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Introducing a Figure of Merit for Predicting Microstructure Formation in Organic Photovoltaic Blends Jose Dario Perea, Stefan Langner, Michael Salvador, Benjamin Sanchez-Lengeling, Ning Li, Chaohong Zhang, Gabor Jarvas, Janos Kontos, Andras Dallos, Alán Aspuru-Guzik, and Christoph J. Brabec J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03228 • Publication Date (Web): 05 Jul 2017 Downloaded from http://pubs.acs.org on July 8, 2017

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The Journal of Physical Chemistry

Introducing a Figure of Merit for Predicting Microstructure Formation in Organic Photovoltaic Blends José Darío Perea,† Stefan Langner,† Michael Salvador,∗,†,‡ Benjamin Sanchez-Lengeling,¶ Ning Li,† Chaohong Zhang,† Gabor Jarvas,§ Janos Kontos,§ Andras Dallos,§ Alán Aspuru-Guzik,¶ and Christoph J. Brabec∗,†,k Institute of Materials for Electronics and Energy Technology (i-MEET), Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstrasse 7, 91058 Erlangen, Germany, Instituto de Telecomunicações, Instituto Superior Tecnico, Av. Rovisco Pais, P-1049-001 Lisboa, Portugal, Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA, Department of Chemistry, University of Pannonia, H-8200 Veszprém, Egyetem street 10, Hungary, and Bavarian Center for Applied Energy Research (ZAE Bayern), Immerwahrstrasse 2, 91058 Erlangen, Germany E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Institute of Materials for Electronics and Energy Technology (i-MEET), Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstrasse 7, 91058 Erlangen, Germany ‡ Instituto de Telecomunicações, Instituto Superior Tecnico, Av. Rovisco Pais, P-1049-001 Lisboa, Portugal ¶ Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA § Department of Chemistry, University of Pannonia, H-8200 Veszprém, Egyetem street 10, Hungary k Bavarian Center for Applied Energy Research (ZAE Bayern), Immerwahrstrasse 2, 91058 Erlangen, Germany †

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Abstract A theoretical understanding of the microstructure of organic semiconducting polymers and blends is vital to further advance the optoelectronic device performance of organic electronics. We outline the theoretical framework of a combined numerical approach based on polymeric solution theory to study the microstructure of polymer:small molecule blends. We feed the results of ab − initio density functional theory quantum chemistry calculations into an artificial neural network for the determination of solubility parameters.

These solubility parameters are used to calcu-

late Flory-Huggings intermolecular parameters. We further show that the theoretical values are in line with experimentally determined data. Based on the FloryHuggings parameters we establish a figure of merit as a relative metric for assessing the phase diagrams of organic semiconducting blends in thin films. This is demonstrated for polymer:fullerene blend films based on the prototypical polymers Poly(3hexylthiophene-2,5-diyl) (P3HT) and Poly[(5,6-difluoro-2,1,3-benzothiadiazol-4,7-diyl)alt-(3,3-di(2-octyldodecyl)-2,2,5,2;5,2-quaterthiophen-5,5-diyl)] (PffBT4T-2OD). This combined model informs design criteria and processing guidelines for existing and new highperformance semiconducting blends for organic electronics applications with ideal and stable solid state morphology.

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Introduction A fundamental understanding of the thermodynamics that governs the complex nanostructural properties of organic semiconductors is of utmost relevance for both basic science and technological applications. For instance, thermodynamic driving forces determine such important processes as film formation, drying and crystallization, thereby controlling the optoelectronic properties of the semiconductor. In the case of photovoltaic polymer blends, the thermodynamics of mixing may determine the evolution of the local morphology and, consequently, alter the charge transport behavior as well as the light harvesting capabilities and overall performance lifetime of the final device. 1,2 Notably, the efficiency of the bulk heterojunction (BHJ) architecture in organic solar cells relies on the spontaneous organization energy (free energy) that forces the active layer into (in the simplest case) bi-continuous donor rich and acceptor rich regions mixed on a sufficiently fine length scale. 3 This microstructure evolution into ”phases” has been proposed as being essential to the understanding of optimum organic photovoltaic (OPV) performance. 4,5 As such, the miscibility of the donor and acceptor materials, the size and composition of the phase-separated domains, their crystalline character, the formation of percolating charge transport networks, and the vertical concentration gradient are all important factors that must be considered experimentally and theoretically for establishing guidelines towards ideal photovoltaic blends. In this context, the development of a predictive model for morphology formation is a long-lasting endeavor. Its realization would represent a powerful toolbox in the quest for highly efficient and stable device performance. While important framework has emerged in recent years in an attempt to draw a critical link between molecular interaction parameters and (experimental) polymer phase behavior in thin films, the latter is not well established for many material systems of interest. Describing the microstructure evolution of a solution that contains two components (e.g., a polymer and fullerene/small molecule derivative) is considered an important intermediate step. For instance, Janssen et al. estimated the temporal evolution of phase separation em3



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ploying the homogeneous Flory-Huggins free energy of a solvent:polymer:fullerene mixture to demonstrate that experimentally observed morphologies could be explained through spinodal liquid-liquid demixing. 6 Similarly, Dastoor et al. employed Flory-Huggins classical thermodynamics of high polymer solutions to describe the morphology evolution of polymer:fullerene nanoparticles under thermal annealing. 7 Richter et al., on the other hand, used Flory-Rehner theory, originally developed to describe swelling of a rubbery polymer, to rationalize the formation of mixed polymer:fullerene phases, 8 while Epps et al. assessed polymer-polymer interaction parameters using solvent-vapor swelling experiments to reconstruct the phase diagram of polystyrene: P3HT solutions. 9 At the same time, elaborate theoretical attempts have been presented to computationally characterize the 3D heterogeneous nanostructure of polymer blends exploring, e.g., morphological descriptors combined with graph theory, 10 dissipative particle dynamics, 11 and molecular dynamics theory. 12 These examples while short of being comprehensive underscore the practical relevance of thermodynamics approaches for organic electronics. Importantly, a wide range of spectroscopic, microscopic and calorimetric techniques are available to probe the validity of models describing the thermodynamics of mixing. 13 Despite these advances, and in light of recent results that highlight spinodal demixing as the origin for early performance instability in high-performance organic photovoltaics, 6,14 there is immediate need for a universal thermodynamics concept capable of predicting the mixing compatibility of semiconducting polymer blends. In this work, we outline a conceptually new figure of merit for describing the phase evolution (mixing thermodynamics) of prototypical polymer:fullerene bulk heterojunctions. This new model predicts relative stabilities and emerges from relating the relative Flory-Huggins interaction parameter to the spinodal demixing interaction parameter (also referred to as the spinodal line). This approach involves the calculation of relative Flory-Huggins interaction parameters using a semi-empirical routine based on an artificial neural network and expands upon our previous work for predicting the solubility parameters of fullerenes. 15 Conversely, the computation

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of the spinodal line uses the well-established thermodynamic model based on Flory-Huggins solution theory. 16 We propose that this approach is general in nature and could be employed to establish structure-morphology relationships and tailored processing conditions critical for optimal device performance.

Experimental and Computational Methods Computational Methods In previous work, we have presented in detail a computational approach for determining the Hansen solubility parameters (HSPs) of fullerenes based on combined density functional theory (DFT) and artificial neural networks (ANN). 15 The development of ANN for materials science is particularly exciting, because it allows the prediction of thermodynamic and other fundamental properties upon a thorough training routine of the neural network using molecules with diverse chemical building blocks. 17 In this work, we use the ANN as part of a comprehensive computational approach for describing the miscibility of polymers and fullerenes, which we believe is intimately associated with the microstructure of these blends. 18 The overall computational flowchart is depicted in Figure 1. Briefly, we applied ab − initio DFT to calculate the surface charge screening density σ (Figure 1, top) using the conductor-like screening model for real solvents (COSMO-RS). 19,20 COSMO-RS gives access to fundamental thermodynamic properties of solutes by translating the surface charge screening density of solvation into a regression function - called σ-profile (Figure 1, top graph). The σ-profile can be expressed through the so-called sigma(σ)-moments. Importantly, the σ-moments, which relate material characteristics to molecular properties (e.g., molecular surface area, electrostatic interaction, hydrogen bonding capability, etc.), can be employed as input parameters for ANN (right branch of the computational flowchart in Figure 1). The ANN can be trained to deliver Hansen solubility parameters as outputs. In the case of the most widely used methano-fullerenes the HSPs determined via ANN have been shown to be 6


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in good agreement with experimental values. 15 More technical details are provided in the Supplementary Information. Based on a polymeric solutions approach the HSPs are then used to establish a relative stability metric for evaluating the phase evolution of photovoltaic polymer blends, as described in the main text.

Materials The Materials chosen for verifying the theoretical framework include the polymers PffBT4T2OD (also widely known as PCE11) and P3HT, and the fullerenes PC61 BM and ICBA. P3HT and PffBT4T-2OD were obtained from BASF and 1-Materials, respectively, while PC60BM and ICBA were acquired from SolenneBV.

Experimental Determination of Hansen Solubility Parameters The determination of absolute solubility was done by preparing oversaturated solutions of PffBT4T-2OD in binary solvent blends, followed by stirring for 24 hours at room temperature. Afterwards, the samples were centrifuged at 10000 rpm for five minutes. The centrifuged saturated solutions were subsequently diluted to allow measurements of the optical density. Absorption spectra were recorded using a Perkin Elmer Lambda-950 spectrometer from 300 to 800 nm at room temperature. The absolute solubility for each solution was calculated by comparing its optical density to a calibration curve with known concentration. We employed the binary solvent gradient method (BGM) 21 to probe the surface of the Hansen sphere for a series of different solvent mixtures based on non-solvents and a good solvent. Each series consists of a fraction of chlorobenzene (CB) X / (X+Y) and a fraction of a non-solvent Y / (X+Y), where X+Y=100%. Chlorobenzene offers usually good solubility for many organic semiconductors used in organic electronic devices and is therefore used as processing solvent. As non-solvents we used: cyclohexane, pyrimidine, 1-butanol and propylene carbonate. Using BGM we then determined the Hansen solubility parameters ( δd , δp , and δhb ) of PffBT4T-2OD. This requires that the solubility is measured stepwise from 7




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the comparison of solubilities, which is readily accessible from the HSPs, is provided by the solubility distance parameter (Ra ) between two materials. Ra predicts the differences between the Hansen parameters of a solvent (δ2,d , δ2,p , and δ2,hb ) and the solute (δ1,d , δ1,p , and δ1,hb ) (here the solute is either a polymer or a fullerene) according to

Ra =

q 4(δ1,d − δ2,d )2 + (δ1,p − δ2,p )2 + (δ1,hb − δ2,hb )2 ,

(1)

where the weighting factor 4 for the dispersion component was introduced by Hansen from empirical testing. 26 A small Ra in the HSP space indicates similar intermolecular binding energies between solute and solvent, resulting in higher solubility. While seemingly simple, the solubility distance parameter is limited in its ability to comparing the solubility among different solutes, as elaborated in the following. It is well established that solvents featuring Hansen parameters close to the Hansen values of the polymer (or fullerene) represent good solvents. 26 We can test this by calculating the distance in the Hansen space, Ra (Eq. 1), for PC61 BM and P3HT in different solvents. We employed the HSPs δd =20.60 MPa1/2 , δp =4.93 MPa1/2 , δhb =4.23 MPa1/2 of the fullerene PC61 BM and δd =18.50 MPa1/2 , δp =4.60 MPa1/2 , δhb =1.40 MPa1/2 of the polymer P3HT as yielded by the artificial neural network and the binary gradient method, respectively. 15 The HSPs of the solvents were taken from the literature. 26 The results of Ra are shown in Table 1 side by side with experimental values. The trends for the solubilities among the different solvents as represented by Ra are in good agreement with the experimental values, justifying the validity of Ra as a metric of comparison for the solubility of conjugated polymers and fullerenes. However, in general, Ra allows comparability only for one solute among different solvents, but provides inadequate comparability in the case of different solutes in a common solvent. This circumstance originates from the fact that the dependence of the experimental solubility on Ra can be very different from solute to solute. Consequently, fullerenes like PC61 BM and PC71 BM show different solubilities for the same value of Ra , rendering Ra

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inappropriate for predicting the miscibility of organic semiconductors in terms of structure solubility properties. 21 An effective way of granting qualitative comparability of the solubility is to evaluate the relative interaction parameter of Flory-Huggins χ. 27 We evoke that χ describes the degree of interaction between solute macromolecules and solvent molecules, i.e., molecules of significantly dissimilar size, in the thermodynamic model based on FloryHuggins solution theory and thus provides a simple yet powerful approach for describing the phase equilibrium for most mixtures. 28 Following the Flory-Huggins regular solution theory, the interaction parameter for polymer(fullerene):solvent mixtures χ1,2 was estimated according to: 9 χ1,2 = χe + χs =

v0 (δT 1 − δT 2 )2 + 0.34 RT

(2)

where v0 is the molar volume of the solvent, R is the gas constant, T is the absolute temperature, δT 1 and δT 2 are the Hildebrand solubility parameters for the polymer and the solvent, 2 respectively (δT2X = δd2 + δp2 + δhb ). The first term of equation 2 represents the enthalpic

contribution (χe ) to the total interaction parameter and χs is the correction factor due to the entropic contribution, which is approximately 0.34. 29 Its exact value did not significantly affect the outcome of the calculations performed in this work. Table 1 shows the interaction parameter for mixtures of polymer(fullerene):solvent. We recall that similarly to Ra a smaller value of χ is indicative of good miscibility. Significantly, the interaction parameters are in better agreement with the experimental solubility data than Ra . The solubility parameters and the molar volume of the solvents employed are summarized in the Supporting Information. We now consider the Flory-Huggins interaction parameter for polymer-fullerene blend components by invoking the argument that polymer and fullerene are dissimilar enough in size to obey Flory-Huggins solution theory. This has been shown to produce consistent results. 9,30 From calculated Hildebrand solubility parameters and molar volumes shown in Table 2, we can determine a relative polymer:fullerene interaction parameter according to

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Table 1: Solubility S in mg/mL, Solubility distance Ra in MPa1/2 and Interaction parameter χ1,2 for P3HT, PC61 BM in a selection of processing solvents at room temperature. Solvents Chlorobenzene O-Dichlorobenzene Chloroform O-Xylene Toluene

S 15.9 14.7 14.1 2.7 0.7

P3HT Ra 1.20 2.91 4.76 3.67 3.41

χ1,2 0.34 0.41 0.34 0.36 0.37

PC61 BM S Ra χ1,2 35.3 3.95 0.47 44.9 3.25 0.39 30.1 6.07 0.52 21.3 6.42 0.75 10.5 6.67 0.73

Table 2: The calculated molecular weight, molar volume, liquid density and Hildebrand parameter δT for P3HT, PCE11 * Simulation 15 /Experimental (for P3HT reference 21 ). Molecule

Mol.weight (g/mol) calc. calc. exp. tot. red. 173.8 166.1 P3HT PCE11 616.9 226.4 910.5 PC61 BM 910.9 936.8 952.5 ICBA 1 cal. = calculated, exp.

Mol.volume (cm3 /mol) L.density (g/cm3 ) δT (MPa1/2 ) calc. calc. calc. calc. exp. exp. calc. exp. tot. red. tot. red. 148.7 151 1.17 1.1 19.11 467.6 187.2 1.32 1.21 19.14 548.0 607 1.66 1.5 21.60 20.48 542.7 635 1.72 1.5 20.81 21.74 = experimental, tot. = total, red. = reduced.

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eq. 3 χ1,2 =

v1,2 (δT 1 − δT 2 )2 RT

(3)

in which χ1,2 is the polymer:fullerene interaction parameter, v1,2 is the geometric mean of the polymer:fullerene molar volumes, and δT 1 and δT 2 are the Hildebrand solubility parameters for the polymer and fullerene, respectively. The entropic contribution for polymer blends is usually between 10−6 and 10−2 , i.e., much smaller in magnitude than the entropic contribution for regular solutions (≈0.34). 9 In the case of polymer:fullerene blends the entropic contribution is not well established in the literature. For this reason, we did not consider the entropic contribution to the interaction parameters in the polymer:fullerene blends. An additional complication arises when considering the molar volume (molar weight) of fairly complex co-polymers when compared with the simpler homo-polymers (e.g. P3HT). We suggest the existence of a size limit, above which the repeating unit should be treated like a polymer rather than a monomer. In case that the molecular weight of the polymer is well known, an alternative model can be employed, in which the fullerene forms the lowest lattice molar volume (v2 ). 31 This alternative model is described in the Supporting Information and its implications are described below. A look at the determined enthalpy of fusion (delta Hf0 ) for PCE11 and P3HT, listed in Table 3, shows that the values are very close to each other. This can be explained by the similar monomer structures in both polymers. We therefore propose a general method that consists of categorizing the monomer units of co-polymers into repeating building blocks. In the case of the PCE11-monomer we define three contributing groups A, B and C (Figure 1, left branch). The representation of each group can then be used as a weighting factor according to the original idea of Flory Huggins, leading to reduced material properties, which we shall call here moiety-monomer-structure-properties (MP). The resulting reduced material parameters are summarized in Table 2 (cf. Supporting Information for details). Conversely, Table 3 displays the resulting relative interaction parameters for mixtures of polymer:fullerene blends using total (uncorrected) and reduced parameters and compares the results to experimentally determined data using differential 13



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scanning calorimetry (DSC). It is possible to measure the Flory-Huggins interaction parameter (χ) by plotting the inverted temperature difference

1 Tm

− T10 as a function of the volume m

fraction φs , employing the well-known equation for melting temperature depression: 7 R vm 1 R vm 1 − 0 = φs − χ1,2 φ2s 0 Tm Tm ∆Hf vs ∆Hf0 vs

(4)

where Tm is the melting point of the polymer in the polymer:fullerene blend, Tm0 is the melting point of the pristine polymer, φs is the volume fraction of the fullerene, ∆Hf0 is the enthalpy of fusion of the polymer (for a hypothetical degree of crystallinity of 100 %), vm is the molar volume of the polymer monomer and vs is the molar volume of the fullerene. Thus, fitting

1 Tm

− T10 vs. φs with a function of the form y = ax+bx2 allows to extract χ1,2 from the m

ratio of the fitted parameters b and a. Note that Eq. (4) is only valid for diluted systems, in which a diluent (small molecule, fullerene or nanoparticle) is mixed into the polymer. The general expression for melting point depression can be found in the Supporting Information.

Table 3: Calculated relative intermolecular parameter χ1,2 for polymer:fullerene mixtures based on the total and the reduced molar volume, the experimentally determined (DSC) intermolecular parameters and the enthalpy of fusion ∆Hf0 (100 % crystallinity). χ1,2 ∆Hf0 (J/g) calc. calc. exp. P3HT PCE11 tot. red. P3HT:PC61 BM 0.71 0.78 50.3 0.33 P3HT:ICBA 0.51 49.7 54.5 PCE11:PC61 BM 1.24 0.78 0.96 0.57 0.36 0.74 PCE11:ICBA 46.2 2 cal. = calculated, exp. = experimental, tot. = total, red. = reduced. Blends

Figure 4 plots the melting point depression together with the best fits for P3HT:PC61 BM, P3HT:ICBA, PCE11:PC61 BM and PCE11:ICBA. The experimentally determined interaction parameters compare well with the computed semi-empirical values (Table 3). We observe the right trend, however, without quantitative agreement. To further verify the quality 14


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highest probability for phase separation, giving rise to the critical interaction parameter χc . As such, a homogenous mixture across the entire volume fraction requires a Flory-Huggins interaction parameter smaller than χc . The liquid (melt) - solid transition of P3HT:ICBA is overall slightly upshifted compared to P3HT:PC61 BM and P3HT:TC61 BM, indicating that P3HT:ICBA is less susceptible to phase separation. Yet, in this representation it is the distance between the interaction parameter (vertical lines) and the spinodal line that is most meaningful. A larger distance suggests a more stable, but still metastable, one-phase mixture. This can be rationalized considering vitrification effects due to fast drying of the wet film during film processing. As a result, the created morphology is trapped in a metastable state. This procedure is thought beneficial for the generation of an optimized electrical interplay between donor and acceptor and is kinetically driven rather than thermodynamically. Importantly, the absence of the solvent (after drying) - a key driver for controlling the morphology - in Eq. 5 renders this model a simplified representation for thin films. 34 While still valuable for correctly describing trends, this model may yield an underestimation of the driving force leading to phase separation, as is apparent from the rather large values for χc when compared with previous results. 7,18 At this point, we emphasize that by neglecting the degree of polymerization we overestimate χc and, as a result, obtain a rather symmetrical spinodal line. Knowledge of the degree of polymerization allows the regular solution theory to be employed, in which case the fullerene plays the role of the solvent. Such a model leads to more asymmetric, i.e., more realistic spinodal lines, as shown in the Supporting Information. We have made the code for the computation of the spinodal line and the FoM available online (https://github.com/beangoben/relative_miscibility_fom). To remove possible ambiguity associated with v1,2 and improve the accuracy of polymer blend theory (Eq. 5) for predicting the mixing behavior of polymer - small molecule blends in thin film we propose the following figure of merit (FoM) with respect to the relative miscibility: FoM =

χ1,2 χSpinodal

=

(δT 1 − δT 2 )2 2 ρ2 ) RT ( Mρ11φ1 + M2 (1−φ 1) 17


(6)



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Figure 5. This suggests that replacing PC61 BM with ICBA should result in a polymer blend that is less prone to phase separation. To validate this outcome we carried out photoluminescence quenching experiments (PL) on blend films of PCE11:PC61 BM and PCE11:ICBA before and after 72 hours of thermal annealing (80 ◦ C) (Figure 7). While the PL signal of the PCBM-based blend increases by more than 40 %, the PL signal of ICBA blends changes by less than 10 %. An increase in PL intensity reflects phase separation beyond the length scale of the exciton diffusion length, typically in the order of tens of nanometer. This is frequently followed by precipitation and re-crystallization of fullerene domains (Figure 7 a & b and S11). The occurrence of fullerene crystallites is clearly apparent from optical micrographs in the case of PCE11:PC61 BM (Figure S11). No such crystallites emerge in the case of PCE11:ICBA when probed on the same length and time scale. A more robust microstructure when substituting PCBM for ICBA has also been observed in the case of P3HT. 7 Thus, the figure of merit put forward in this work provides a metric of comparison for evaluating the thermodynamic compatibility of current and future semiconducting polymer blends.

Conclusion In conclusion, we propose a Figure of Merit (FoM) on the basis of Flory-Huggins theory for spinodal demixing as a metric for describing relative trends of microstructure evolution in semiconducting polymer - fullerene bulk heterojunction blends. The amenability of the computational model for determining molecular interaction parameters via well-established molecular simulations allows to extend this approach to other selected classes of materials that obey the Flory-Huggins principle. A particular interesting scenario could be the comparison with the emerging class of non-fullerene acceptors when blended with conjugated polymers. We envision that the FoM suggested in this work will allow us to rationalize structure-morphology relationships such as donor-acceptor morphology, crystallinity, and interfacial area; properties that are relevant to optoelectronic device functionality. This also

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ysis; photoluminescence measurements.

Author Information Author Contributions J.D.P. and S.L. contributed equally to this work.

Corresponding Authors ∗ M.S. email: [email protected] ∗ C.J.B. email:[email protected]

Notes The authors declare no competing financial interest.

Acknowledgements J.D.P. is funded by a doctoral fellowship grant of the Colombian Agency COLCIENCIAS. M.S. acknowledges primary support from a fellowship by the Portuguese Fundação para a Ciencia e a Tecnologia (SFRH/BPD/71816/2010).Partial Financial support was provided for the Deutsche Forschungsgemienschaft (DFG) in the framework of SFB 953 (Synthetic Carbon Allotropes) and Cluster of Excellence "Engineering of Advanced Materials", Solar Technologies go Hybrid (SolTech) and Umweltfreundliche Hocheffiziente Organische Solarzellen (UOS). C.Z. would like to acknowledge the financial support from the China Scholarship Council (CSC). N.L. acknowledges the financial support from the ETI funding at FAU, the DFG grant: BR 4031/13-1, and the Bavarian Ministry of Economic Affairs and Media, Energy and Technology by funding the HI-ERN (IEK11) of FZ Jülich. B.S.L and A.A.G are supported as part of the Center of Excitonics, and Energy Frontier Research Center funded 21



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by the US Department of Energy, Office of Basic Sciences (DE -SC0001088). Acknowledgements are also given to Dr. Tayebeh Ameri and Dr. Anders Fröseth for their generous support for this work.

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