Strategy to Manipulate Molecular Orientation and Charge Mobility in D

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Strategy to Manipulate Molecular Orientation and Charge Mobility in D-A Type Conjugated Polymer through Rational Fluorination for Improvements of Photovoltaic Performances Meng Qiu, Dangqiang Zhu, Linyin Yan, Ning Wang, Liangliang Han, Xichang Bao, Zurong Du, Yingli Niu, and Renqiang Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03756 • Publication Date (Web): 20 Sep 2016 Downloaded from http://pubs.acs.org on September 23, 2016

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The Journal of Physical Chemistry

Strategy to Manipulate Molecular Orientation and Charge Mobility in D-A Type Conjugated Polymer through Rational Fluorination for Improvements of Photovoltaic Performances Meng Qiu, † Dangqiang Zhu, † Linyin Yan, § Ning Wang, † Liangliang Han, † Xichang Bao, † Zurong Du, † Yingli Niu*, ‡ and Renqiang Yang*, † †

CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess

Technology, Chinese Academy of Sciences, Qingdao 266101, China. ‡

Key Laboratory of Standardization and Measurement for Nanotechnology, Chinese Academy

of Sciences, National Center for Nanoscience and Technology, Beijing 100190, China. §

The National Key Laboratory of Biochemical Engineering Institute of Process Engineering,

Chinese Academy of Sciences, Zhongguancun North Second Street 1, Beijing 100190, China.

ABSTRACT: Improving the photoelectric conversion efficiency of organic solar cells (OSCs) is an essential issue for large scale commercial applications. Introducing the fluorine (F) atoms onto the electron-accepting unit and/or electron-donating unit on donor (D)-acceptor (A) type conjugated polymer is an effective strategy to enhance the overall solar cell performance. Here,

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the optimum sites for fluorination in favor of boosting the optical and photovoltaic properties of polymers are fully investigated by density functional theory (DFT) calculation and molecular dynamics (MD) simulation. Especially, the interchain charge mobility is calculated by means of Marcus theory, to investigate the charge transport process quantitatively. The results of theoretical modeling indicate that, except for the enhanced absorption spectra and deep lying HOMO level, more importantly, a higher hole mobility could be achieved when F is introduced onto the 3,6 position (outer site) of quaterthiophene for two reasons: 1. More effective face-on orientation formed by subtle manipulation of interchain π-π stacking pattern; 2. Reduce reorganization energy during the process of charge transport. These results elucidate that specific fluorination sites can influence the photoelectric properties of donor polymers, highlight the fluorination effect on the interchain interactions and orientation correlations in governing the key parameters of OSCs, and raise the hope of achieving even higher efficiencies by means of rational molecular designing.

1. Introduction Bulk-heterojunction (BHJ) OSCs have attracted great attention due to their unique virtue of light weight, easy fabrication, flexibility and solution processing property.1-4 State-of-the-art OSCs photoelectric conversion efficiencies (PCEs) have exceeded 10%.5,6 Yet the PCE of OSCs is far less than silicon solar cell, and the synthesis crafts of most polymers are too complex. Therefore, polymers with potentially high performance and simple synthetic route are of great interest. Although the P3HT based OSCs has high hole mobility and robust performance,7-9 the relative large bandgap around 2.0 eV and high HOMO level limit further enhancement of short circuit current (JSC) and open circuit voltage (VOC). The bandgap can be reduced effectively by


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incorporating acceptor moieties into polymer mainchain. Copolymers of thiophene and commonly used acceptor moiety benzothiadiazole (BT) have been explored in OSCs with various numbers of thiophene units in one repeat unit.10-13 Though the bandgaps of polymers are lowered to improve the absorption properties, the PCEs of corresponding devices are less than 2.23%.13 Among which, BT and quaterthiophene copolymer (BT4T) shows a bright prospect in OSCs. Osaka reported PBTz4T with PCE of 2.6%.14 Chen et al. synthesized POD2T-DTBT as a candidate for high performance OSCs, exhibiting both high hole carrier mobilities of 0.20 cm2 V1

s-1 and promising PCEs of 6.26%.15 However, further improvement on the photovoltaic

performance continues to be challenging to researchers. Recently, fluorination of donor polymers is adopted as a good strategy to enhance the PCEs of polymer-based BHJ solar cells.16,17 The PCEs of fluorinated BDT-DTBT copolymers have been successfully pushed from less than 3% to over 8% compared with their non-fluorinated counterpart.18-22 This achievement is due to the electron-withdrawing properties of fluorine substituents, which could lower the HOMO energy level of conjugated polymers and result in increased VOC.23 Furthermore, increased interchain interaction would also afford higher hole mobility that account for high JSC and fill factor (FF).24 Could the same strategy be equally applicable to BT4T series? Chain-Shu Hsu et al. introduced F to BT unit to induce a stronger intermolecular non-covalent interactions, forming an ordered solid-state structure, and pushing PCE to 6.82%.25 Yong Cao et al. reported that difluoro-BT copolymerized with quaterthiophene with side chains attached on the two terminal thiophene rings showed unexpected strong interchain aggregation with high hole mobility, and the device fabricated with thicker active layer showed a PCE of 7.64%.26 Won Ho Jo et al. investigated the effect of fluorination position on BT4T polymer, and found that polymer with


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fluorinated D unit or A unit exhibited PCE of 7.10% and 6.41%, respectively, which was due to the former polymer exhibiting low bimolecular recombination and high hole mobility.27 Later they investigated fluorination on both D and A units of copolymer of difluoro-quaterthiophene and BT with various number of F substitution, and found that polymer with mono-fluorinated BT exhibited a better PCE of 9.14% than its non-fluoro and difluoro counterparts.28 Recently, He Yan et al obtained the PCE of several difluoro-BT and quaterthiophene copolymers above 10%.29 Since the reduction of π-π stacking distance between donor polymer chains could facilitate the charge transport process, a reasonable optimization of the π-π interaction between polymer chains is of great importance in developing high performance device. Despite the great progress made in the above works, the question of which site to fluorinate for optimal π-π interaction is difficult to answer, due to the complex experimental conditions, including molecular weight, solubility and device technology etc. In addition, the fluorination of 3,6 position (outer site) of quaterthiophene has not been explored to our knowledge. For the purpose of solving the above problems, we employ theoretical modelling to investigate the intrinsic nature of the fluorination effect on BT4T system. In this study, the effect of fluorination site on D-A polymer has been investigated systematically. A series of benzothiadizole (BT) and quaterthiophene (4T)-based copolymers (BT4T) and their various F-substituted derivatives are designed, namely, BT4T, BTff4T, BT4Tffi (inner position fluorination of the central dithiophene), BTff4Tffi, BT4Tffo (outer position fluorination of the central dithiophene), BTff4Tffo, shown in Scheme 1. Quantum chemical calculations and molecular dynamic simulations are employed to investigate their optical and electronic properties as well as the stacking patterns in details, and the interchain hole


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mobility has been estimated to uncover the underlying mechanism for the improvement of PCE. It is expected that the introduction of F onto the outer position of quaterthiophene can not only significantly enhance absorption spectra and reduce the HOMO level of polymer which could increase VOC in solar cells, but also promote a more effective π-π stacking pattern and reduce reorganization energy to increase hole mobility which lead to the enhancement of JSC and FF in comparison to other BT4T analogues.

Scheme 1. Molecular structures of BT4T and its F-substituted derivatives 2. Computational Methods Density functional theory (DFT) calculations were employed to investigate the geometric and electronic structures of the BT4T and its fluorinated derivatives. The computational procedure was similar with our previous work.30 Briefly, the molecular structures were optimized by Gaussian 09 program with B3LYP functional and 6-31G(d,p) basis set levels in gas phase.31 The absorption and emission spectra of the polymers were calculated using time-dependent density functional theory (TD-DFT). Oligomers with two repeating units were used as the model molecules. The alkyl side chains were replaced with ethyl groups to reduce the calculation time.


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Molecular dynamic (MD) simulations were adopted to imitate the thermodynamic equilibrium polymer bulk phase with polymer consistent force field (PCFF).32 The simulation process was similar with our previous work.30 Specifically, there were four polymer chains in the simulation system to simulate the polymer stacking pattern. The Marcus theory is adopted to describe the hole transport process of the polymers investigated. The transfer integral calculation was performed with M06-2X functional.33,34 3. Results and Discussion 3.1. Molecular structures Semiconducting polymers with high planarity often show better photovoltaic performance than their counterparts with twisted backbone configuration, due to the facts that a planar backbone guarantees an efficient conjugation along the polymer backbone that is benefit for a narrower band gap.35 Furthermore, the planarity ensures a close π-π stacking distance which is in favor of interchain aggregation and charge carrier transport.36-38 The molecule model and optimized structures of various polymers are shown in Figure 1 and Figure S1, the values of diheral angles are summarized in Table 1. As can be seen from Table 1, when the hydrogens on BT are replaced by F atoms, the dihedral angles between BT and neighbouring thiophene ring reduce from 4.5o to 0.2o, which is in accordance with Hugo Bronstein’s theoretical analysis that fluorinated BT will significantly increase the planarity of the polymer structure and derease the torsional disorder in comparison to unfluorinated BT.39 While when F atoms are introduced on quaterthiophene, the dihedral angles between thiophene rings reduce from above 10 o to less than 1 o. In addition, the cumulative dihedral angles, ie. the summation of all angles within one repeating unit, as an indicator of the mainchain twisting are also shown in Table 1, that the


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introduction of F atoms on the backbone will significantly improve the planar structure, especially for BT4Tffo and BTff4Tffo, thus probably leading to more ordered stacking pattern and effective face-on orientation which is benefit for improved intermolecular interaction. Besides the reduced backbone torsion angle, an enhanced rigidity of polymer backbone would be expected as well, due to the F---S noncovalent bond.

Figure 1. Molecule model and dihedral angle of polymer backbone. Table 1. Dihedral angle and cumulative dihedral angle of polymer backbone cumulative θ (deg.)

θ1 (deg.)

θ2 (deg.)

θ3 (deg.)

θ4 (deg.)

BT4T

4.5

15.8

7.5

13.0

40.8

BTff4T

0.2

16.5

8.4

13.7

38.8

BT4Tffi

3.2

11.7

0.7

6.3

21.9

BTff4Tffi

0.2

10.9

0.8

5.6

17.5

BT4Tffo

1.6

0.4

11.7

0.7

14.4

BTff4Tffo

0.2

0.9

10.4

1.3

12.8

3.2. Absorption and fluorescence spectra The optical absorption property of donor polymer is an important parameter for OSCs. An intense and broad absorption spectrum is advantageous to harvest as large as possible of the solar radiation. Therefore, investigation of the absorption spectra of the above donor polymers is necessary. The absorption spectra of polymers are displayed in Figure 2, and the main absorption peaks are summarized in Table 2. All polymers exhibit π-π transition bands centered at ~500


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nm.40,41 And the broader and red-shifted bands arise from intramolecular charge transfer (ICT) transitions. Apparently, the absorption spectra of BT4T and its derivatives are not greatly affected by different F substitution, indicating that F atoms do not change the optical band gaps of polymer significantly, thus keeping the good nature of the narrow band gap polymer. As is shown in Figure 2, the absorption maxima of BT4T and BTff4T are 747.2 and 751.3 nm, respectively. When the inner positions of central bithiophene are substituted by F atoms, the absorption maxima of BT4Tffi and BTff4Tffi are slightly red-shifted to 754.0 and 759.8 nm, which is in consistent with Won Ho Jo’s work.27 While when the outer positions of central bithiophene are substituted by F atoms, the absorption maxima of BT4Tffo and BTff4Tffo are blue-shifted to 738.2 and 738.5 nm, respectively. In addition, the outer position of central bithiophene fluorination leads to the enhancement of the oscillator strength and wider FWHM compared with other polymers, and this is beneficial to OSCs since it will increase the light harvesting ability of the material. In addition, with the rigid enhancement of backbone, due to the F---S noncovalent interaction, a broad absorption spectrum with strong vibronic absorption peaks are also expected, which will further increase the utilization of solar radiation.27


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Figure 2. Calculated absorption and fluorescence spectra of BT4T and its F-substituted derivatives. To quantitatively estimate the regular spectral response of BT4T upon fluorination, the optical parameters of various polymers are summarized in Table S2. The maximum absorption of all polymers are mainly from the ground state (S0) to the first excited state (S1) electron transition, i.e. the transition from HOMO to LUMO. There are also several other absorption transitions from HOMO to LUMO + 2 and HOMO to LUMO + 3. Table 2. Absorption and fluorescence maximum peaks of BT4T and its F-substituted derivatives Abs. (nm)

Flu. (nm)

Stokes shift (nm)

BT4T

747.2

887.9

140.7

BTff4T

751.3

897.3

146.0

BT4Tffi

754.0

883.0

129.0

BTff4Tffi

759.8

891.7

131.9

BT4Tffo

738.2

866.7

128.5

BTff4Tffo

738.5

867.4

128.9

In addition, it is also observed that the introduction of F atoms onto the quaterthiophene moity of BT4T causes a blue shift of emission spectra relative to their non-fluoro and difluoro-BT counterparts. Especially, the emission spectra of BT4Tffo and BTff4Tffo are significantly blueshifted, compared with other polymers, leading to a markedly reduced Stokes shift of 128.5 and 128.9 nm, respectively, which is benefit for the energy and charge transfer properties of polymers, due to the rigid reinforcement of the mainchain. 3.3. Frontier molecular orbitals (FMO) and VO


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Energy level alignment at the material interfaces is critical for the device performance of solar cells.42 Appropriate matching of HOMO of donor and LUMO of acceptor is prerequisite for exciton separation and interfacial charge transfer. So it is important to precisely predict the FMO of various BT4T polymers. HOMO of BT4T and its derivatives are calculated with PBE0 functional with 6-311G(d,p) basis set, which is useful in predicting accurate HOMO values of polymers in similar D-A copolymer systems,24 and the values of FMO are summarized in Table 3. One can observe that, the HOMO values of polymers decrease with increasing F content, indicating that the fluorination can effectively lower the HOMO energy level of polymer. The total energies, FMOs and electronic band gaps of polymers are also calculated based on various methods and basis sets. The energy dependences on substituted F atoms show almost the same trend for different functionals and basis sets, thus proving the credible results. For details, see Talbe S3, S4 and Figure S3 in the supporting information. The distribution of FMO of polymers is shown in Figure S4. Table 3. Calculated frontier molecular orbital, electronic band gap and open circuit voltage of BT4T and its fluorination derivatives HOMO (eV)

LUMO (eV)

Eg，ele (eV)

VOC (V)

BT4T

-5.11

-3.17

1.94

0.61

BTff4T

-5.21

-3.28

1.93

0.71

BT4Tffi

-5.20

-3.29

1.91

0.70

BTff4Tffi

-5.29

-3.39

1.90

0.79

BT4Tffo

-5.19

-3.23

1.96

0.69

BTff4Tffo

-5.29

-3.33

1.96

0.79


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It is well known that VOC is an important parameter of OSCs, which is proportional to the energy difference between the HOMO of the donor and the LUMO of the acceptor,23 and can be expressed as: Donor Acceptor VOC  (1/ e)( EHOMO  ELUMO )  0.3V

(1)

Donor Acceptor Here e is elementary charge, the value of 0.3 is an empirical factor. EHOMO and ELUMO are the

HOMO energy of the donor and the LUMO energy of the acceptor (PC71BM). The VOC of BT4T/PC71BM-based solar cell is ca. 0.74 V. From equation 1, the calculated VOC of BT4T/PC71BM based solar cell is 0.61 V. The lower VOC compared to experimental one is due to the overestimation of DFT to the FMO of polymer, whereas it does not affect our study on comparing the HOMO of various F-substituted BT4T derivatives. The VOC of F-substituted polymer/PC71BM-based solar cells are shown in Table 3. The predicted VOCs of fluorinated BT4T derivatives increase with increasing F content. Generally, the VOC of BT4T/PC71BM-based solar cells increase 0.1 V with every two F atoms substitutes. Therefore, device fabricated from BTff4Tffi or BTff4Tffo are expected to exhibit the highest VOC, whose HOMO are stabilized by fluorination to the maximum degree. 3.4. Excitonic property In the process of excitons splitting into free charge carriers at the heterojunction interface of the donor and acceptor materials, exciton binding energy (Eb) should be overcome. For a charge transfer reaction, the difference of electron affinities between the acceptor (EAA) and donor (EAD) should be greater than Eb.43 Eb and the energy difference of EAA and EAD are listed in Table 4. As shown in Table 4, all polymers have small Eb from 0.269 to 0.282 eV, which is less than


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energy difference between EAA and EAD, indicating that all polymers can guarantee an efficient exciton dissociation at the donor/acceptor interface. Table 4. Calculated exciton binding energy (Eb) and electron affinity (EA) of BT4T and its derivatives Eg (elec.)

Eg (opt.)

Eb

EAA-EAD

BT4T

1.939

1.659

0.280

0.74

BTff4T

1.933

1.650

0.282

0.63

BT4Tffi

1.914

1.644

0.269

0.62

BTff4Tffi

1.903

1.632

0.271

0.52

BT4Tffo

1.959

1.680

0.279

0.68

BTff4Tffo

1.960

1.679

0.281

0.58

The charge density difference (CDD) between S0 and S1 could show the spatial distribution of the excitons. The CDD analysis is carried out for BT4T and the fluorinated derivatives. The obtained charge-transfer morphologies upon excitation are presented in Figure 3. The corresponding amount of intramolecular charge transfer and distance of centroid of hole and electron (DCHE) are summarized in Table 5. The CDD map depicts that there is apparent charge transfer from the quaterthiophene to the BT moiety upon S0→S1 transition in all polymers. Normally, more amount of intramolecular charge transfer and larger DCHE lead to weaker Coulomb attraction and easier the separation of the exciton. In this work, when the F atoms are introduced on BT moiety, especially for BTff4Tffi and BTff4Tffo, the dipole of excited state and the dipole change are larger, leading to a substantial intramolecular charge transfer and a larger DCHE, thus an easier separation of excitons occurs.


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Table 5. Calculated DCEH, transferred charges, µg, µe and Δµge of BT4T and its fluorinated derivatives DCEH (Å)

Δq (C)

µg (D)

µe (D)

Δµge (D)

BT4T

3.19

0.52

2.02

21.85

20.09

BTff4T

3.54

0.57

1.78

23.27

21.71

BT4Tffi

3.45

0.54

1.98

23.08

21.43

BTff4Tffi

3.83

0.58

1.63

24.64

23.15

BT4Tffo

3.05

0.47

2.25

21.48

19.58

BTff4Tffo

3.62

0.52

1.86

23.45

21.70

Figure 3. CDD maps of F-substituted polymers. The blue represents where the electrons are coming from, and the red represents where the electrons are going. From Table 5, it can be seen that the dipole moments of the excited states (µe) are affected more strikingly than the ground states (µg) upon irradiation. Jea-Woong Jo et al. has demonstrated that a large dipole change from S0 to S1 state (Δµge) lowers the Coulombic binding


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and facilitates exciton dissociation and generation of charge-separated state.16 Dipole moments were calculated for repeating units of the six polymers, as summarized in Table 5. It can be seen that Δµge tends to maximum when F atoms are introduced on BT moiety, while Δµge tends to minimum when F atoms are introduced on quaterthiophene moiety. Especially, when F atoms are introduced on both BT and quaterthiophene simultaneously, Δµge are maximized, i.e. BTff4Tffi (23.15 D) and BTff4Tffo (21.70 D), suggesting reduced recombination losses and higher JSC values. 3.5. Stacking patterns and molecular orientation It is well known that the values of FF and JSC are sensitive to the active layer morphology and the charge transport ability. So the inter chain stacking pattern of polymer materials should be investigated under the influence of different fluorination. In order to accurately predict the stacking pattern of polymer materials, the conformation of the structural unit should be determined prior to MD simulation. Initially, two conformations of polymer main chain, i.e. BT4T with trans-DTBT and cis-DTBT denoted as trans- and cis-BT4T, respectively, are tested to find a stable equilibrium structure, shown in Figure 4. MD simulations indicate that trans-BT4T with substantial side chain interdigitation is energetically favorable, which is 25 kJ/mol per monomer lower than cis-BT4T, due to the alternated side chains, shown in Figure S5. This is in consistent with Wei You’s single crystals for X-ray diffraction analysis of DTBT.16 In addition, John E. Northrup proposes that interdigitation is benefit for improving structural ordering, leading to higher mobility.44


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Figure 4. The initial and equilibrated structures of (A, B) trans-BT4T and (C, D) cis-BT4T extracted at 0 and 2 ns in the time-trace. (grey, C; yellow, S; light blue, F; blue, N, hexyl side chains are shown in wire for clarity) It is known that intrachain carrier mobility is higher than interchain one.42 However, in reality the intrachain transport is limited by the finite length of polymer chain. From a microscopic view, hole mobility measured by field effect transistor (FET) method contributes much by interchain transport. Generally, interchain transport could occur through both amorphous and crystallized regions. Obviously, transport in closely packed zones is much faster than that in loosely packed zones, and can be treated with hopping mechanism. So, promoting ordered molecular packing can effectively improve interchain transport of polymers in active layer. Fluorinated backbones of polymers have been proven as an effective way to reduce the stacking distance by virtue of F chemistry.17 Here, MD simulation is employed to accurately


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predict the intermolecular packing motif, especially for π-π stacking distance and tilt angle, which is critical to figure out the carrier mobility of polymer.

Figure 5. (A) Time-traces of π-π stacking distances of various BT4T derivatives up to 2 ns, (B) Distributions of π-π stacking distances of various BT4T derivatives between 0.3 and 2 ns. (C) Time-traces of tilt angles of various BT4T derivatives up to 2 ns, (D) Distributions of tilt angles of various BT4T derivatives between 0.3 and 2 ns.

Figure 6. Stacking patterns of (A) BT4T and (B) BTff4Tffo.


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Figure 5 (A) presents the time-trace of the π-π stacking distance of various polymers from 0 to 2 ns during MD simulations. And the distributions of π-π stacking distances of six polymers are plotted in Figure 5 (B), and the values of peaks corresponding to the stacking distances are summarized in Table 6. The π-π stacking distance of BT4T is 3.81 Å. The π-π stacking distance of BTff4T, BT4Tffi and BTff4Tffi are 3.77, 3.77 and 3.76 Å, respectively, which agrees well with the reported values.28 The slight decrease in π-π stacking distance, compared with BT4T system, indicate that F atoms can effectively promote interchain packing. Whereas, the π-π stacking distance of BT4Tffo and BTff4Tffo significantly decreases to 3.66 and 3.62 Å, indicating that outer position fluorination of quaterthiophene result in more effective π-π stacking, due to dramatically reduced backbone twisting angles (see Table 1), which is pivotal to achieve a high hole mobility. Table 6. Experimental and calculated π-π stacking distances and backbone tilt angles of BT4T and its derivatives π-π distance (Å)

tilt angle (degree)

BT4T

3.81

33.9

BTff4T

3.77

33.2

BT4Tffi

3.77

32.1

BTff4Tffi

3.76

31.3

BT4Tffo

3.66

30.8

BTff4Tffo

3.62

29.0

In addition to π-π stacking distance, tilted backbone is energetically favorable in polymer film. However, according to John E. Northrup’s theoretical work, the reduced tilt angle of conjugated chains increases the overlap of π orbitals and reduces the effective mass in the π-π stacking


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direction, leading to higher carrier mobility.44 So Higher mobility could be expected from a smaller tilt angle of polymer backbone. It can be seen from the MD simulation that, the tilt angles decrease from 33.9o of BT4T to 29.0o of BTff4Tffo monotonously, probably due to the enhanced F---π interaction. So a decreased tilt angle can maintain a greater degree of orbital overlap and a smaller effective mass, thus keeping high carrier mobility. The equilibrated structures of BT4T and BTff4Tffo from MD simulation at 2 ns are presented in Figure 6. 3.6. Charge carrier transport Transport of charge is a fundamental process in optoelectronic devices, and effective charge transport leads to improved device performance. To gain a deep understanding, an in-depth description of these dynamic processes should be performed. As is well known, intrachain charge transport is higher than the interchain one.42 However, the intrachain carrier mobility will be disrupted by the finite length of the polymers in the real active layer materials of OSCs. So the macroscopic carrier mobility of polymer layer is mainly determined by interchain charge transport process. Under this condition, the hopping model within Marcus theory is adopted to describe the charge carrier mobilities along interchain direction. The interchain hole transfer can be described by uncorrelated hopping processes, and the hole mobility µ is proportional to the hole transfer rate kif, that can be described by the Einstein equation as follows,



er 2 kif k BT

(2)


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Here e, r, kB, and T correspond to the electronic charge, the transport distance, the Boltzmann constant, and the temperature, respectively. And the charge transfer rate kif can be described by Fermi golden rule:

kif 

2

| tif |2  ( E f )

(3)

where tif is the electronic coupling describing the transition between the two electronic states of i and f, and ρ(Ef) is the density of states. Furthermore, the Gold-rule rates can be realized by the Marcus-Hush theory.45,46 So the hole transfer rate kif between the adjacent polymer chains can be expressed as follows:

kif 

2

 (G o   ) 2  1 | tif |2 exp   4 kBT  4 kBT 

(4)

where ∆G°is the difference of the Gibbs free energy of the initial and final state of the system, which is equal to zero because all chains are equal. The inner reorganization energy λ the transfer integral t are calculated following our previous work.30 Table 7. The calculated transfer integral (t), inner reorganization energy (λ), hole transport rates (kif), center-of-mass distances (r), and hole mobilities (μh) of BT4T and its derivatives t (eV)

λ (eV)

kif (s-1)

R (A)

μh (cm2V-1s-1)

μh* (cm2V-1s-1)

BT4T

0.101

0.387

6.452e+012

3.81

0.181

0.2015

BTff4T

0.159

0.398

1.428e+013

3.77

0.393

BT4Tffi

0.116

0.339

1.460e+013

3.77

0.401

0.3328

BTff4Tffi

0.131

0.351

1.633e+013

3.76

0.446

0.6228


19


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BT4Tffo

0.149

0.273

5.091e+013

3.63

1.297

BTff4Tffo

0.198

0.273

8.922e+013

3.62

2.261

* Experimental values derived from reference. The calculated transfer integral (t), inner reorganization energy (λ), hole transport rates (kif), center-of-mass distances (r), and hole mobilities (μh) of polymers investigated are summarized in Table 7. It is shown that the electron coupling is highly sensitive to the molecular packing. As can be seen from Table 7, polymers exhibit gradually increasing transfer integral as F is introduced onto BT, inner position and outer position of quaterthiophene in steps, because of the synchronized reduction of stacking distances and tilt angles in the π-π stacking direction, leading to a more effective face-to-face orientation. In the meantime, the fluorination of outer site of quaterthiophene makes the backbone more planar and rigid compared with inner site fluorination, thus a minor internal relaxation occurred during charge transport process, leading to a smaller reorganization energy. According to equation 3, polymers with larger transfer integral and lower reorganization energy possess relatively larger hole mobility. So with π-π stacking distances calculated from MD simulation, we predict from equation 2 that the newly designed polymers BT4Tffo and BTff4Tffo have the largest hole mobilities of 1.297 and 2.261 cm2 V-1 s-1, respectively, along interchain direction, which are nearly one order of magnitude larger than other fluorinated polymers. In summary, the results show that outer site of quaterthiophene fluorination can increase the hole mobility of the polymer dramatically via the stacking arrangement modification. Therefore, the designed polymer BT4Tffo and BTff4Tffo may show better carrier transport performance, compared with other BT4T derivatives. 4. Conclusions


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We have designed and simulated the photoelectric properties of a series of BT4T and its fluorinated derivatives, which can be used for the construction of donor polymer material for OSCs. And the underlying working mechanisms have been elucidated by DFT calculation and MD simulation. The introduction of F onto the outer site of quaterthiophene of BT4T has been verified as an effective way to enhance the photovoltaic performance of OSCs theoretically. In addition to the enhanced absorption spectrum and deep lying HOMO energy level, more importantly, a higher hole mobility could be achieved owing to the more effective face-on orientation formed by subtle manipulation of interchain π-π stacking pattern as well as reduced reorganization energy during the process of charge transport. Thus a better photovoltaic performance could be expected from BTff4Tffo compared with other BT4T analogues. This article highlighted the fluorination effect on the interchain interactions and orientation correlations in governing the key parameters of OSCs, and opened up new ideas to improve the device performance. These theoretical results predict that even higher PCE would be expected by rational molecular design, and related experiment are in progress in our laboratory. ASSOCIATED CONTENT Supporting Information. Optimized structures, calculated absorption spectra, FMO energies, distributions and reorganization energies of BT4T and its fluorinated derivatives. Potential energy as a function of time of trans- and cis-BT4T. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (Y. N.); [email protected] (R. Y.)


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* Tel: +86-18612520701 (Y. N.); +86-532-80662700 (R. Y.) Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (21204097, 21274161, 51173199, 51573205, 51503219), the Ministry of Science and Technology of China (2010DFA52310).

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Page 26 of 26

Table of Contents Graphic and Synopsis The introduction of F onto the outer site of quaterthiophene of BT4T has been verified as an effective way to enhance the overall performance of OSCs theoretically. Except for the enhanced absorption spectrum and deep lying HOMO energy level, more importantly, a higher hole mobility could be achieved owing to the more effective face-on orientation formed by subtle manipulation of interchain π-π stacking pattern as well as reduced reorganization energy during the process of charge transport, leading to potentially better photovoltaic performance.


26

Strategy to Manipulate Molecular Orientation and Charge Mobility in D

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