Design Proposals for Organic Materials Exhibiting a Low Exciton

Article pubs.acs.org/JPCC

Design Proposals for Organic Materials Exhibiting a Low Exciton Binding Energy Stefan Kraner,*,† Reinhard Scholz,†,‡ Christian Koerner,† and Karl Leo† †

Institut für Angewandte Photophysik, and ‡Dresden Center of Computational Materials Science, Technische Universität Dresden, D-01062 Dresden, Germany ABSTRACT: Organic photovoltaics (OPV) have the potential for a low cost energy conversion from solar to electrical power. However, minimizing voltage losses, inherent to the currently used intermolecular donor−acceptor system, represents the main challenge to make this technology suitable for commercial large area applications. One key parameter to overcome is the high exciton binding energy in organic materials. Based on density functional theory (DFT) simulations, it is shown how polar side chains may significantly increase the dielectric constant, which lowers the exciton binding energy and enables charge generation in organic materials without a donor− acceptor system. Furthermore, based on time dependent (TD)-DFT calculations, we show another path for low exciton binding energy organic materials, by inducing a charge transfer state between two hydrogen bonded oligomers along the backbone. The charge transfer is achieved by fluorination of the acceptor oligomer investigated, leading to a wide-range intermolecular exciton, where the frontier orbitals are spatially separated from each other. Furthermore, we show that intramolecular charge transfer (CT) states and CT states between two π-stacked molecules do not significantly influence the Coulomb interactions.

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INTRODUCTION Organic photovoltaic (OPV) is a promising technology for large area and low cost devices, converting sun light into electrical energy. Recently, a power conversion efficiency (PCE) of 12% was achieved.1−3 The stability of air exposed devices could be increases by using oxides as transport materials,4 whereas device encapsulations based on atomiclayer-deposition seems to be a promising protection method.5,6 However, for commercially relevant applications, the PCE must be further improved. Here, we focus on the deficiencies of the current OPV working principle, that is, the voltage loss of the donor−acceptor system. The open circuit voltage (VOC) of a working organic solar cell relies on the effective gap, Egeff, and a temperature dependent recombination term,7 where Egeff is the difference between the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor (see Figure 1).

For analyzing the open circuit voltage via the charge transfer state across the donor−acceptor interface, this effective gap has to be corrected by the screened Coulomb interaction between opposite charged ionized donor and acceptor sites directly at the interface.8 Lowering the energy difference between the optical gap and the effective gap increases VOC and therefore the PCE. However, a certain energy difference is needed to overcome the exciton binding energy.9,10 Thus, in order to reduce the losses, originating from the donor−acceptor electron transfer step, the exciton binding energy in organic materials needs to be lowered. The temperature dependent recombination term lowers the open circuit voltage due to Shockley−Read−Hall (SRH) and direct bimolecular recombination.11 A higher charge carrier mobility decreases the recombination and increases the short circuit current.12,13 Thus, a smaller exciton binding energy and a higher charge carrier mobility are crucial for a higher PCE in OPV. In organic materials, an efficient charge generation requires small (5−10 nm) but interconnected phases, since the exciton diffusion length is in this range.14 However, the problem in the concept of current OPV devices is the need of a high charge carrier mobility to prevent recombination losses, which could be achieved by a higher crystallinity, which on the other hand increases the size of the phases and therefore reduces charge generation. One approach to overcome this problem is to avoid a heterojunction based on two different phases, meaning that the charge separation must take place within one phase. In this case, crystallinity would not affect charge separation, enabling larger crystals in the active absorber layer, and thus using only

Figure 1. Energies involved in the electron transfer from the donor to the acceptor. The difference between the optical gap Eopt and the effective gap Egeff represents the energy loss for the charge transfer of an electron from the donor to the acceptor. © 2015 American Chemical Society

Received: July 22, 2015 Revised: September 21, 2015 Published: September 23, 2015 22820

DOI: 10.1021/acs.jpcc.5b07097 J. Phys. Chem. C 2015, 119, 22820−22825

Article

The Journal of Physical Chemistry C one phase may improve the PCE significantly. Dissociating an exciton within a phase can either be accomplished by a high dielectric constant, or by a charge transfer (CT) state.15,16 The exciton binding energy is the energy needed to dissociate the hole and the electron into free, mobile charge carriers. Reported exciton binding energies for organic materials range from 0.1 to 1 eV.17−21 In inorganic materials, an exciton can be described as a Wannier−Mott (WM) exciton with the binding energy EWM, E WM =

a 0E R , aWMεr

aWM = a0

meεr μ

(1)

where a0 is the Bohr radius, ER the Rydberg energy, aEW the radius of the Wannier exciton, εr the relative dielectric constant, me the rest mass of an electron, and μ the reduced mass. Thus, a higher dielectric constant induces a larger exciton radius, whereas the exciton binding energy is reduced. For a localized Frenkel exciton, the binding energy EBF can be described by the Coulomb attraction between the hole and the electron,

EF ≈

e2 4πε0εraF

(2)

where e is the elementary charge, ε0 represents the vacuum permittivity, and aF measures the average electron−hole distance. The Frenkel exciton exhibits, therefore, the same dependence on the dielectric constant; that is, increasing the dielectric constant or the electron hole distance aF leads to a lower exciton binding energy. According to eqs 1 and 2, an extended exciton is needed for a lower binding energy. Gallium nitride (GaN) exhibits a dielectric constant of 9.8 and an exciton radius of 3.9 nm, leading to an exciton binding energy as small as 20 meV,22 which is sufficiently low to dissociate the exciton thermally (≈25 meV). Thus, in order to provide space for a weakly bound exciton, the π-system, hosting the exciton, must expand over at least the exciton radius of GaN, that is, a few nanometers. In this work, we use ab initio calculations to show new pathways for organic materials with a high dielectric constant. We show that zwitterionic side chains attached to a ladder polymer give a dielectric constant of up to 17. Furthermore, we investigate the feasibility of three different CT states based on a modified ladder polymer, leading to a Coulomb binding energy around 0.24 eV. We want to point out that we do not claim that the proposed polymers can be synthesized. Instead, we want to encourage chemists to synthesize polymers based on the same idea, which might behave similarly. In the following investigation we focus on the ladder polymer poly(benzimidazobenzophenanthroline) (BBL), since its π-system extends over several repetition units, and the dielectric tensor and exciton extension were investigated previously.15,16

Figure 2. Chemical structures of molecules and side chains investigated with their short name.

cell characteristics was observed for a polymer with nitrile side chains, which increases the dielectric constant from 3.5 to 5, and reduces nongeminate recombination.26 For the following investigation, we use a BBL monomer with two additional carbon atoms at the linker position, reflecting the basis molecule to attach the different side chains introduced in Figure 2. The influence of four attached fluorine atoms is denoted by the molecule F4-BBL. The side chains, cyanopentyl (nitrile), TEG, CYPHE, and a zwitterionic side chain, are attached to the BBL monomer and simulated in terms of polarizability volume. Extraction of the ionic and electronic polarizability of the BBL monomer and F4-BBL are carried out as reported in ref 16. Briefly, we use the hybrid functional PBE027 with the basis set def2-SVPD28 in the Turbomole software,29,30 where the functional PBE0 was successfully used in refs 16, 28, and 31 to calculate the polarizability volumes of organic conjugated materials. TD-DFT calculates the electronic polarizability of the simulated molecule. To obtain the electronic and the ionic part of the dielectric constant, an electric field (0.0002 and 0.0004 atomic units (a.u.)) is applied during the geometry optimization. The difference between the dipole of the molecule under an applied electric field as compared to the same calculation without an electric field, divided by the applied electric field, results in the polarizability volume with electronic and ionic contributions. Subtracting the electronic part results in the purely ionic part of the polarizability volume. For more details, we refer to ref 16. The BBL monomer with the CYPHE side chain exhibits its lowest energy for the conformation where the dicyanophenoxy group is parallel to the molecular plane of the BBL monomer, forming a π-stack. For the DFT simulation of the CYPHE side chain, we therefore added a D3 dispersion to include the van der Waals interaction.32 To improve the ability of the DFT calculation to converge, and to decrease the

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CALCULATION OF THE DIELECTRIC CONSTANT OF BBL WITH POLAR SIDE CHAINS As GaN shows an exciton binding energy in the range of thermal energy and a dielectric constant of about 10, polymers with a dielectric constant in a similar range could provide a route toward reduced exciton binding energies. Hyperbranched copper phthalocyanine (CuPc) with the side chains 2-(3,4dicyanophenoxy)-phenoxy (CYPHE), shown in Figure 2, exhibits a dielectric constant of 15.23 For polymers with triethylene glycol (TEG) side chains, an enhanced dielectric constant of 6 was measured.24,25 An improvement of the solar 22821

DOI: 10.1021/acs.jpcc.5b07097 J. Phys. Chem. C 2015, 119, 22820−22825

Article

The Journal of Physical Chemistry C

We use a modified Onsager theory33 to estimate the dielectric constant of BBL with a single zwitterionic side chains attached to each monomer,

computational time during the geometry optimization with an applied electric field, we fixed the atoms of the backbone (BBL monomer), except for the carbon atom involved in the bond with the side chain. Thus, for the side chains calculated (except F4-BBL), the ionic part exhibits its origin only from the side chain, since all other atoms are fixed. These calculations are performed in the x-, y-, and z-direction, leading to a dielectric tensor which should be symmetric. However, due to favorable movements with respect to the backbone, especially for the more complex side chains, deviations from a symmetric tensor are observed. This deviation together with the deviation obtained by applying different electric fields (0.0002 and 0.0004 au) during geometry optimization compared to their mean value are represented by the standard deviations Δαi, shown in Table 1. This Table further summarizes the

(εs − εe)(2εs + εe) 4παi′ = εs(εe + 2) 3VM

where the left part of eq 3 consists of εs and εe, representing the static and electronic dielectric constant, respectively. In the Onsager theory developed for liquids, for a molecule, the temperature dependent right part of eq 3 is replaced by a term consisting of the ionic polarizability volume α′i and the molecular volume VM. Solving eq 3 for εs results in a quadratic equation with the following solutions: εe + (εe + 2)2 εs1,2 =

Table 1. Ionic Polarizability Volumes and the Calculated Dielectric Constants for the Side Chains Introduces in Figure 2a

αi′ Δαi α′e VM αi εs

BBL mono.

F4-BBL

cyanopentyl

TEG

CYPHE

zwitterionic

30 5 346 2578 0.01 4.1

28 4 351 2759 0.01 4.1

82 21 426 3472 0.09 5.2

107 52 461 3833 0.09 5.3

169 59 517 4331 0.10 5.9

943 290 496 4338 0.54 16.8

(3)

( ) 4παi′ 3VM

4

(

εe + (εe + 2)2

±

2

( ))

4

4παi′ 3VM

+ 8εe 2 (4)

where only the positive sign gives reasonable results, that is, εS > 0. Equation 4 is used to calculated the static dielectric constant εs shown in Table 1, representing the dielectric constant at a frequency below the vibrational modes. For the polarizability volume αi for the BBL monomer and F4-BBL, the values according to Table 1 are taken. Since the backbone of the polymer is fixed during the calculations of the polarizabilities of the side chains, we added the ionic polarizability volume of the side chain to the polarizability volume from the BBL monomer. The electronic dielectric constant of εe = 3.6 for the BBL polymer is taken from ref 16, For the respective molecular volume VM, the sum of the volume of one BBL monomer (2602 bohr3, ref 16) and the volume of the side chain (VM+sidechain − VM−BBL from Table 1) is taken. The static dielectric constant obtained for BBL is in agreement with ref 16. Even though different polymer backbones are used, similar enhancements of the dielectric constant with or without a polar side chains are obtained for the cyanopentyl and the TEG side chains.24,26 For the CYPHE side chain, a dielectric constant of 15 or higher was published.23 Our calculations result in a dielectric constant of 5.9. These calculations are based on the energetically lowest conformation. However, in reality, due to vibrations and intermolecular interactions, the side chain might be oriented differently with respect to the backbone, which strongly affects the freedom of movement of the side chain and therefore its polarizability. Finally, we obtain a high dielectric constant of 16.8 for the BBL polymer with zwitterionic side chains attached. For this calculation, intermolecular interactions are not taken into account, and only the energetically lowest conformation is simulated. Based on the calculations performed, we propose to use zwitterionic side chains to increase the dielectric constant of organic materials significantly. However, for all the polar side chains, intermolecular interactions are crucial for their polarizability. For the usage of polar side chains, it is recommended to prevent intermolecular interactions of the polar side chains, since they might hinder each other in the freedom of movement. Guo achieved this by a hyperbranched CuPc film, consisting of the disklike CuPc molecules, connected by the ionic 2-methoxyphenoxy bridge, where a part of the

a αi′ represents the polarizability volumes (bohr3), Δαi corresponds to the standard deviation for the ionic contributions (bohr3), α′e is the electronic polarizability volume (bohr3), VM is the molecular volume (bohr3), αi is the ionic polarizability of the molecule (two left columns) or the side chains (four right columns), and εs is the calculated dielectric constant.

simulation results for the mean ionic polarizability volume α′i and the mean electronic polarizability volume α′e, together with the standard deviations Δαi compared to their mean values. In order to know the molecular volume of the side chains, the COSMO-solvation method of Turbomole is used to calculate the molecular volume of the molecules introduced. In Table 1, the calculated molecular volumes VM are shown. The ionic polarizability volume for F4-BBL enhances neither the ionic nor the electronic polarizability volume. The general increase of the electronic polarizability α′e can be attributed to the increasing molecular volume, which increases the number of atoms, and therefore the number of electrons participating in the screening. Attaching a cyanopentyl side chain with its internal dipole moment increases the ionic polarizability volume from 30 to 82. Due to the ethoxy groups, the TEG side chain contains several dipoles, resulting in an increased ionic polarizability volume of 107. However, calculating the ionic polarizability αi = α′i / (VM−TEG − VM−BBL), which is independent of the molecular volume, we obtain the more meaningful ionic polarizability, which remains at 0.09, comparable to the cyanopentyl side chain. Thus, the higher polarizability volume of TEG compared to the cyanopentyl side chain can be attributed to an increased volume of the side chain. The CYPHE side chain increases the polarizability slightly from 0.09 to 0.10. The zwitterionic side chain induces a more than five times higher polarizability compared to the other side chains investigated. This can mainly be attributed to the strong internal dipole of the zwitterionic side chain. 22822

DOI: 10.1021/acs.jpcc.5b07097 J. Phys. Chem. C 2015, 119, 22820−22825

Article

The Journal of Physical Chemistry C unconnected linkers consists of the CYPHE side chain. We assume that the disklike shape of CuPc enables intermolecular cavities, which are used by the ionic side chains to move freely,23 leading to a high screening and therefore a high dielectric constant. In principle, the same can be achieved with zwitterionic side chains. For more accurate conclusions concerning intermolecular interactions of ionic side chains and their influence on the dielectric constant, further investigations will be needed.

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CALCULATION OF CT STATES ON MODIFIED BBL OLIGOMER FORMATIONS The exciton binding energy consists of the Coulomb attraction between the electron and the hole, which is lowered by the kinetic energy of these quasi-particles. Interpreting the HOMO as the hole and the LUMO as the electron, the Coulomb interaction in an anisotropic medium can be calculated as15,34 EC =

e2 4πε0 det|ε|

∫∫

|ψHOMO( r1⃗)|2 |ψLUMO( r2⃗ )|2 (x1 − x2)2 εxx

+

(y1 − y2 )2 εyy

+

(z1 − z 2)2 εzz

d3r1d⃗ 3r2⃗

(5)

where e is the elementary charge, ε0 is the vacuum permittivity, det|ε| is the determinant of the dielectric tensor, ψ represents the wave functions of the HOMO and LUMO orbital, and r1⃗ and r2⃗ their coordinates, respectively. Recently, we showed a doubling of the exciton size for the intramolecular CT transition S3 as compared to the optically more relevant S1 transition.15 According to eqs 1 and 2, a doubling of the exciton radius leads to a decrease of the exciton binding energy by a factor of 1/2. However, the intramolecular CT state was an S3 state with a negligible oscillator strength.15 It is well-known that fluorination of an organic molecule increases the ionization potential,35 and thus exhibits the energetics of an acceptor molecule compared to the unfluorinated molecule. We investigate the Coulomb binding energies of the S1 state of a partially fluorinated oligomer shown in Figure 3a, denoted by F12BBL6, where the three BBL monomer units on the right side exhibit six substituted fluorine atoms. Their respective frontier Kohn−Sham (KS) orbitals of the intramolecular S0 state are shown in Figure 3b and c. Both the KS-HOMO and the KS-LUMO are localized on the left and right side of the molecule, respectively. However, the relevant hole and particle (electron) orbitals in the S1 state are delocalized over the molecule (see Figure 3d and e), which holds true especially for the particle. This can be explained by the neglecting of the Coulomb interaction between the hole and the electron in the S0 state, since the respective KS orbitals in Figure 3b and c were calculated in the ground state configuration. Thus, in contrast to Frenkel excitons,15 Coulomb interactions of CT excitons need to be evaluated by means of natural transition orbitals (NTO), that is, the particle and the hole. From the calculations above, we know that the fluorination of the backbone does neither significantly influence the electronic nor the ionic contribution to the dielectric constant. For the calculation of the exciton binding energy, we therefore take the published values from ref 16, that is, εxx = 8.3, εyy = 2.9, and εzz = 3.4. In order to reduce computational time, the geometry optimizations are calculated with the SVP28 basis set and the PBE0 functional by the software Turbomole. For the molecule BBL3-h-F12BBL3, exhibiting van der Waals interaction, the D3 dispersion is included during geometry

Figure 3. Isosurfaces (0.01) of the calculated frontier orbitals of three different molecular structures. Except for BBL3-π-F12BBL3, the three fluorinated monomer units are on the right side of the molecule or on the right molecule.

optimization.32 TD-DFT calculations are performed with the hybrid functional B3LYP36 and with the basis set def2-SVPD. The response vector of the TD-DFT calculation is further processed by using software TheoDORE,37,38 generating the NTOs of the S1 transition. The particle and hole wave function is then discretized by the MOLDEN program,39 where a grid resolution of 2, 2.5, and 3.9 points/Å is taken for the F12BBL6, BBL3-h-F12BBL3, and BBL3-π-F12BBL3 molecule, respectively.15 After normalizing the square of the orbitals to unity, eq 5 is calculated.15 By this procedure, we calculate the Coulomb binding energy for the partially fluorinated molecule shown in Figure 3a, denoted with F12BBL6, and obtain a Coulomb binding energy of 0.43 eV (see Table 2). The Coulomb interaction obtained is in the same range as the value of 0.4 eV reported for unfluorinated BBL.15 Therefore, to prevent a delocalization of the electron in the LUMO, we separate the molecule F12BBL6 into two parts, as shown in Figure 3f and g. The three BBL monomer units on the left side and the three fluorinated BBL units on the right side are connected by hydrogen bonds, leading to the molecule denoted by BBL3-h-F12BBL3. The hole and particle orbitals in Figure 3f and g show a strong localization on the BBL3 and on the F12BBL3, respectively. Thus, the S1 state is a CT-state. The Coulomb binding energy 22823

DOI: 10.1021/acs.jpcc.5b07097 J. Phys. Chem. C 2015, 119, 22820−22825

Article

The Journal of Physical Chemistry C

one-half side of the BBL oligomer is fluorinated in order to create an electron accepting part, leading to an efficient splitting of the HOMO and LUMO orbitals. The Coulomb binding energy of an intramolecular CT state or a CT state between two π-stacked planar molecules is in a similar range as the Coulomb binding energy on a pure BBL polymer. However, a CT state along the backbone of two hydrogen bonded oligomers results in a calculated Coulomb binding energy of only 0.24 eV. We assume that an enhancement of the conjugation length of the hydrogen bonded BBL oligomers would further lower the Coulomb binding energy. Proposals to overcome the inevitable decrease in absorption of a wide range intramolecular donor−acceptor system are discussed. Hence, we propose two new paths for exciton dissociation within an organic phase in order to reduce the voltage losses and to increase the charge carrier mobilities in OPV.

Table 2. Resulting S1 Excitonic Properties for the Molecular Structures Shown in Figure 3, That Is, the Coulomb Binding Energy without Screening, the Coulomb Binding Energy with Screening, the Effective Dielectric Constant εeff, the Osillator Strength, and the Transition Energy ΔES1 molecular structure

EC w/o screen. (eV)

EC (eV)

εeff

osc. strength

ΔES1 (eV)

F12BBL6 BBL3-h-F12BBL3 BBL3-π-F12BBL3

1.57 0.79 1.96

0.43 0.24 0.48

3.6 3.3 4.0

3.0 0.005 0.001

1.6 1.4 1.6

obtained is strongly reduced to 0.24 eV, as compared to the connected BBL. We propose that an enhancement of the conjugation length of hydrogen bonded BBL3 the F12BBL3 would lower the Coulomb binding energy even more. The Coulomb interaction for a CT exciton between three BBL monomer units and three fluorinated BBL units (BBL3-πF12BBL3) arranged in a π-stack with a distance of 3.78 Å16 is calculated, resulting in a Coulomb binding energy of 0.48 eV (see NTOs in Figure 3h). Table 2 summarizes the Coulomb interaction without screening, the Coulomb interaction with screening, the ratio of the Coulomb interactions giving the effective dielectric constant εeff, the oscillator strength, and the transition energy ΔES1. The Coulomb binding energy of BBL3π-F12BBL3 is higher as compared to the value reported for six pure BBL monomer units. The reason for this behavior is the localization of the wave functions on three, as compared to six,15 BBL monomer units. However, its effective dielectric constant, representing the apparent exciton screening, is highest. The reason for the higher dielectric constant is that the dielectric constant perpendicular to the transition dipole moment is crucial for the screening,20,40 thus the higher dielectric constant along the polymer backbone enhances the screening for CT state. The transition energies ΔES1 are in a similar range around 1.4−1.6 eV. The oscillator strength is low for both CT transitions, the hydrogen bonded (BBL3-hF12BBL3) and the π-bonded (BBL3-π-F12BBL3), respectively, indicating a low overlap of the frontier orbitals. The more separated the hole and particle orbitals are, the lower is the Coulomb binding energy, but also the transition dipole moment, leading to a poor absorption coefficient. Thus, it remains questionable whether an efficiently dissociating exciton can absorb enough light for solar cell applications. One approach to overcome this problem would be to use the strong absorption of the energetically higher lying intramolecular transitions on the respective molecule, as utilized in current OPV. Another approach is to outsource the absorption to an efficient dye, transferring the energy of the exciton41−43 to the dissociating part of the molecule. Thus, for highly efficient organic solar cells with minimized voltage losses, the main tasks of a solar cell, i.e. absorption, dissociation and transport, might be attributed to specific organic molecules with specialized properties, designed for their task.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +49-351-463-35117. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Koen Vandewal for helpful discussions and reviewing, and Felix Plasser for providing the TheoDORE software platform. The work leading to these results has received funding from the European Community’s Seventh Framework Programme under Grant Agreement No. FP7-267995 (NUDEV).

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REFERENCES

(1) Yusoff, A. R. B. M.; Kim, D.; Kim, H. P.; Shneider, F. K.; da Silva, W. J.; Jang, J. High Efficiency Solution Processed Polymer Inverted Triple-Junction Solar Cell Exhibiting Conversion Efficiency of 11.83%. Energy Environ. Sci. 2015, 8, 303−316. (2) www.heliatek.com; accessed March 6, 2015. (3) Green, M. A.; Emery, K.; Hishikawa, Y.; Warta, W.; Dunlop, E. D. Solar Cell Efficiency Tables (Version 45). Prog. Photovoltaics 2015, 23, 1−9. (4) Sun, Y.; Takacs, C. J.; Cowan, S. R.; Seo, J. H.; Gong, X.; Roy, A.; Heeger, A. J. Efficient, Air-Stable Bulk Heterojunction Polymer Solar Cells Using MoO(x) as the Anode Interfacial Layer. Adv. Mater. 2011, 23, 2226−30. (5) Singh, A.; Nehm, F.; Müller-Meskamp, L.; Hoß bach, C.; Albert, M.; Schroeder, U.; Leo, K.; Mikolajick, T. OLED Compatible WaterBased Nanolaminate Encapsulation systems Using Ozone Based Starting Layer. Org. Electron. 2014, 15, 2587−2592. (6) Hossbach, C.; Nehm, F.; Singh, A.; Klumbies, H.; Fischer, D.; Richter, C.; Schroeder, U.; Albert, M.; Müller-Meskamp, L.; Leo, K.; et al. Integration of Molecular-Layer-Deposited Aluminum Alkoxide Interlayers into Inorganic Nanolaminate Barriers for Encapsulation of Organic Electronics with Improved Stress Resistance. J. Vac. Sci. Technol., A 2015, 33, 01A119. (7) Widmer, J.; Tietze, M.; Leo, K.; Riede, M. Open-Circuit Voltage and Effective Gap of Organic Solar Cells. Adv. Funct. Mater. 2013, 23, 5814−5821. (8) Scholz, R.; Luschtinetz, R.; Seifert, G.; Jägeler-Hoheisel, T.; Körner, C.; Leo, K.; Rapacioli, M. Quantifying Charge Transfer Energies at Donor-Acceptor Interfaces in Small-Molecule Solar Cells with Constrained DFTB and Spectroscopic Methods. J. Phys.: Condens. Matter 2013, 25, 473201. (9) Vandewal, K.; Ma, Z.; Bergqvist, J.; Tang, Z.; Wang, E.; Henriksson, P.; Tvingstedt, K.; Andersson, M. R.; Zhang, F.; Inganäs, O. Quantification of Quantum Efficiency and Energy Losses in Low

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CONCLUSIONS We simulate the polarizability and the dielectric constant of several polar side chains attached to a BBL monomer. We show that zwitterionic side chains enable dielectric constants above 10, and thus might be an interesting path to reduce the exciton binding energy. Furthermore, we have tested the ability of onedimensional oligomers to dissociate the exciton by an intramolecular or intermolecular CT states. For this purpose, 22824

DOI: 10.1021/acs.jpcc.5b07097 J. Phys. Chem. C 2015, 119, 22820−22825

Article

The Journal of Physical Chemistry C Bandgap Polymer:Fullerene Solar Cells with High Open-Circuit Voltage. Adv. Funct. Mater. 2012, 22, 3480−3490. (10) Kraner, S.; Widmer, J.; Benduhn, J.; Hieckmann, E.; Hoheisel, T.; Ullbrich, S.; Schütze, D.; Radke, K. S.; Cuniberti, G.; Ortmann, F.; et al. Influence of Side Groups on the Performance of Infrared Absorbing Aza-BODIPY Organic Aolar Cells. Phys. Status Solidi A 2015, 1−7. (11) Tress, W.; Leo, K.; Riede, M. Dominating recombination mechanisms in organic solar cells based on ZnPc and C60. Appl. Phys. Lett. 2013, 102, 163901. (12) Love, J.; Nagao, I.; Huang, Y.; et al. SilaindacenodithiopheneBased Molecular Donor: Morphological Features and Use in the Fabrication of Compositionally Tolerant, High-Efficiency Bulk. J. Am. Chem. Soc. 2014, 136, 3597−3606. (13) Proctor, C. M.; Albrecht, S.; Kuik, M.; Neher, D.; Nguyen, T.-Q. Overcoming Geminate Recombination and Enhancing Extraction in Solution-Processed Small Molecule Solar Cells. Adv. Energy Mater. 2014, 4, 1400230. (14) Shaw, P. E.; Ruseckas, A.; Samuel, I. D. W. Exciton Diffusion Measurements in Poly(3-hexylthiophene). Adv. Mater. 2008, 20, 3516−3520. (15) Kraner, S.; Scholz, R.; Plasser, F.; Koerner, C.; Leo, K. Exciton Size and Binding Energy Limitations in One-Dimensional Organic Materials. J. Chem. Phys.2015, submitted. (16) Kraner, S.; Koerner, C.; Leo, K.; Bittrich, E.; Eichhorn, K.-J.; Karpov, Y.; Kiriy, A.; Stamm, M.; Hinrichs, K.; Al-Hussein, M. Dielectric Function of a Poly(benzimidazobenzophenanthroline) Ladder Polymer. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 195202. (17) Nayak, P. K. Exciton Binding Energy in Small Organic Conjugated Molecule. Synth. Met. 2013, 174, 42−45. (18) Dkhissi, A. Excitons in Organic Semiconductors. Synth. Met. 2011, 161, 1441−1443. (19) Hummer, K.; Ambrosch-Draxl, C. Oligoacene Exciton Binding Energies: Their Dependence on Molecular Size. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 081202. (20) van der Horst, J.-W.; Bobbert, P. A.; Michels, M. A. J.; Bässler, H. Calculation of Excitonic Properties of Conjugated Polymers Using the BetheSalpeter Equation. J. Chem. Phys. 2001, 114, 6950. (21) Knupfer, M. Exciton Binding Energies in Organic Semiconductors. Appl. Phys. A: Mater. Sci. Process. 2003, 77, 623−626. (22) Adachi, S. Optical Properties of Crystalline and Amorphous Semiconductors: Materials and Fundamental Principles; Springer Science +Business Media LLC: Berlin, Heidelberg, 1999. (23) Guo, M.; Hayakawa, T.; Kakimoto, M.-A.; Goodson, T. Organic Macromolecular High Dielectric Constant Materials: Synthesis, Characterization, and Applications. J. Phys. Chem. B 2011, 115, 13419−13432. (24) Torabi, S.; Jahani, F.; Van Severen, I.; Kanimozhi, C.; Patil, S.; Havenith, R. W. a.; Chiechi, R. C.; Lutsen, L.; Vanderzande, D. J. M.; Cleij, T. J.; et al. Strategy for Enhancing the Dielectric Constant of Organic Semiconductors Without Sacrificing Charge Carrier Mobility and Solubility. Adv. Funct. Mater. 2015, 25, 150−157. (25) Chang, W.-H.; Gao, J.; Dou, L.; Chen, C.-C.; Liu, Y.; Yang, Y. Side-Chain Tunability via Triple Component Random Copolymerization for Better Photovoltaic Polymers. Adv. Energy Mater. 2014, 4, 1300864. (26) Cho, N.; Schlenker, C. W.; Knesting, K. M.; Koelsch, P.; Yip, H.-L.; Ginger, D. S.; Jen, A. K.-Y. High-Dielectric Constant Side-Chain Polymers Show Reduced Non-Geminate Recombination in Heterojunction Solar Cells. Adv. Energy Mater. 2014, 4, 1301857. (27) Furche, F.; Rappoport, D., III. Density Functional Methods for Excited States: Equilibrium Structure and Electronic Spectra. Theor. Comput. Chem. 2005, 16, 93−128. (28) Rappoport, D.; Furche, F. Property-Optimized Gaussian Basis Sets for Molecular Response Calculations. J. Chem. Phys. 2010, 133, 134105. (29) Turbomole V6.5, a Development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH (1989−2007) TURBOMOLE

GmbH, since (2007), available from http://www.turbomole.com, accessed March 09, 2015. (30) Ahlrichs, R.; Bär, M.; Häser, M.; Horn, H.; Kölmel, C. Electronic Structure Calculations on Workstation Computers: The program system Turbomole. Chem. Phys. Lett. 1989, 162, 165−169. (31) Ruuska, H.; Arola, E.; Kannus, K.; Rantala, T. T.; Valkealahti, S. Feasibility of Density Functional Methods to Predict Dielectric Properties of Polymers. J. Chem. Phys. 2008, 128, 064109. (32) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (33) Onsager, L. Electric Moments of Molecules in Liquids. J. Am. Chem. Soc. 1936, 58, 1486−1493. (34) Landau, L.; Lifschitz, E. Lehrbuch der Theoretischen Physik VIII, Elektrodynamik der Kontinua, 3rd ed.; Akademie Verlag: Berlin, 1980. (35) Brendel, M.; Krause, S.; Steindamm, A.; Topczak, A. K.; Sundarraj, S.; Erk, P.; Höhla, S.; Fruehauf, N.; Koch, N.; Pflaum, J. The Effect of Gradual Fluorination on the Properties of FnZnPc Thin Films and FnZnPc/C60 Bilayer Photovoltaic Cells. Adv. Funct. Mater. 2015, 25, 1565−1573. (36) Becke, A. D. A New Mixing of Hartree-Fock and Local DensityFunctional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (37) Plasser, F.; Wormit, M.; Dreuw, A. New Tools for the Systematic Analysis and Visualization of Electronic Excitations. I. Formalism. J. Chem. Phys. 2014, 141, 024106. (38) Bäppler, S. A.; Plasser, F.; Wormit, M.; Dreuw, A. Exciton analysis of Many-Body Wave Functions: Bridging the Gap Between the Quasiparticle and Molecular Orbital Pictures. Phys. Rev. A: At., Mol., Opt. Phys. 2014, 90, 052521. (39) Schaftenaar, G.; Noordik, J. Molden: a Pre- and Post-Processing Program for Molecular and Electronic Structures. J. Comput.-Aided Mol. Des. 2000, 14, 123−134. (40) Brazovskii, S.; Kirova, N. Physical Theory of Excitons in Conducting Polymers. Chem. Soc. Rev. 2010, 39, 2453−2465. (41) Weil, T.; Vosch, T.; Hofkens, J.; Peneva, K.; Müllen, K. The Rylene Colorant Family-Tailored Nanoemitters For Photonics Research and Applications. Angew. Chem., Int. Ed. 2010, 49, 9068−93. (42) Elemans, J.; vanHameren, R.; Nolte, R.; Rowan, a. E. Molecular Materials by Self-Assembly of Porphyrins, Phthalocyanines, and Perylenes. Adv. Mater. 2006, 18, 1251−1266. (43) Hoeben, F. J. M.; Jonkheijm, P.; Meijer, E. W.; Schenning, A. P. H. J. About Supramolecular Assemblies of Pi-Conjugated Systems. Chem. Rev. (Washington, DC, U. S.) 2005, 105, 1491−546.

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DOI: 10.1021/acs.jpcc.5b07097 J. Phys. Chem. C 2015, 119, 22820−22825