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A Combined Computational Approach Based on Density Functional Theory and Artificial Neural Networks for Predicting the Solubility Parameters of Fullerenes Jose Dario Perea, Stefan Langner, Michael Salvador, Janos Kontos, Gabor Jarvas, Florian Winkler, Florian Machui, Andreas Goerling, András Dallos, Tayebeh Ameri, and Christoph J. Brabec J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00787 • Publication Date (Web): 12 Apr 2016 Downloaded from http://pubs.acs.org on April 17, 2016
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A Combined Computational Approach Based on Density Functional Theory and Artificial Neural Networks for Predicting The Solubility Parameters of Fullerenes J. Darío Perea,∗,† Stefan Langner,† Michael Salvador,†,‡ Janos Kontos,¶ Gabor Jarvas,¶ Florian Winkler,† Florian Machui,§ Andreas Görling,k Andras Dallos,¶ Tayebeh Ameri,† and Christoph J. Brabec†,§ 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, University of Pannonia, H-8200 Veszprém, Egyetem street 10, Hungary, Bavarian Center for Applied Energy Research (ZAE Bayern), Haberstrasse 2a, 91058 Erlangen, Germany, and Lehrstuhl für Theoretische Chemie and Interdisciplinary Center for Interface Controlled Processes, Friedrich-Alexander-Universität Erlangen-Nürnberg, Egerlandstrasse 3, 91058 Erlangen, Germany E-mail:
[email protected]
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Abstract The solubility of organic semiconductors in environmentally benign solvents is an important prerequisite for the widespread adoption of organic electronic appliances. Solubility can be determined by considering the cohesive forces in a liquid via Hansen solubility parameters (HSP). We report a numerical approach to determine the HSP of fullerenes using a mathematical tool based on artificial neural networks (ANN). ANN transforms the molecular surface charge density distribution (sigma-profile) as determined by DFT calculations within the framework of a continuum solvation model into solubility parameters. We validate our model with experimentally determined HSP of the fullerenes C60 , PC61 BM, bisPC61 BM, ICMA, ICBA, and PC71 BM and through comparison with previously reported molecular dynamics calculations. Most excitingly, the ANN is able to correctly predict the dispersive contributions to the solubility parameters of the fullerenes although no explicit information on the van der Waals forces is present in the sigma-profile. The presented theoretical DFT calculation in combination with the ANN mathematical tool can be easily extended to other πconjugated, electronic material classes and offers a fast and reliable toolbox for future pathways that may include the design of green ink formulations for solution-processed optoelectronic devices.
∗
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, University of Pannonia, H-8200 Veszprém, Egyetem street 10, Hungary § Bavarian Center for Applied Energy Research (ZAE Bayern), Haberstrasse 2a, 91058 Erlangen, Germany k Lehrstuhl für Theoretische Chemie and Interdisciplinary Center for Interface Controlled Processes, Friedrich-Alexander-Universität Erlangen-Nürnberg, Egerlandstrasse 3, 91058 Erlangen, Germany †
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Introduction The imminent impact of climatic change as well as the world’s growing demand for energy requires fostering new forms of sustainable energy conversion involving low-waste, low-energy manufacturing. Because solution processing can facilitate large scale industrial deployment at reduced energy consumption accurate theoretical predictions of the thermodynamic, transport, chemical reactions, and electronic structure properties of solutes in solvents can effectively advance sustainable technologies. In this context, organic semiconductors bear a pivotal role because, as opposed to most traditional inorganic semiconductors, these material systems provide access to optoelectronic devices with tailored semiconductor properties, innovative form factors, low specific weight and color tunability at potentially very low cost. 1 To realize these advantages high solubility, ideally in environmental benign "green" solvents, has to be ensured. 2 This calls for a calculation approach of the cohesive forces of organic semiconductors in solution and makes the ability to predict solubility parameters very desirable. Importantly, the solubility of organic semiconductors not only affects the processability but may have important implications on the electronic performance of a finished device. For instance, the solubility of organic semiconductors may determine the sensitive morphology of both neat semiconductors and bulk heterojunction blends, particularly when considering the drying process of printed films. 3,4 The solubility, and equally important, the electronic and morphological compatibility of fullerenes with a plethora of p-type semiconductors makes fullerenes widely suited n-type semiconductors for organic and hybrid electronic devices. Conversely, the molecular structure properties, such as the rigidness and well-defined spheroid-like geometry, combined with relatively low-lying LUMO energy levels and resulting efficient three dimensional electron transport in pristine as well as blended composites are unique attributes, which render fullerenes a highly attractive model system for the experimental and theoretical calculation of solubility parameters. 5 Previous reports have provided theoretical correlations between thermodynamic properties, electronic properties and solubility parameters for model fullerenes 3
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While it has been shown before that it is possible to calculate HSP via molecular dynamics techniques and structure-interpolating group contribution methods (GCMs) those methods explore discrete molecular interaction models and require knowledge of the corresponding interaction parameters, respectively, for calculating thermodynamic properties. 6,7,10–13 Here, we demonstrate an alternative theoretical method for the determination of the solubility parameters of various fullerenes using combined first principles quantum mechanics and a mathematical tool based on artificial neural networks (ANN). Previously, high quality quantum chemical calculations have been used for predicting HSP for rather simple, lowdimensional molecules. 14 The computation of fullerenes adds an additional level of structural complexity and is of high scientific and technological relevance. We determine Hansen solubility parameters from solubility experiments and find excellent agreement between our theoretical predictions and experimental data. Furthermore, our method delivers results of significant accuracy as compared to data from GCMs and molecular dynamics (MD) calculations reported in the literature. 7,15,16 Our computational multiphysics approach is not limited by molecular structure motifs, electronic properties or empirical parameters. We thus provide a theoretical toolbox for studying thermodynamic and electronic parameters and for determining the solubility of arbitrary material classes.
Computational Model and Methodology The disentanglement of the well-known Hildebrand solubility parameter δT into the Hansen Solubility Parameters (HSPs) forms the basis for developing predictive solubility theories. 17 The Hildebrand solubility parameter is related to the density of the cohesive energy ET , which is defined as the increase in internal energy upon removal of the molecular interactions and can be thought as the energy required to fully separate a unit volume of molecules from the nearest neighbor when going into solution: 18
δT =
r 5
∆ET , V
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where V is the molar volume. The Hildebrand theory predicts that molecules with similar δT interact more closely, leading to improved miscibility. The later Hansen theory accounts for the fact that the cohesive forces in a liquid are not limited by only one type of interaction but are rather described by the combined effect of non-polar bonding (dispersive) forces, polar bonding (dipole-dipole) forces and hydrogen bonding forces: 18
ET = Ed + Ep + Ehb ,
(2)
where Ed , Ep , and Ehb correspond to dispersive, polar and hydrogen bonding energies, respectively. Accordingly, the Hildebrand solubility parameter splits into the Hansen solubility parameters (HSPs) as: 2 δT2 = δd2 + δp2 + δhb ,
(3)
with ∆Ed , V ∆Ep δp2 = , V ∆Ehb 2 δhb = . V δd2 =
δhb is the hydrogen bonding parameter, which becomes relevant in substances where hydrogen bonding to highly electronegative atoms is predominant. The polar parameter δp depends on the dipolar moment according to the Beerbower correlation. 19 This term is particularly relevant when non-symmetrical molecules are considered. Finally, the non-polar contributions, mainly originating from dispersive interactions, are contained in the dispersion parameter δd , which is related to the enthalpy of vaporization of homomorphous bondings. 20 We note that the Hansen theory is an approximation and that the molecular interactions can be more complex and thus underrepresented. Nevertheless, Hansen solubility parameter have been shown to provide a good estimation of the Flory-Huggins mixing parameter (χ) and thus 7
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of functional groups. 14 The overall computational flowchart is depicted in figure 3. While it is well known that molecular dynamics (MD) can simulate HSPs based on intermolecular forces the motivation for the present work is to demonstrate a fast and equally accurate method for the determination of the solubility parameters. We now return to the computational procedure involving COSMO-RS. COSMO-RS was originally developed for studying the thermodynamic properties of solutions and mixtures based on computation of the chemical potential of a molecule in solution via statistical thermodynamics of interacting molecular surface segments. 24–26 As opposed to the discrete model (figure 4a), which describes the molecular free energy of solvation as a sum of single solvent-solute point interactions (typically the basis for molecular dynamics calculations), COSMO-RS is based on a continuous, polarizable solvation medium, thereby reducing the number of interactions (figure 4b). The basic idea of this approach is to represent the surface charge density σ of the real solvation in form of a molecular distribution called σ-profile (P (σ)) and consequently use P (σ) in a regression function, relating material characteristics (P (σ)) to molecular properties, also referred to as quantitative structure property relationships (QSPR): X X PsX (σ) = C0 + C1 M0X + C2 M1X + C3 M2X + C10 Mhb,acc + C14 Mhb,don
(4)
where MiX is the i-th σ-moment of the solute X. The coefficients (CX ) can be derived by multilinear regression of the σ-moments using a reliable set of experimental data (Supporting Information). 27 Some of the σ-moments have a rather simple physical meaning. M0X repreX sents the total surface area of the solute X, M0X = Marea and M1X the electrostatic interaction X energy (E.I) M1X =ME.I , which is an estimation of the overall ability of the solute to interact
electrostatically with a polarizable continuum. The third moment lacks a simple physical X analogy and is best described as skewness of the σ−profile of the solute M2X =Mskew , which X X is directly related to the asymmetry of the σ-profile. The final terms Mhb,acc , and Mhb,don
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Table 1: σ-moments (MiX ) for C60 , PC61 BM, bisPC61 BM, ICMA, ICBA, PC71 BM calculated by COSMOtherm. Area (nm2 ) E. I. Skew 4.10 20.90 -8.69 5.66 83.57 17.82 6.96 136.97 -22.97 4.82 54.67 -4.80 5.37 75.30 -6.17 6.02 95.58 27.90
Molecule C60 PC61 BM bisPC61 BM ICMA ICBA PC71 BM
Hb acc Hb don 0.0 0.0 4.45 0.002 0.36 0.0 0.09 0.0 1.05 0.0 3.13 0.0
E. I. : electrostatic interaction Hb acc: Hydrogen bonding, acceptor Hb don: Hydrogen bonding, donor
quantify the ability of the solute to interact as a hydrogen-bond acceptor and donor, respectively. 25 Table 1 shows the five calculated basic σ-moments for the selected fullerenes in this work to illustrate the QSPRs involved in the regression and prediction process using ANN. We emphasize that full representation of the σ-profile (equation 4) may involve a wider range of σ-moments, which is considered in the Supporting Information.
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Results and Discussion Table 2: Experimental and computed Hildebrand parameter δT (MPa1/2 ) and Hansen parameters δd ,δp +δhb (MPa1/2 ) for the fullerenes C60 ; PC61 BM; bisPC61 BM; ICMA; ICBA; and PC71 BM. Componend C60
PC61 BM
bisPC61 BM
ICMA
ICBA
PC71 BM
δT δd δp + δhb δT δd δp + δhb δT δd δp + δhb δT δd δp + δhb δT δd δp + δhb δT δd δp + δhb
Exp.-HSPiP 28 20.10 19.70 5.60 -
Exp.-BGM 20.48 19.70 7.80 21.78 20.83 8.92 20.30 19.50 7.90 21.74 21.00 7.50 20.90 20.20 7.30
Exp.-FGAT 35 20.70 19.70 8.60 20.50 19.80 7.00 -
MD 7,36,37 21.78 20.18 7.97 20.45 20.04 4.09 21.58 20.06 7.37
DFT-ANN 20.97 20.44 6.65 21.60 20.60 9.16 25.41 24.32 8.75 20.56 20.40 2.90 20.81 20.44 5.53 21.20 20.95 4.44
Exp.:experiment; BGM: Binary Gradient Method; FGAT: Functional Group Additive Terms Method; MD: Molecular Dynamics.
The Hansen Solubility Parameters for C60 were first determined by Hansen et al. using a semi-empirical correlation method with 89 solvents. 28 HSPs for PC61 BM and PC71 BM were recently re-evaluated using the experimental binary gradient method (BGM) thus improving upon the previous values. 29,30 The HSPs for bisPC61 BM, ICMA and ICBA were determined both experimentally (BGM) and theoretically in this work for the first time (see Supporting Information for experimental details). These fullerenes are of significant scientific value because they can be used, e.g., for increasing the open-circuit voltage or preventing fullerene dimerization in organic solar cells. 31–33 Figure 1(a-f) displays the molecular structure, figure 2(a-f) the surface charge screening density and figure 5(a-f) the three-dimensional solubility space (Hansen solubility sphere) 11
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for the fullerenes PC61 BM, bisPC61 BM, ICMA, ICBA, and PC71 BM. The Hansen solubility sphere defines the solubility space. When moving inside the sphere the solubility of the solute-solvent is considered to be good. The surface charge density as calculated by the COSMO-RS model is represented by green, blue, and red color zones, which represent the neutral, negative, and positive charge density values, respectively, or, in other words, the specific polarity on the molecular surface (figure 2(a-f)). Note that the molecular polarity is of opposite sign as compared to the polarity of the surrounding solvent. As such, the negative surface charge density of the molecule is located on the right side of the σ−profile graph and has positive σ values, while the positively charged parts are located on the left side and feature negative σ values (supporting information, figure S5). 34 In general, the central region of the σ−profile is associated with non-polar or weakly polar parts of the molecule, while strongly polar and potentially hydrogen bonding acceptor regions appear at the right hand side and donor regions at the left hand side of the σ−profiles. Due to the common buckyball structure, all fullerene molecules under study have similar σ−profiles (Supporting Information). The fullerene buckyballs consist predominantly of non-polar regions (green color in the surface charge screening density visualizations in figure 2(a-f)), which can be linked to exposed surfaces of carbon atoms. The peaks located in the hydrogen bonding acceptor zones correspond to oxygen atoms (red colored areas in the surface charge density). Conversely, the peaks located in the hydrogen bonding donator region of the σ−profile correspond to hydrogen atoms of the alkyl side chain (light blue colored regions). Based on these considerations, and with respect to the Hildebrand and Hansen parameters, we can expect a significant contribution to δp + δhb , the polar region, which is indeed confirmed by our experimental measurements (cf. Table 2). Table 2 compiles the experimental Hildebrand and Hansen solubility parameters from BGM measurements as well as the theoretical predictions resulting from combined σ−moments and artificial neural network calculations. To evaluate the general validity of this approach, we compared our data against available literature data from Molecular Dynamics (MD) cal-
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culations 7,36,37 and experimental data from the Functional Group Additive Terms Method (FGAT), 35 which estimate the polar and non-polar solubility parameters, δp + δhb and δd , respectively. In all cases, we observe a very close agreement between the experimental data and our combined first principles-ANN assessment, underlining the reliability of our method for determining HSPs of novel fullerenes and derivatives thereof. Moreover, COSMO-RS features distinctive computational characteristics. Similar to the binary gradient method, the intermolecular hydrogen bonds are not explicitly induced in modern force fields. For that reason, hydrogen bonds are described as Coulomb interactions of atomic point charges. Consequently, the simulation of molecules in a solvent is based on an implicit solvent or polarizable continuum model (figure 4b), which, as shown here, affords solubility results with similar predictive power than MD. To put our theoretical data into a context of practical relevance, e.g., for organic photovoltaics, we have used the computed HSP to evaluate the solubility of the fullerenes presented here in a wide range of solvents (Table 3). A useful metric for comparison of solubilities, which is readily accessible from HSP, 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 ) according to q Ra = 4(δ1,d − δ2,d )2 + (δ1,p − δ2,p )2 + (δ1,hb − δ2,hb )2 ,
(5)
where the weighing factor 4 for the dispersion component was introduced by Hansen as a result of empirical testing. The shorter the solute-solvent distance Ra in the HSP space, the higher the solubility. Good solubility is a decisive requirement for the processing of organic semiconductor thin films into functional devices. 29 A series of three halogenated, three nonhalogenated and three commonly referred to as green or eco-friendly solvents was introduced into the HSPiP (HSP in Practice) 13 software together with the theoretically determined HSP of PC61 BM, PC71 BM, bisPC61 BM, ICMA and ICBA to determine the solubility distance
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parameter (solubility limit was set to 10 mg/mL). The results are summarized in Table 3. Note that a quantitative comparison of the solubility within this metric is only meaningful for one fullerene and different solvents (within one column in Table 3). The reason is the dependence of the experimental solubility on the distance parameter Ra , which is typically shifted for different materials. This is illustrated in Figure 6 for PC61 BM and PC71 BM using a range of solvents. Since Ra reflects the dissimilarity of the weak binding forces between solvent and solute high solubility is expected for small values of Ra while large values of Ra should translate into low solubility. This behavior is clearly apparent from Figure 6 and from comparison between experimental solubility and Ra in the case of PC61 BM, as depicted in Table 3. Furthermore, the same solubility at larger Ra values or higher solubility at the same Ra indicates that PC71 BM is generally easier to dissolve than PC61 BM. Table 3 allows additional conclusions. As expected, the best solubilities are achieved for chlorinated solvents with cholorobenzene performing typically better than dichlorobenzene while both feature superior solubility than chloroform. The non-halogenated solvents and eco-friendly solvents shown in Table 3 present similar solubilities. Several of these non-halogenated solvents are commonly employed for organic solar cell fabrication, suggesting that these green solvents could potentially be considered for device preparation. Overall, this approach could be used for fast screening of solubility spaces and thus for establishing applicationsensitive guidelines of solvent-structure properties, which could be extended to accommodate more complex solvent combinations.
Conclusion In conclusion, we explored the binary gradient method (BGM) and a multivariate nonlinear framework to derive experimentally and theoretically, respectively, Hansen solubility parameters for some of the most widely used electron accepting molecules in organic photovoltaics, i.e., the fullerene C60 and its derivatives PC61 BM, bisPC61 BM, ICMA, ICBA, and PC71 BM.
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Table 3: Absolute solubility distance Ra (MPa1/2 ) for the fullerenes PC61 BM; bisPC61 BM; ICMA; ICBA; and PC71 BM in a selection of solvents. Sol. = Solubility. HSPs for the solvents were taken from HSPiP. ?
Ra (MPa1/2 )
Sol. PC61 BM
HSPs (MPa1/2 )
δd
δp
δhb
mg/mL
PC61 BM
PC71 BM
bisPC61 BM
ICMA
ICBA
Chlorobenzene
19.00
4.30
2.00
59.5
3.95
4.28
11.04
3.70
3.25
o-Dichlorobenzene
19.20
6.30
3.30
42.1
3.25
5.32
10.43
5.36
4.24
Chloroform
17.35
1.92
1.87
28.8
7.54
7.23
14.91
6.32
6.30
o-Xylene
17.80
1.00
3.10
22.1
6.93
6.60
14.53
6.12
5.64
Toluene
18.00
1.40
2.00
15.6
6.67
6.01
13.92
5.22
5.15
Benzaldehyde
19.40
7.40
5.30
20.8
3.61
6.69
10.54
7.26
5.62
Anisole
17.80
4.40
6.90
25.6
6.23
8.26
14.38
8.63
6.97
p-Anisaldehyde
19.10
9.90
7.40
-
6.61
9.91
12.27
10.55
8.88
2-Methyl-THF
16.90
5.00
4.30
-
7.40
8.80
15.26
8.42
7.57
Solvents Halogenated
non − Halogenated
Eco − f riendly
The computation of the Hansen solubility parameters is an optimized multi-step process, which derives surface charge screening density (σ) moments from chemical potentials using the conductor-like screening model for real solvents (COSMO-RS). A key step of the present technique is the combination of nonlinear structure−property relationships with artificial neural network approaches for reliably predicting the Hansen solubility parameter from σ moments. The reliability of this strategy is apparent from the excellent agreement between our experimental and theoretical data as well as from the comparison with literature results from molecular dynamics (MD) simulations and the functional group additive terms (FGAT) method. This result is exciting because it opens up the possibility of predicting fundamental molecular properties in an early stage of molecular design, even prior to the synthesis of new molecules, which could allow a very tailored synthetic approach. As expected, the carbon heavy buckyball, the dominant structural element in the present group of fullerenes, procures the dispersion Hansen parameter as the major contribution to the Hildebrand solubility parameter. Future research should be focused on exploring artificial neural networks for anticipating device relevant performance parameters that are determined by the solubility of small molecule and polymer semiconductors in organic solvents and solvent mixtures. 16
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200
PC61BM PC71BM 150
Solubility (mg/mL)
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100
50
0 0
2
4
6
8
10
12
14
16
18
20
1/2
Ra (MPa )
Figure 6: Experimental solubility as a function of the solubility distance (Ra ) in Hansen space for PC61 BM and PC71 BM. For calculating Ra , we employed the Hansen Solubility Parameters of the HSPiP (HSP in Practice) database for the solvents and the theoretical HSPs from this work for the fullerenes. The lines are guides to the eye and represent gaussian fits to the data points.
Associated Content The Supporting Information is available free of charge on the ACS Publications website. The detailed results for the experimental determination of solubilities and the computational procedure are shown here.
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 Ciência e a Tecnologia (SFRH/BPD/71816/2010). The authors thank Peter Hausmann, Dr. Liudmila Mokrushina, and Professor Wolfgang Arlt for their kind support in the introduction to COSMO-RS. Partial Financial support was provided by the Deutsche Forschungsgemienschaft (DFG) in the framework of SFB 953 (Synthetic Carbon Allotropes) and Cluster of
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