterojunction interface where the energy offset between the lowest unoccupied molecular orbital (LUMO) of donor (D) and that of acceptor (A) (or between the highest occupied molecular orbital (HOMO) of donor and that of acceptor) acts as the driving force [4-6], free charge carriers can be generated upon photo-excitation in small well-ordered conjugated molecule crystals [7]. Recently, Tautz et al. found that upon higher energy photo-excitation pronounced polaron pairs [8] can be detected in D-A type poly(4, 7-benzo[2, 1, 3]thiadiazole-2, 6-(4, 4-bis(2-ethylhexyl)-4H-cyclopenta[1, 2-b; 3, 4-b$'$]dithiophene-4, 7-benzo[2, 1, 3]thiadiazole) (PCPDTBT) and the oligomer CPDTBT (as shown in FIG. 1) [9].

 FIG. 1 Potential energy curve of CPDTBT dimer at equilibrium with respect to the distance between two monomers.

It was found that long-wavelength excitation (530 nm) cannot generate polaron pairs while short-wavelength excitation (370 nm) can generate in oligomer CPDTBT, indicating that the excess energy plays a key role [9]. TDDFT simulations, however, showed that there was significant spatial overlap between hole and electron wave functions for both lower and higher energy excitations [9]. Thus, one hypothesis is that there is certain intermediate excited state that has charge transfer character after the initial higher energy excitation. It was also found that polaron pairs had longer life-time in oligomer CPDTBT than in polymer PCPDTBT. The above mentions seem to point toward the intermolecular process in generating polaron pairs in oligomer CPDTBT. Apart from the proposed intramolecular charge separation picture [9], the intermolecular charge transfer is thus also of important significance in understanding the generation of polaron pairs in oligomer CPDTBT.

It is well known that the conformational change can introduce the substantial variation in the electronic structure of conjugated oligomer. If such conformational change happens in one monomer of CPDTBT while the nearest neighbor monomer remains unchanged, then it will constitute a dimer that has the character of heterojunction, with one CPDTBT monomer as a donor and another one as an acceptor. To verify this hypothesis, we perform the density functional calculations on the CPDTBT dimer with a little conformational change in one monomer, namely, rotating one BT [10] group (see FIG. 2) in CPTBT monomer against the conjugation plane with a small angle. The density functional theory (DFT) method is one of the most taken approaches in calculating the charge transfer state in organic semiconductors [11, 12].

 FIG. 2 The potential energy curve of CPDTBT dimer with respect to the rotational angle of right BT group in the upper monomer against the conjugated plane. Inset shows the structure of CPDTBT dimer (upper CPDTBT as an acceptor (A) and the lower CPDTBT as a donor (D)) and BT group.

In this work, we employ the conventional DFT method in which a ground state occupied orbital is substituted with a ground state unoccupied orbital to simulate the excited state (after self consistent process) of CPDTBT dimmers [13]. We first give the validation of DFT method on the first peak of photo-absorption and photoluminescence spectra of CPDTBT monomer. Then we perform the calculations on the electronic structure of excited states of CPDTBT dimer, including the DA* (or D*A) and D$^+$A$^-$ type excitations. Based on the calculations of charge transfer exciton (D$^+$A$^-$), we rationalize the generation of polaron pairs under the higher energy photo-excitation, especially from the indirect path, i.e., from S$_0$ (DA) to S$_n$ (DA*) and then to CT$_n$ (D$^+$A$^-$).

Ⅱ. COMPUTATIONAL DETAILS

The geometry of CPDTBT in ground state is at first optimized by means of hybrid density functional B3LYP with basis set of 6-31G*. We scan the potential energy curve of CPDTBT dimer (two monomers are placed on the same plane) with respect to the separation distance between two monomers. Then at the equilibrium conformation we rotate the right acceptor group BT in the upper monomer (lower monomer fixed) to construct the CPDTBT dimer that has the character of heterojunction. The key point in our DFT calculations on the excited states is to directly excite one electron from occupied orbital to the unoccupied orbital by exchanging the corresponding two orbitals, and then make the self consistent calculation [13]. It is a single configuration method, in contrast to the TDDFT method that involves multiconfigurations. Orbitals in TDDFT configurations are the same as those in the ground state configuration, but they have been changed in the consistent single configuration method. The single configuration method is thus convenient for the discussion in terms of electron and hole, since the electrostatic Columbic attraction between electron and hole is in fact taken account of during the self consistent process. When an occupied orbital is exchanged with an unoccupied orbital in the same monomer, the Frenkel exciton can be simulated, and when an occupied orbital in one monomer is exchanged with an unoccupied orbital in another monomer then the charge transfer exciton can be calculated. In this work, all calculations are performed using the Gaussian 09 package [14].

Ⅲ. RESULTS AND DISCUSSION A. Validation of calculations on excited states

Based on optimized geometry of CPDTBT, we calculate the vertical excitation and get the excitation energy of first low lying excited state (HOMO$\rightarrow$LUMO). The geometry of the first low lying excited state of CPDTBT is then optimized to estimate the first photoluminescence peak. As a test, our computational result of the first peak in photo-absorption (photoluminescence) spectrum of CPDTBT is 2.30 (1.89) eV, in good agreement with the experimental value of 2.34 (1.93) eV [9].

B. Ground state geometry of model CPDTBT dimer

Since there is no experimental data of the crystal structure of oligomer CPDTBT at the present time, we use the simplest geometry of model CPDTBT dimer in this work. The two CPDTBT monomers are placed at the same plane. We scan the potential energy curve of CPDTBT dimer with respect to the separation distance between two monomers (see FIG. 1). The equilibrium separation distance of 9.0 Å is found. Then at the equilibrium conformation we rotate the right acceptor group BT in the upper monomer (lower monomer fixed), and the potential energy curve with respect to the rotational angle is shown in FIG. 2. The equilibrium dihedral angle as depicted in the inset of FIG. 2 is about 3°. The rotational barrier with the dihedral angle of 90° is about 0.25 eV.

C. Photo-excitation and charge transfer

To explain the possible intermolecular photo-generation of experimental polaron pair, we investigate the charge transfer state in the CPDTBT dimer junction, as shown in the inset of FIG. 2. Our findings indicate that the intermolecular charge transfer can happen in high probability, generating the separated polaron pair. With BT in one monomer (e.g. in the upper CPDTBT in FIG. 2) deviating against the conjugated plane, we find the charge transfer state in which electron is excited from the lower monomer to the upper one.

1. Intramolecular exciton (S$_n$) and intermolecular charge transfer state (CT$_n$)

Because the intermolecular charge transfer state can be generated in two paths, namely, the indirect path in which the intramolecular exciton dissociates at interface of CPDTBT dimer and the direct path in which it is generated directly upon photo-excitation from the ground state, both intramolecular exciton and intermolecular charge transfer state are discussed. Our calculations show that CPDTBT dimer has no intermolecular charge transfer states at the equilibrium conformation. All the tested intermolecular charge transfer excitations of electron in the occupied molecular orbital of one CPDTBT monomer to the unoccupied molecular orbital of another CPDTBT monomer collapse to the intramolecular excitonic states. The onset torsion angle of BT against the conjugated plane of CPDTBT for effective intermolecular charge transfer in CPDTBT dimer is about 20°. Energy needed for this conformational change is only 0.01 eV, as shown in FIG. 2, less than the thermal energy $k_{\rm{B}}T$ ($k_{\rm{B}}$ is the Boltzmann constant and $T$ is the temperature) at room temperature.

The example of intramolecular exciton and intermolecular charge transfer states of this tortured CPDTBT dimer can be found in FIG. 3. The electrostatic potential distributions of electron and hole of the third DA* type intramolecular exciton, S$_3$, are shown in FIG. 3 (a) and (b) respectively. Although the S$_3$ excitonic state has higher excitation energy, the involved orbitals of electron and hole are still delocalized, as found previously with TDDFT method [9]. The electrostatic potential distributions of electron and hole of the first and the second intermolecular charge transfer states, CT$_1$ and CT$_2$, are shown in FIG. 3 (c) and (d) respectively. The essential difference between intramolecular exciton and intermolecular charge transfer exciton is that the centers of electron and hole are at the same CPDTBT monomer in the former case and they are separated, locating on different CPDTBT monomers, in the latter case. The two lower lying charge transfer states CT$_1$ and CT$_2$ are of excitation energy of 2.94 and 3.24 eV, enough to be generated in the experimental higher energy photo-excitation (3.35 eV, 370 nm).

 FIG. 3 Examples of electrostatic potential distributions of intramolecular exaction ((a) hole and (b) electron in S$_3$ of DA*) and intermolecular charge transfer states ((c) CT$_1$ and (d) CT$_2$ of D$^+$A$^-$) in CPDTBT dimer with the rotational angle (20°) of right BT group in the upper monomer against the conjugated plane. Detailed information of S$_3$ of DA* and CT$_1$, CT$_2$ of D$^+$A$^-$ see FIG. 5.
 FIG. 5 Energy state diagram involved in the charge photo-generation of CPDTBT dimer with a BT group in one monomer tortured of 20°. The DA* type singlet (S) exciton excitation of this CPDTBT dimer is shown in the left column, the D$^+$A$^-$ charge transfer states (CT) in the middle column, and the D$^+$/A$^-$ charge separated state (CS) in the right column. Charge transfer states can be reached indirectly by the path of ground state S$_0$$\rightarrowS_n$$\rightarrow$CT$_n$ or directly by S$_0$$\rightarrowCT_n. The charge transfer states in CPDTBT dimer with different torsion angle of BT against the conjugated plane can be found in FIG. 4. The same excitation with larger torsion has larger excitation energy, e.g., the HOMO\rightarrowLUMO+2 excitation energies for torsion angle of 20°, 40°, and 90° are 3.23, 3.27, and 3.87 eV respectively. This is because that electron in the tortured CPDTBT will be more localized at the side BT group that is deviated from the conjugated plane, resulting in the larger separation distance between the centre of electron and hole (see FIG. 4).  FIG. 4 Charge transfer states (HOMO\rightarrowLUMO+2) with the torsion angle (BT against the conjugated plane) of (a) 40° and (b) 90°. The distances between the centre of positive charge and negative charge in (a) and (b) are about 9.0 and 11.3 Å respectively. 2. Energy state diagram In the next statement, the energy of the ground state of DA is set as the zero point of energy. The energy state diagram summarizing the photo-generation of electron-hole pairs in CPDTBT dimer with the torsion angle of 20° is shown in FIG. 5. In general, each CPDTBT can act as the donor or acceptor. Here, we only show the case with the tortured CPDTBT as acceptor and the pristine CPDTBT as donor. Detailed information of orbital excitation in S_n and in CT_n can be seen in FIG. 6 to FIG. 8. The experimental lower energy excitation (2.34 eV, 530 nm) [9] can thus only excite S_1 (excitation energy of which is about 1.74 eV), but cannot generate the charge transfer states either in the indirect path (S_0$$\rightarrow$S$_n$$\rightarrowCT_n) or in the direct path (S_0$$\rightarrow$CT$_n$) [12, 15, 16]. In contrast, the experimental higher energy photo-excitation (3.35 eV, 370 nm) [9] is enough to excite the intermolecular electron-hole pair both indirectly and directly. The indirect photoexcitation path is through S$_0$$\rightarrow$S$_3$ (HOMO$-$7$\rightarrow$LUMO) and then$\rightarrow$lower lying CT$_1$ and CT$_2$. Moreover, our computational results of charge transfer states provide the possibility to identify the transitions between states corresponding to the transient absorption spectra in pump-probe experiments [9] by investigating the energy difference between charge transfer states.

 FIG. 6 The D*A type excitations in CPDTBT dimer with the BT group in one monomer rotated 20° against the conjugated plane, S$_1$(HOMO$\rightarrow$LUMO+1), S$_2$(HOMO$-$2$\rightarrow$LUMO+1), S$_3$(HOMO$-$6$\rightarrow$LUMO+1), S$_4$(HOMO$-$4$\rightarrow$LUMO+3 and HOMO$-$2$\rightarrow$LUMO+5 degenerated), S$_5$(HOMO$\rightarrow$LUMO+11), and S$_6$(HOMO$-$2$\rightarrow$ LUMO+7). Energy levels are shown in two columns to represent whether corresponding states on CPDTBT (left, the lower one in FIG. 2) or CPDTBT monomer in which BT group is rotated 20° against the conjugated plane (right, the upper one in FIG. 2).
 FIG. 7 The DA* type excitations in CPDTBT dimer with the BT group in one monomer rotated 20° against the conjugated plane, S$_1$(HOMO$-$1$\rightarrow$LUMO), S$_2$(HOMO$-$3$\rightarrow$LUMO), S$_3$(HOMO$-$7$\rightarrow$LUMO), S$_4$ (HOMO$-$7$\rightarrow$ LUMO+2), S$_5$(HOMO$-$3$\rightarrow$LUMO+4), S$_6$ (HOMO$-$1$\rightarrow$LUMO+10), and S$_7$(HOMO$-$3$\rightarrow$ LUMO+6). Energy levels are shown in two columns to represent whether corresponding states are located on CPDTBT (left, the lower one in FIG. 2) or CPDTBT monomer in which BT group is rotated 20° against the conjugated plane (right, the upper one in FIG. 2).
 FIG. 8 The direct D$^+$A$^-$ type charge transfer excitations in CPDTBT dimer with the BT group in one monomer rotated 20° against the conjugated plane, CT$_1$ (HOMO$\rightarrow$LUMO), CT$_2$ (HOMO$\rightarrow$LUMO+2), CT$_3$ (HOMO$-$2$\rightarrow$LUMO+2). Energy levels are shown in two columns to represent whether corresponding states are located on CPDTBT (left, the lower one in FIG. 2) or CPDTBT monomer in which BT group is rotated 20° against the conjugated plane (right, the upper one in FIG. 2).
3. Electronic structures of charge transfer exciton

Electronic structures involved in generating the charge transfer state are shown in FIG. 9. In the indirect path, hole generated in S$_3$ of DA* jumps to the HOMO of D, forming the charge transfer state CT$_1$ of D$^+$A$^-$. The characteristics of the electronic structures of the charge transfer state CT$_1$ is that energy level of the electron enters into the unoccupied orbital region and the energy level of the hole into the occupied region of CPDTBT dimer. This can be understood by seeing how the separated electron (A$^-$) and hole (D$^+$) form the Coulombically bound charge transfer exciton as they approach with each other. In comparison with the electronic structures of CPDTBT monomer, all the energy levels in D$^+$ drop because of the attraction of electron by the positive charge, and in contrast, all the energy levels in A$^-$ rise because of the repulsion of electron by the negative charge [17-19].

 FIG. 9 Orbital diagram of S$_3$ of DA* and CT$_1$ of D$^+$A$^-$ in the charge photo-generation of CPDTBT dimer with a BT group in one monomer tortured of 20°. Energy levels of electronic states in DA* and D$^+$A$^-$ are shown in two columns to denote the orbital distribution (left: totally on D; right: totally on A; middle: bridge states in which part of the state on D and other part on A). Orbitals of D$^+$ and A$^-$ are shown for understanding the formation of the charge transfer state of CT$_1$. The solid red line and the dashed blue line represent the electron and the hole respectively.
4. Process of charge photo-generation

Potential energy curves of ground state, excitonic state S$_1$ of D*A and S$_3$ of DA*, and the charge transfer states CT$_1$ of D$^+$A$^-$ with respect to the separation distance between two monomers are shown in FIG. 10. One can refer to the explanation of the potential energy curves in Morteani et al.'s work [20]. For clear understanding, we give a brief description here: (ⅰ) Exciton generated somewhere first diffuses to the interface; (ⅱ) Then the exciton dissociates into Coulombically bound charge transfer state; (ⅲ) The charge transfer state can either become the separated state or (ⅳ) collapse into the exciplex; (ⅴ) The exciplex can then go back to the exciton state or directly recombine to the ground state S$_0$. It is interesting that there is no charge transfer state as the separation distances lower than the equilibrium distance of the ground state (9.0 Å). Our calculations indicate that in this region the charge transfer states degenerate into the excitonic state S$_1$ of D*A.

 FIG. 10 Potential energy diagram of the ground state S$_0$ of DA (solid triangle in black), S$_3$ of DA* (hollow circle in navy), S$_1$ of D*A (hollow square in blue), and CT$_1$ of D$^+$A$^-$ (solid circle in orange) of CPDTBT dimer junctions with respect to the distances between two monomers (with a BT group in upper monomer tortured of 20°). The processes from (i) to (v) represent the main approach of charge photo-generation and recombination in the indirect path.
Ⅳ. CONCLUSION

In general, we employ the DFT method to theoretically investigate the photo-generation of electron-hole pair in CPDTBT oligomers. We find that the deviation of BT group against the conjugated plane of CPDTBT results in the efficient intermolecular charge transfer. We confirm that the lower energy excitation (2.34 eV, 530 nm) can only generate the intramolecular singlet excitonic state, while the higher energy excitation (3.35 eV, 370 nm) can generate the intermolecular electron-hole pair with charge dissociation, in good agreement with the experiment. Our computational results of the electronic states and the potential energy diagram of CPDTBT dimer in the ground state, the intramolecular excitonic state, and the intermolecular charge transfer state provide the detailed information for understanding the charge photo-generation in CPDTBT oligomers.

Ⅴ. ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (No.21473092), and the Jiangsu Province Production and Joint Innovation Fund-Prospective Joint Research Project (No. BY2014007-01).

Reference
 [1] T. M. Clarke, and J. R. Durrant, Chem. Rev. 110 , 6736 (2010). DOI:10.1021/cr900271s [2] F. Etzold, I. A. Howard, N. Forler, D. M. Cho, M. Meister, H. Mangold, J. Shu, M. R. Hansen, K. Müllen, and F. Laquai, J. Am. Chem. Soc. 134 , 10569 (2012). DOI:10.1021/ja303154g [3] C. B. Zhao, Z. H. Tang, X. H. Guo, H. G. Ge, J. Q. Ma, and W. L. Wang, Chin. J. Chem. Phys. 30 , 268 (2017). DOI:10.1063/1674-0068/30/cjcp1702016 [4] M. M. Wienk, J. M. Kroon, W. J. H. Verhees, J. Knol, J. C. Hummelen, P. A. Van Hal, and R. A. J. Janssen, Angew. Chem. Int. Ed. 42 , 3371 (2003). DOI:10.1002/anie.200351647 [5] G. Grancini, M. Maiuri, D. Fazzi, A. Petrozza, H. J. Egelhaaf, D. Brida, G. Cerullo, and G. Lanzani, Nat. Mater. 12 , 29 (2013). DOI:10.1038/nmat3502 [6] A. A. Bakulin, S. D. Dimitrov, A. Rao, P. C. Y. Chow, C. B. Nielsen, B. C. Schroeder, I. McCulloch, H. J. Bakker, J. R. Durrant, and R. H. Friend, J. Phys. Chem. Lett. 4 , 209 (2013). DOI:10.1021/jz301883y [7] F. A. Hegmann, R. R. Tykwinski, K. P. H. Lui, J. E. Bullock, and J. E. Anthony, Phys. Rev. Lett. 89 , 227403 (2002). DOI:10.1103/PhysRevLett.89.227403 [8] R. Tautz, E. Da Como, T. Limmer, J. Feldmann, H. J. Egelhaaf, E. von Hauff, V. Lemaur, D. Beljonne, S. Yilmaz, I. Dumsch, S. Allard, and U. Scherf, Nat. Commun. 3 , 970 (2012). DOI:10.1038/ncomms1967 [9] R. Tautz, E. Da Como, C. Wiebeler, G. Soavi, I. Dumsch, N. Fröhlich, G. Grancini, S. Allard, U. Scherf, G. Cerullo, S. Schumacher, and J. Feldmann, J. Am. Chem. Soc. 135 , 4282 (2013). DOI:10.1021/ja309252a [10] N. Blouin, A. Michaud, D. Gendron, S. Wakim, E. Blair, R. Neagu-Plesu, M. Belletête, G. Darocher, Y. Tao, and M. Leclerc, J. Am. Chem. Soc. 130 , 732 (2008). DOI:10.1021/ja0771989 [11] Y. Kanai, and J. C. Grossman, Nano Lett. 7 , 1967 (2007). DOI:10.1021/nl0707095 [12] J. Lee, K. Vandewal, S. R. Yost, M. E. Bahlke, L. Goris, M. A. Baldo, and J. V. Manca, T. Van Voorhis, J. Am. Chem. Soc. 132 , 11878 (2010). DOI:10.1021/ja1045742 [13] Details for the keyword of Guess=Alter can be seen in the Gaussian09 user's reference. www.gaussian.com. [14] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian09, Revision A01, Gaussian, Inc., Wallingford CT, (2009). [15] T. Drori, C. X. Sheng, A. Ndobe, S. Singh, J. Holt, and Z. V. Vardeny, Phys. Rev. Lett. 101 , 037401 (2008). DOI:10.1103/PhysRevLett.101.037401 [16] A. A. Bakulin, A. Rao, V. G. Pavelyev, P. H. M. Van Loosdrecht, M. S. Pshenichnikov, D. Niedzialek, J. Cornil, D. Beljonne, and R. H. Friend, Science 335 , 1340 (2012). DOI:10.1126/science.1217745 [17] H. Cao, T. Fang, S. H. Li, and J. Ma, Macromolecules 40 , 4363 (2007). DOI:10.1021/ma0703857 [18] P. P. Debye, and E. M. Conwell, Phys. Rev. 93 , 693 (1954). DOI:10.1103/PhysRev.93.693 [19] S. Suzuki, F. Maeda, Y. Watanabe, and T. Ogino, Phys. Rev. B 67 , 115418 (2003). DOI:10.1103/PhysRevB.67.115418 [20] A. C. Morteani, P. Sreearunothai, L. M. Herz, R. H. Friend, and C. Silva, Phys. Rev. Lett. 92 , 247402 (2004). DOI:10.1103/PhysRevLett.92.247402