Solubility Characteristics of PCBM and C60 - The ... - ACS Publications

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Solubility Characteristics of PCBM and C60 David Boucher*,† and Jason Howell‡ †

Department of Chemistry and Biochemistry and ‡Department of Mathematics, College of Charleston, 66 George St., Charleston, South Carolina 29424, United States S Supporting Information *

ABSTRACT: Empirical data indicate that several good solvents for C60 and [6,6]-phenylC61-butyric acid methyl ester (PCBM) have substantial polar and hydrogen-bonding components, which are not intrinsic to the structure of the C60 and PCBM molecules themselves. Functional solubility parameter (FSP) and convex solubility parameter (CSP) computations are performed on C60 and PCBM using solubility data available in the literature. The CSP and FSP results are compared to previously reported Hansen solubility parameters (HSPs) and to the parameters calculated using additive functional group contribution methods. The CSP and FSP methods confirm the anomalously large polar and hydrogen-bonding parameters, δP and δH, obtained experimentally for C60 and PCBM. This behavior, which is quite irregular given the structure of the molecules, is due to the fact that several good solvents have high δP and δH values. Thus, these irregularities are highlighted by the CSP and FSP calculations. Additional contradictory solubility characteristics are disclosed by comparing the experimental solubility parameters to a linear solvation energy relationship (LSER) model, additive functional group calculations, and COSMO-RS computations. The FSP solubility function strongly suggests that the solubility parameters do not accurately represent the cohesive energy density properties of C60 and PCBM, as intended, but rather they manifest the properties of the solvents, e.g., high δP and δH values, that are necessary to accommodate these molecules in the liquid phase.

1. INTRODUCTION The chemical, mechanical, and optical properties of fullerene (C60) and fullerene derivatives make them outstanding molecules for a multitude of applications including photovoltaic and optoelectronic devices, chemical sensors, hydrogen gas storage, cancer therapies, and as antibacterial agents. For example, [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) is a fullerene derivative that has emerged as a benchmark electron acceptor in organic photovoltaic (OPV) materials. Typically, PCBM is combined with an electron donor polymer moiety in solution, and the mixture is processed to form functional optoelectronic and photovoltaic materials. Endohedral fullerenes, wherein additional compounds are inserted within the fullerene cage, are promising as drug carriers or for delivering contrast agents for imaging. To harness the full potential of fullerene and PCBM in the biological and material sciences, it is vital to know their solubility behavior as well as their mutual solubility and miscibility in material blends. Operating under fundamental solubility assumptions (i.e., the “like-dissolves-like” rule), it is expected that good solvents generally reflect physicochemical properties of the solute molecule. However, several studies in the literature empirically indicate that several good solvents for C60 and PCBM have substantial contributions from polarity and hydrogen-bonding aspects of their structure. This behavior is peculiar given the composition and structure of C60 and PCBM themselves. In this paper we investigate these anomalies by analyzing the solubility characteristics of C60 and PCBM using several different approaches. © 2016 American Chemical Society

Solubility parameters, which are a basic physicochemical property of a substance, have played a critical role in the screening and selection of solvents. The solubility parameters of a compound are typically obtained by studying the solubility of a substance in a series of solvents. Based on the solubility characteristics of the substance, solvents are then divided into two categories: good solvents and poor solvents. The solvents are plotted in a three-dimensional Hansen space that partitions the internal cohesive solvent forces between the dispersion (δD), permanent dipole (δP), and hydrogen bonding (δH) interactions in the solvent. In Hansen theory, (1) the δD parameter accounts for nonspecific intermolecular interactions related to dispersion forces, (2) polar interactions attributed to permanent dipole−permanent dipole forces are registered by the δP parameter, and (3) the δH is the “hydrogen-bonding” parameter. Under the binary classification of solvents, a sphere in the δDδPδH parameter space is constructed based on the notion that good solvents for the solute should lie within the sphere, while nonsolvents should lie on the outside of the sphere. The coordinates of the center of the sphere are then used to represent the Hansen solubility parameters (HSPs) of the solute under investigation. Based on similarity criteria, solutes should be more soluble in solvents with comparable solubility parameters. A more thorough discussion of Hansen Received: September 13, 2016 Revised: October 17, 2016 Published: October 17, 2016 11556

DOI: 10.1021/acs.jpcb.6b09273 J. Phys. Chem. B 2016, 120, 11556−11566

Article

The Journal of Physical Chemistry B Table 1. FSP, HSP, and CSP Values of C60 Using Data in Hansen and Smith3 a type FSP CSP

HSPc a

threshold, X 1 1 1 1 1

× × × × ×

10−3 10−4 10−5 10−6 10−3

δD (MPa1/2)

δP (MPa1/2)

δH (MPa1/2)

δP + δH (MPa1/2)

δTb (MPa1/2)

18.9 19.3 18.6 18.2 17.8 19.7

3.8 3.0 5.1 4.9 5.6 2.9

4.6 3.2 4.7 4.8 5.9 2.7

8.4 6.2 9.8 9.7 11.5 5.6

19.9 19.8 19.9 19.5 19.5 20.1

The FSP and CSP parameters were computed using the mole fractions concentrations (X) of C60. bδT = (δD2 + δP2 + δH2)1/2. cFrom ref 4.

2. METHODS 2.1. Solubility Parameter Calculations. The solubility data and Hansen solubility parameters (HSPs) in for C60 and PCBM were taken from the literature. The reader is referred to those references for a complete description of the experimental procedures and the methods used to calculate the HSPs. Using the data from the literature, we calculated the convex solubility parameters (CSP) and functional solubility parameters (FSP) using methods recently developed in our group.1,9,10 The CSPs were computed using multiple thresholds of the dissolved concentration (mg mL−1 units) or mole fraction (X) of the solute in each solvent. A binary classification system was used to define solvents with concentrations above the threshold as “good” solvents and those with concentrations below the threshold as poor solvents. The solubility region of the solute in the δDδPδH space was taken to be the convex hull of the good solvents. The solubility parameter of the solute was found as the centroid of the solubility region, treating it as a solid with constant density.1 Functional solubility parameters (FSPs) were calculated using the convex hull of all solvents. In this approach a threshold concentration was not used. Instead, the affinity of the solvent for the solute, regardless of how small the solubility, was used to define a spatial domain and a solubility function f that interpolates the dissolved concentration of the solute in each solvent was constructed in this domain. The solubility parameter of the solute was calculated by finding the centroid of the spatial domain while treating f as a weighting, or density, function.9 2.2. COSMO-RS Calculations. The initial step of the COnductor-like Screening MOdel for Realistic Solvation (COSMO-RS) quantum chemical calculations is performed on C60, PCBM, and methyl 5-phenylpentanoate (M5PP) in the presence of a virtual perfect conductor surrounding the solute outside a solvent accessible cavity. This state is called the COSMO reference state.11 The molecular geometry of the three molecules was optimized by full DFT/COSMO calculations, using the TURBOMOLE program package8 with Becke−Perdew (BP) density functional12,13 and a TZVPD basis set.14 The COSMOtherm program was then used for statistical thermodynamics calculations of σ-potentials and chemical potentials using a BP_TZVPD_FINE_C30_1501 parametrization.8 For each compound the logarithmic activity coefficient, ln(γ), in each pure solvent was computed by with the COSMOtherm program. By default, this option computed the chemical potentials of the pure compounds, μj,pure, and subsequently the chemical potentials at infinite dilution in a given solvent compound S, μj,S. The logarithmic activity coefficients were then calculated as

solubility parameter theory is given in the Supporting Information (section SII). Recently, we investigated the solubility region of a polymer as a subset of the δDδPδH space formed by the convex hull of all known good solvents of the polymer and introduced the convex solubility parameters (CSPs).1 Mathematically, the convex hull of a set of points is the smallest possible set that contains all convex combinations of those points, and the CSPs are a focal point of the space of good solvents. The solubility region is computed using empirically determined parameters of solvents that are known to dissolve the polymer. In this way, the uncertainty in selecting a good solvent is reduced when the solvent lies within the compatibility region. In that paper we provided a convincing case to employ the convex hull representation of the solubility region of a polymer and to use the center of mass of the solid formed by the hull as the convex solubility parameter (CSP) for the polymer. We also showed that the CSP approach has several advantages and addresses several issues that have risen in the use of the Hansen sphere and Hansen solubility parameters (HSPs). In a follow-up study, we introduced the functional solubility parameter (FSP). The FSP method extends the main ideas behind the convex hull/CSP approach by incorporating quantitative solubility data. This new approach utilizes a function defined on a subset of the δDδPδH space whose output gives the dissolved concentration of the solute (in mg mL−1) in a solvent with coordinates (δD, δP, δH). The solubility function can be approximated using observed solubilities in a small or moderate number of solvents, the domain of the approximate function is taken to be the convex hull of all solvents with affinity, and the approximate FSP can be calculated using numerical integration. The FSP approach overcomes several limitations of the HSP and CSP approaches and gives a solubility parameter much more consistent with experimentally observed solvent affinity data. In this paper we apply the FSP and CSP methodologies to fullerene (C60) and PCBM using solubility data available in the literature.2−5 We compare our results to previously reported solubility parameters obtained using the Hansen sphere approach as well as the solubility parameters calculated from additive group contribution methods.6,7 Finally, the activity coefficients of PCBM, C60, and the methyl 5-phenylpentanoate (M5PP) side group of PCBM in the experimental solvents are computed using COSMO-RS.8 Correlations between activity coefficients and the experimental solubility data are used to investigate the impact of the fullerene and M5PP side group moieties on the solubility behavior of PCBM. Our computational results are in good agreement with recent atomistic molecular dynamics simulations of the solubility behavior of C60 and PCBM.

ln(γ ) = (μj ,S − μj ,pure )/RT 11557

(1) DOI: 10.1021/acs.jpcb.6b09273 J. Phys. Chem. B 2016, 120, 11556−11566

Article

The Journal of Physical Chemistry B

3. RESULTS AND DISCUSSION 3.1. Solubility Parameters of C60. The solubility parameters for C60 obtained by fitting the data from Hansen and Smith are presented in Table 1. The CSP and FSP parameters in Table 1 were computed using the mole fraction solubility of C60, X, shown in Table S1 of the Supporting Information. For comparison, the FSPs and CSPs calculated using the mg mL−1 concentrations, C, are given in Table S5. Because there is a reasonable correlation between X and C (Figure S1), there is good agreement between the FSPs and CSPs obtained using both concentration units. As discussed in more detail later, the structure and symmetry of C60 are expected to give δP = δH ≈ 0, but the plots in Figures 1b and 1c show that relatively high C60 solubilities are observed

The varying behavior of the fullerene solubility with respect to the δD, δP, and δH axes is visualized by the solubility function in Figure S3. Additional plots and projections of the convex hulls and solubility function of C60 in the δD, δP, and δH planes are shown in Figures S2 and S3. The HSP values in Table 1 most closely agree with the CSPs that are computed using a relatively high threshold concentration, X = 1 × 10−3. The cutoff for the HSP calculation was log(X) = −3 (X = 1 × 10−3) and any solvent wth log(X) < −3 was deemed to be a “poor” solvent. Based on this criterion, the last solvent included in the set of good solvents is chlorobenzene with log(X) = −2.99 (C ≈ 6.2 mg mL−1). Using this cutoff, only 15 of the 86 solvents are deemed to be “good” solvents, and it omits a large set of solvents with realtively high concentrations in the range X ≈ 2 × 10−4−7 × 10−4 (C ≈ 1− 5.5 mg mL−1). Reducing the threshold to X ≈ 1 × 10−4 causes notable increases of ∼70% and 50% in the δP and δH CSP values, respectively. Thus, it appears that a good deal of information is squandered by omitting 71 of the 86 solvents. However, the question of which concentration value to use as the good/poor solvent threshold is not easily answered. As can be observed in Table 1, lowering the concentration threshold to very small values produces CSP results that seem to produce very large δP and δH values. This is due to the fact that the CSP approach treats all good solvents equally, and this is overcome by the FSP approach, which takes the quality of solvent into account when computing the solubility parameters. The experimental data in Figures 1b and 1c, as well as the HSP, CSP, and FSP values in Table 1, highlight a recurring issue with the solubility parameters for semiconductors like C60 and PCBM: anomalously large δP and δH parameters. We observe similar behavior for the semiconducting polymer, poly(3-hexylthiophene) (P3HT), which will be presented in a separate publication. Later, we will further address the irregular behavior of the δP and δH parameters in terms of a linear solvation energy relationship (LSER), additive functional group calculations, and COSMO-RS computations. We assessed the relationship between similarity criteria (“like-seeks-like”) and the solubility of C60 in a much broader sense using the solvent classification system developed by Aubry et al.15 Aubry and co-workers used a principal component analysis to divide 153 common organic solvents into 10 classes, or clusters, based on the characteristics of their σ-potentials and σ-profiles obtained using COSMO-RS. We are able to classify 56 of the 86 using the assignments reported by Aubry et al., and the cluster assignment of each solvent is given in Table S1. Based on the structure of C60 and the similarity criteria associated with Hansen solubulity parameter theory, one would predict higher C60 solubilities in apolar solvents. Although 23 of the 56 solvents in Table S1 are classified as apolar (cluster V), these solvents cover the full range of solubilities. Moreover, in the group of solvents at the bottom of the table in which the concentration of C60 is X ≤ 2 × 10−5 (C ≤ 0.1 mg mL−1), there are 11 solvents belonging to the amphiprotic cluster (VII) and 9 classified as apolar. There is no apparent trend in the solubility of C60 in terms of the solvent classifications. The one obvious relationship in Table S1 is that, with the exception of carbon disulfide, C60 is more soluble in large polycyclic hydrocarbons and aromatic hydrocarbons with halogen substitution. This trend could be because an increase in solvent molecular size supports solvation of the large fullerene molecules and/or it is an indication of the dominant role of the dispersions interactions, which are enhanced by large halogen

Figure 1. Dissolved concentrations of C60 plotted as a function of (a) δD, (b) δP, and (c) δH. The vertical lines denote the values of each solubility parameter for C60 computed using the Hansen sphere (HSP), the convex hull (CSP) at the solubility threshold X = 1 × 10−3, and the solubility function (FSP).

in solvents with moderate polar and hydrogen-bonding parameters. For both the δP and δH parameters of the solvents the full range of the fullerene solubility is observed within the range 0−6 MPa1/2, and there is a notable number of solvents in the 6−9 MPa1/2 region that have reasonably high concentrations. In contrast, as shown in Figure 1a, the solubility of C60 exhibits a reasonably monotonic increase with increasing δD. 11558


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The Journal of Physical Chemistry B Table 2. Coefficients and Fitting Parameters for LSER Model of C60 N

C1

C2

C3

C4

R2

σ

F

82 26 26

−0.143 ± 0.008 −0.138 ± 0.015 −0.135 ± 0.011

1.158 ± 0.389 0.154 ± 0.642 N/A

0.209 ± 0.020 0.198 ± 0.044 0.196 ± 0.043

−0.051 ± 0.005 −0.046 ± 0.016 −0.046 ± 0.015

0.9737 0.9837 0.9837

0.752 0.665 0.651

740 332 462

atoms and cyclic structures.2,3 The latter is consistent with the trends observed in Figure 1. Although the solubility of fullerene is primarily influenced by dispersion interactions, the forces associated with the polar and hydrogen-bonding parameters of the solvents do play a significant role augmenting the solvent affinity for C60. Solvents and solutes do not interact with one another in the same way that they interact with themselves in their pure state, yet we are using the cohesive energy density (CED) of the pure solvents to evaluate the corresponding interactions and CED of the solute. The nonzero polar and hydrogen-bonding parameters of fullerene may actually register auxiliary solvent−solvent interactions required to create a stable cavity to accommodate the solute. These parameters may be a manifestation of geometric, structural, and energetic effects ascribed to free volume changes that take place during solvation, which are not accounted for in the theory of regular solutions upon which the solubility parameter theory is based. From this perspective the dependence of the fullerene solubility on the size of the solvent molecules is practical because the latter defines the characteristic length scale of the solvent and for a liquid composed of larger molecules the free volume is distributed into larger packets,16−18 thereby more readily transforming into a cavity size distribution that can accommodate the large C60 molecules. 3.2. Linear Solvation Energy Relationship Model of C60. To explore the effect of the solvent size in greater detail, we used the multivariate statistical analysis reported by Marcus and co-workers.19 We applied a linear solvation energy relationship (LSER) model to the perform a multiple regression of mole fraction solubility of C60, XS,C60. log(XS,C60) = C1ET (30) + C2β + C3R m + C4Vm

cavity to accommodate the solute molecule(s), and the correlation between the solubility and Vm reveals the extent of direct solvation interactions. Within this model the ET(30) and β parameters describe specific solvent−solute interactions, while Rm and Vm are used to account for nonspecific interactions attributable to solute size, dispersive interactions, or from the solvent acting as a dielectric medium.25,26 The values of the parameters used in eq 2 are given in Table S2 of the Supporting Information. Table 2 shows the coefficients, Ci, obtained for our regression analyses. In the first trial we fit all the solvents (N = 82) in Table S2. For direct comparisons with PCBM, which is discussed in the next section, we repeated the fullerene fit using a similar set of solvents (N = 26) as PCBM. The relative contribution of each parameter to the overall variance is estimated from the ratio of the coefficient to the standard error of the coefficient.19 For the larger set of solvents (N = 82) ET(30) contributes the most to the variance (∼43%), followed by Rm (∼25%), Vm (∼25%), and β (∼7%). For the smaller set of solvents the R2 increases and σ decreases, thereby implying a better fit. However, the standard error of the β parameter coefficient, C2, is 6 times larger than the value of C2. Also, the p-value for C2 (N = 26), 0.812, is much larger than α = 0.05, whereas for N = 82 the p-values of all four coefficients are less than 0.05. As shown in the bottom row of Table 2, omission of the β parameter in eq 2 does not appreciably change the values of coefficients, the standard errors, R2, or σ, and in fact, the F factor increases slightly. Therefore, the β parameter is not required to perform the regression for the smaller set of solvents. Here we choose to use the smaller set taken from the literature for our analysis of PCBM, but it is evident that a solubility study of PCBM in a large set of disparate solvents similar to those used for C60 is desirable to conduct a parallel LSER study of PCBM. The LSER results are similar to those reported by Marcus et al., but in our study we used a different set of solubility data. The first significant result is the failure of the total solubility parameter, δT, to be substituted for Vm as the cavity term. Not only is the p-value for the coefficient ≫0.05, but this substitution forces the p-value of the β parameter above 0.05 as well. The same result is observed if we perform the fit using the individual HSPs (δD, δP, and δH) of the solvents. The complete failure of the δ parameter to act as the cavity term is notable because, by definition, δT is a measure of the total cohesive energy density of the solvent. Specifically, δT registers the energy required to separate solvent molecules from one another, and it would appear to be a good measure of the solvent−solvent interactions that are interrupted to create a cavity for the solute. The second notable observation is the negative dependence of the solubility of C60 on the molar volume of the solvent, C4 = −0.051. As discussed above, the trend in Table S1 suggests that C60 is more soluble in large polycyclic hydrocarbons and aromatic hydrocarbons, but this result contradicts the notion that the solubility increases with increasing molar volume of the solvent. When the effect of the molar volume is evaluated using

(2)

The four variables in eq 2, e.g., ET(30), β, etc., which are taken from the literature, have been used extensively in linear solvation energy relationship (LSER) expressions to develop predictive structure−activity relationships for a variety of configurational properties in solution.20 ET(30) is a solvatochromic parameter developed by Reichardt and co-workers that is a measure of “general polarity”, or overall solvating capabilities, of the solvent.21−23 The ET(30) parameter of a solvent is defined using the transition energy (kcal mol−1) of the π−π* transition of the betaine dye, which is sensitive to the polarity and acidity (hydrogen-bond donor ability) of the solvent. The latter makes ET(30) sensitive to the selfassociation behavior of the solvents and, as a result, with the work needed to create a cavity for the solute. The β parameter registers the electron pair donor−acceptor interactions between the solvent and the solute, wherein the solvent acts as the hydrogen-bond acceptor (electron pair donor), i.e., type B hydrogen bonding.24 The molar refraction, Rm, is a function of the refractive index, n, that is calculated from the molar volume and molar polarization, Pm, of the solvent, Rm = VmPm, where Pm is obtained from the Lorenz−Lorentz equation, Pm(n) = (n2 − 1)/(n2 + 2). The last term in eq 2, Vm, is the molar volume of the solvent. The molar volume is used as a cavity term in LSER to account for the free energy (or enthalpy) needed to form a 11559


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The Journal of Physical Chemistry B Table 3. FSP, HSP, and CSP Values of PCBM Using Data in Ref 5a type FSP CSP

HSPc a

threshold, X

δD (MPa1/2)

δP (MPa1/2)

δH (MPa1/2)

δP + δH (MPa1/2)

δTb (MPa1/2)

1 × 10−2 1 × 10−3 1 × 10−4 1 × 10−5 N/Ad

18.8 19.7 18.8 18.4 18.3 19.7

5.1 4.2 4.5 4.4 6.2 2.4

6.2 6.8 6.2 6.7 7.3 7.1

11.3 11.0 10.7 11.1 13.5 9.5

20.4 21.3 20.3 20.1 20.7 21.1

The FSP and CSP parameters were computed using the mole fractions concentrations (X) of PCBM. bδT = (δD2 + δP2 + δH2)1/2. cFrom ref 5. Threshold = 0.5 mg mL−1.

d

Table 4. Experimental Solubility Parameters for Fullerene and PCBM reference 3

C60 (Hansen and Smith) C60 (Ruoff et al.)2 PCBM (Machui et al.)4 PCBM (Machui et al.)5 PCBM (Machui et al.)5 PCBM (Duong et al.)28 PCBM (Vongsaysy et al.)29

δD

δP

δH

δT

method

19.7

2.9

2.7

20.4 21.0 19.7 19.9 20.0

3.5 2.9 7.4 5.7 5.2

7.2 8.1 6.6 3.6 5.9

20.1 20.0 21.9 22.7 22.0 21.0 21.5

data from literature (89 solvents) calibrated HPLC (47 solvents) visual inspection (34 solvents); threshold: 2.5 mg mL−1 UV/vis absorption (36 solvents); threshold: 2 mg mL−1 UV/vis; binary gradient (3 solvent blends); threshold: 2 mg mL−1 UV/vis absorption (27 solvents) threshold: variable visual inspection (34 solvents, 10 mixtures); threshold: 2 mg mL−1

a multivariate LSER model, the fit reveals that the solubility decreases slightly with increasing molar volume. The solubility decrease may be a result of a smaller number of solvent molecules surrounding the C60 molecule, whereby solubility is not so much dependent on the cavity size but in the number of direct solvent−C60 interactions, which was previously posited Marcus et al.19 Similarly, the C1 coefficient indicates that an increase in the general polarity of the solvent, as registered by the ET(30) parameter, acts to decrease the solubility. As noted above, ET(30) is the dominant factor, as evidenced by the large contribution to the variance (∼43%). In light of the anomalously large experimental δH parameter of C60, it is noteworthy that the β parameter is not a more dominant factor in the LSER model, contributing only ∼7% toward the total variance when it is included in the fourparameter fit. However, the δH parameter is not rigorously a “hydrogen-bonding” parameter. The δD parameter accounts for nonspecific intermolecular interactions related to dispersion forces, and δP registers the polar interactions attributed to permanent dipole−permanent dipole forces. As a result, δH is left to account for all of the remaining specific intermolecular interactions such as localized interactions involving specific orbitals, charge-transfer interactions, π−π electron interactions, acid−base interactions, hydrogen bonding, and other complex forming interactions. Thus, the enhanced solubility of C60 in solvents acting as electron pair donors (positive β-dependence) could stem from other processes not rigorously involving hydrogen bonding, the import of which is reflected by the uncharacteristically large δH of C60. 3.3. Solubility Parameters of PCBM. The solubility data for PCBM in 36 solvents, which were taken from Machui et al.,5 are shown in Table S3 of the Supporting Information. For the purposes of this study, all solubilities in Table S3 reported 0), and (3) a decrease in the molar volume of the solvents (C4 < 0). All three trends are similar to the LSER fit for C60, as well as the variance associated with each parameter, wherein ET(30) contributes the most to the variance (∼47%), followed by Rm (∼28%) and Vm (∼24%). The LSER results are somewhat surprising because although the phenyl/butyric acid methyl ester moiety enhances the solubility of PCBM relative to C60, the observed trends indicate that the side group does not significantly impact the nature of the solvent−solute interactions. 3.5. Comparison with Additive Group Contribution Methods. The solubility parameters from the literature in Table 4 exhibit notable variations depending on the details of the experimental method. In effort to obtain an equitable

the PCBM solubilities in Table S3 are plotted as a function of each solubility parameter coordinate, and the locations of the FSPs, as well the CSP and HSP values for the lowest threshold (0.5 mg mL−1), are marked with lines. Additional plots and projections of the convex hulls and solubility function of PCBM in the δD, δP, and δH planes are shown in Figures S4 and S5 of the Supporting Information. For PCBM the FSP approach yields a polarity parameter, δP = 5.1 MPa1/2. Although this value is very close to the parameter reported by Duong et al. and Vongsaysy et al., it is notably larger than the value reported by Machui et al., δP ≈ 3.2 MPa1/2, which is the same data we used to generate the solubility function, thereby highlighting the difference between the HSP and FSP approaches. The most recent investigation by Machui and co-workers using a binary gradient approach yielded an even larger value, δP ≈ 7.4 MPa1/2. Based on the experimental solubility data of PCBM and the location and densities of the high solubility data points in Figure 2b, values of the polarity parameter between 4 and 6 MPa1/2 appear to appropriate. The FSP and CSP δD parameters in Table 3 are lower than the HSP values in Table 4. The δT = 20.4 MPa1/2 from the FSP approach is very close to the δT recently reported by Perea et al. using a binary solvent mixture gradient approach.27 However, the δD = 19.7 MPa1/2 and δP + δH = 7.8 MPa1/2 in that study are appreciably different than the FSP results. The polar and hydrogen-bonding FSPs of PCBM are both ∼30% greater than the FSPs of C60. A larger value for both parameters is expected due to the addition of the phenylbutyl methyl ester side chain, and although we cannot comment on the accuracy of the 30% increase, our values are in good agreement with those recently reported by Vongsaysy et al. The effect that the ellipsoidal restriction has on the solubility parameters is illustrated by the graphs in Figure 2. In Figure 2a there is a high density of data points in the region δD > 18.5 MPa 1/2 that is associated with relatively large PCBM concentrations, CP3HT > 10 mg mL−1. However, for the lowest threshold concentration in Table 3, Cth ≈ 0.5 mg mL−1 (Xth = 1 × 10−5), the δD HSP is observed at a lower value, δD = 17.9 MPa1/2. This value, which is represented by the dotted vertical line in Figure 2a, actually lies at the edge of the high solubility region. Similar behavior is observed for the δP parameter in Figure 2b. In Figure 2c the δH HSP is shifted slightly higher away from the region of high PCBM concentration. In all instances the dependence of PCBM solubility on the solvent− PCBM interactions associated with each parameter is not sufficiently accounted for by an ellipsoidal compatibility region. Because of the symmetry restriction, the ellipsoidal fitting model cannot adequately discriminate between the forces associated with orthogonal axes; i.e., the intermolecular interactions related to the dispersive, polar, and hydrogenbonding parameters contribute equally to the solubility behavior. The CSP and FSP approaches allow the compatibility region to smoothly and independently vary in all three dimensions, thereby providing a qualitative measure of the sensitivity of the solubility behavior to the intermolecular forces associated with the δD, δP, and δH parameters. The structure of the convex hulls and the solubility function in Figures S4 and 11561


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the computed screening charge density surface (σ-surface) contains all relevant information to enable a highly efficient calculation of the chemical potential of a solute, pure liquid, or liquid mixture. The σ-profile, P(σ), represents a histogram or distribution of the charged surface segments of a molecule, and the associated σ-potential, μ(σ), can be represented by a Taylor series with respect to σ-moments, MXi

measure of reliability, we used an functional group contribution method developed by Hoftyzer and van Krevelen (VK-H) to calculate the solubility parameters of PCBM and C60.35 This approach assumes that the contributions of the different functional groups to the cohesive energy of a molecule follow additivity rules. We computed these parameters in two ways, employing (1) the original molar attraction constants reported by van Krevelen and Hoftyzer (Table S7) and (2) an amended set of constants (Table S8) recently published by Leman et al.7 Leman and co-workers developed the constants because the VK-H parameters do not work well for the polar and hydrogen bonding contributions of the organic photovoltaic materials. As mentioned earlier, the experimental δP and δH parameters do not match the calculated solubility parameters using the two methods are presented in Table 6. The details of the calculations are given in the Supporting Information.

n

μ(σ ) =

δD δP δH δT δD δP δH δT

VK-H/MPa1/2 PCBM 18.3 0.8 3.4 18.6 C60 19.7 0 0 19.7

(3)

i

The σ-potential and the set of σ-moments provide an efficient qualitative prediction of solvation phenomena, as well as thermodynamic parameters such as partition coefficients, vapor pressures, and activity coefficients, via a quantitative structure− property relationship (QSPR) approach involving a multilinear regression.38 To avoid overparametrization, the set of σmoments i = 0, 2, and 3 and the hydrogen bonding acceptor and donor moments, MXHBacc3 (MX9 ) and MXHBdon3 (MX13), provide a very good and nearly complete set of molecular descriptors for a linear regression analysis of any problem. Here MX0 is the area of the molecular surface, MX2 is the screening charge, which is an excellent measure of the overall polarity of the molecule, and MX3 is the skewness, or asymmetry, of the σ-profile. The first moment, MX1 , is often omitted because it is just the negative of the total charge of the molecule. The σ-moments of C60, PCBM, and methyl 5-phenylpentanoate (M5PP) calculated by the COSMOtherm program are given in Table 7. For fullerene the hydrogen-bonding

Table 6. Calculated Solubility Parameters of C60 and PCBM: Group Contribution Method6 parameter

∑ ciMiX

Leman et al./MPa1/2 18.8 4.0 4.6 19.4 19.8 5.5 3.6 20.9

Table 7. σ-Moments of C60, M5PP, and PCBM Calculated by COSMOtherm

The two approaches treat the polar and hydrogen-bonding components of the fullerene carbons very differently. On the basis of structure and symmetry, van Krevelen suggested that δP = δH = 0 for the C60 moiety;6 thus, the VK-H method does not attribute a polar or hydrogen-bonding contribution to the carbon atoms in C60. In the revised set of group attraction parameters, Leman et al. do assign polar and hydrogen-bonding contributions to the C60 carbon atoms, which, similar to the experimental measurements, give nonzero polar and hydrogenbonding solubility parameters, δP = 5.5 MPa1/2 and δH = 3.6 MPa1/2. As shown in Table 6, the revised method gives a polarity solubility parameter for PCBM (δP = 4.0 MPa1/2) that is consistent with the experimental values in Table 4. However, referring to Table 6, it is concerning that for C60 the revised constants give a δP parameter that is ∼40% larger than that of PCBM. Moreover, the computed δP = 5.5 MPa1/2 of C60 is twice as large as the experimental HSP value reported by Hansen and Smith and the FSP value. The FSP δD parameter of PCBM in Table 3 is lower than all the other experimental values shown in Table 4, but we observe very good agreement with the δD values predicted by the group contribution method. Also, the revised parameters of Leman et al. give δP and δH parameters that are consistent with the FSP values, wherein δH is ∼15−20% larger than δP. This trend is similar for the values reported by Vongsaysy et al.29 3.6. COSMO-RS. The COSMO-RS (Conductor-like Screening MOdel for Real Solvents) method developed by Klamt is a continuum solvation model that uses screening energies, surface areas, and screening surface charge densities to describe the intermolecular interactions in terms of pairwise interactions of surface segments.36,37 Based only on molecular structures,

compound

area/Å2

MX2

MX3

MXHBacc3

MXHBdon3

VCOSMO/Å3

C60 M5PP PCBM

392 255 566

12.25 68.82 90.90

−5.17 30.15 30.82

0 1.35 2.26

0 0 0

653 260 895

moments MXHBacc3 = MXHBdon3 = 0 are consistent with δH = 0; i.e., there is no hydrogen-bonding contribution to the cohesive energy density. The screening charge of PCBM, MX2 = 90.90, is ∼7.4 times larger than fullerene, so based on the overall polarity of the molecule and the fact that the volume of PCBM is only ∼1.3 times greater than C60, the δP parameter of PCBM should be notably larger than for C60. However, with regard to the available data, the experimental solubility parameters (HSP, CSP, and FSP) do not reflect the computational expectations. It is well-known that functionalization of C60, like other carbon allotropes, was performed to improve the solubility behavior in organic solvents. Thus, it is reasonable to expect that the ester side group will significantly impact the solubility behavior of PCBM relative to C60. In a recent computational study, Wang and Hua used atomistic molecular dynamics simulations to investigate the solubility behavior of fullerene and PCBM in a representative series of organic solvents. The results revealed that the phenyl/butyric acid methyl ester functionality plays a critical role in the aggregation behavior of PCBM compared to C60. As reported by Wang and Hua, the steric hindrance imposed by the side chain of PCBM notably affects the solvent molecule distribution in the first solvation shell, resulting in pronounced anisotropic orientation and differences in the local solvent density. The side chain alters the dynamic stability of a solvation shell to such an extent that the 11562


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Figure 3. σ-surfaces (top row), σ-potentials (middle row), and σ-profiles (bottom row) of C60 (left column), PCBM (middle column), methyl 5phenylpentanoate (right column). The parabolic σ-potential of C60 is characteristic of nonpolar compounds. For M5PP and PCBM the negative region of the σ-potential, σ < −0.01 e Å−1, is reflective of the electron pair donor capability of the ester group, which corresponds to the red regions of the σ-surfaces and the shoulders extending into the positive region of the σ-profiles.

surface of C60 (top, left). Comparing the integrals of the fullerene σ-profile in the ranges −0.01 to 0 and 0 to 0.01 reveals that the profile is slightly skewed toward the region of negative polarity, σ > 0. These characteristics are reflected by the slightly asymmetric, but parabolic, potential of C60, which is consistent with an apolar compound. Most notably, fullerene does not exhibit a feature in the σ-profile or potential that is attributable to hydrogen bonding capabilities. Based on these observations and the hydrogen bonding σ-moments in Table 7, a δH > 0 value seems unreasonable for C60. In the PCBM the σ-profile, the band on the left, is much larger than C60 and is similar to the corresponding feature in M5PP. Additionally, the nucleophilic character of the ester group, which corresponds to the red regions of the σ-surfaces of M5PP and PCBM, gives rise to the bands that extend into the positive region of the σ-profiles; thus, both compounds can function as hydrogen bond acceptors (electron donors). The similarity between these two potentials, and the dissimilarity between PCBM and C60 potentials, emphasizes the importance of the ester side chain functionality on the solubility behavior of PCBM. From an experimental perspective, the solubility of PCBM is markedly higher than C60 in common solvents, thereby highlighting the impact of the ester group on the solvent− solute interactions. In Figure 4a the solubility data of PCBM in Table S3 are plotted along with the C60 data available for the

aggregation mechanism changes from diffusion-limited for C60 to reaction-limited for PCBM. In light of these results one would expect the nature of the solvent−side chain interactions to be manifested, in some way, in the solubility data and solubility parameters of PCBM. To address this issue, we used COSMO-RS to compare the solubility behavior of PCBM, C60, and methyl 5-phenylpentanoate (M5PP), which is a molecular homologue of the PBM side group. The electron donor capability of the ester group in M5PP evident in the σ-potential and σ-profiles in Figure 3 is reflected by the hydrogen-bonding solubility parameter of M5PP, δH = 6.1 MPa1/2, calculated using the group contribution method (see Supporting Information). The region of the σ-potential associated with the nucleophilicity of the ester functionality is preserved in the σ-potential of PCBM; thus, the sensitivity of the solubility function of PCBM to the hydrogen-bonding forces and the large functional solubility parameter, δH = 6.3 MPa1/2, is reasonably supported by COSMO-RS. This sensitivity is particularly intriguing since orientational effects are not rigorously accounted for in the conventional threeparameter theory. In Figure 3 the σ-profile of fullerene is confined to the middle region, −0.01 < σ < 0.01, associated with the lipophilicity of a nonpolar compound. There is a small band in C60 σ-profile that extends out into the region of positive polarity. This shoulder is associated with the blue regions on σ11563


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concentrations, the resulting solubility function lends to a more natural representation of the central tendency of the solvent−solute interactions. Moreover, the solubility function provides a convenient way to visualize and evaluate the solubility characteristics on the δD, δP, and δH parameters. This feature is significant because although the sets of FSPs in the present analysis are in good agreement with some of the previously reported Hansen solubility parameters for C60 and PCBM, the sensitivity of the solubility functions to the δD, δP, and δH parameters facilitates comparison of the solubility behavior in the Hansen space to complementary methods such as LSER modeling, additive functional group calculations, and COSMO-RS computations. The simultaneous assessment across parallel methodologies affords a more complete picture of the of the solubility characteristics. However, in the present analysis we observe some conspicuous discrepancies regarding the interpretation of the solubility characteristics of C60 and PCBM using solubility parameter theory, linear solvation energy relationship and COSMO-RS. The FSP solubility functions of both C60 and PCBM reveal that the solubility of both molecules are highly sensitive to the dispersion parameter, δD, of the solvents. The solubility function of PCBM reveals a strong dependence on δH and a negligible dependence on δP. The solubility of C60 is not particularly sensitive to either δP or δH. In contrast to these observations, the LSER fits reveal that the solubility behavior of C60 and PCBM is dominated by the polarity of the solvent, and that the hydrogen-bonding characteristics of the solvents have a negligible effect. The disconnect between the solubility of C60 and the δP and δH parameters makes sense based on the structure of C60, but the values of both parameters are much larger than expected based on the structure of C60. In fact, the solubility functions of C60 and PCBM are both consistent with the anomalously large δP and δH parameters associated with the experimental data. However, additive group contribution calculations using the unrevised van Krevelen and Hoytzer constants and structural considerations indicate that both molecules should have relatively low polar and hydrogen-bonding contributions to the cohesive energy density, which is supported by the σmoments computed with COSMO-RS. While our results support the revised group contribution parameters reported by Leman et al., the need for the amended parameters is still unclear. Specifically, one of the glaring issues with experimental data is the anomalously large δH parameters of C60 and PCBM. Perhaps the unique electronic characteristics of semiconductors give rise to complex solute−solvent interactions that are not adequately accounted for by the three solubility parameters in terms on their conventional definitions. As a result, the “hydrogen-bonding” parameter acts as a general, or comprehensive, parameter that registers these complex interactions, thereby resulting in large δH values. Alternatively, our contradictory observations may expose a broader issue with the solubility behavior of PCBM and, in particular, C60. The FSP solubility function strongly suggests that the solubility parameters do not accurately represent the CED properties of C60 and PCBM, but rather they manifest the CED properties of the solvents necessary to accommodate these molecules. Thus, similar to other carbon allotropes, such as carbon nanotubes and graphene, the dissolution of C60 is predominantly a problem of dispersibility than solubility, thereby rationalizing the apparent disconnect between the empirical data and the complementary methods used in the

Figure 4. (a) Experimental solubility data of PCBM and C60 in a common set of solvents. (b) Natural logarithm of the activity coefficients, γ, of PCBM, fullerene, and methyl 5-phenylpentanoate (M5PP) computed with COSMO-RS.

same set of solvents. The overlap of the data is better for the small set of amphiprotic solvents (cluster VII) on the right of Figure 4a, which corresponds to poor solubility of both fullerene and PCBM. For the remainder of the solvents (Figure 4a), in which PCBM exhibits modest and high solubilities, the fullerene data does not track very well with PCBM. Figure 4b shows ln(γ) for C60, PCBM, and M5PP computed with COSMO-RS (T = 298 K). Here, the activity coefficient, γ, reflects the difference between the chemical potential of the pure solute, μj,pure, and the solute in the liquid phase, μj,S, ln(γ) = (μj,S − μj,pure)/RT. Figure 4b reveals that M5PP tracks reasonably well with PCBM, except in the region of insolubility (right) where the activity coefficient of PCBM shows a much better correlation with C60. These results and the experimental solubility data in Figure 4a suggest that in general, the ester side chain dictates the solubility behavior of PCBM. Both the fullerene and ester group contribute to the insolubility of PCBM in amphiprotic solvents, but it appears to be driven mainly by the fullerene−solvent interactions. We contend that the δH and δD parameters of PCBM that are observed using the functional solubility parameter approach are consistent with solubility behavior dominated by the ester side group. 3.7. Summary and Comparison of Results. Since the FSP approach does not require a binary classification of solvent affinity for the solute or the use of arbitrary threshold 11564



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present analysis. This premise is partially substantiated by the temperamental nature of the solubility data.39 For instance, as pointed out by Korobov and Smith, the solubility data from different studies are in reasonably good agreement, but measurements of C60 have been described as difficult and irreproducible. 39,40 The inconsistency of the data and incongruence of the models may be further rationalized by the coexistence of crystalline solvates and bare, unsolvated C60.19,41 For PCBM these circumstances are somewhat relaxed owing to the phenyl/methyl ester side group, which promotes solvation. Thus, interactions between the solvents and the nucleophilic ester group on the side chain, which is supported by the COSMO-RS computations, may corroborate the dependence of the PCBM solubility on δH.

AUTHOR INFORMATION

Corresponding Author

*(D.B.) E-mail [email protected]; tel 843-953-6493. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.B. acknowledges the financial support of the College of Charleston, Faculty Research and Development Committee (Teacher-Scholar Grant), and the donors of the American Chemical Society Petroleum Research Fund (55397-UR7) for partial support of this research.

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REFERENCES

(1) Howell, J. S.; Stephens, B. O.; Boucher, D. S. Convex Solubility Parameters for Polymers. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1089−1097. (2) Ruoff, R. S.; Tse, D. S.; Malhotra, R.; Lorents, D. C. Solubility of Fullerene (C60) in a Variety of Solvents. J. Phys. Chem. 1993, 97, 3379−3383. (3) Hansen, C. M.; Smith, A. L. Using Hansen Solubility Parameters to Correlate Solubility of C60 Fullerene in Organic Solvents and in Polymers. Carbon 2004, 42, 1591−1597. (4) Machui, F.; Abbott, S.; Waller, D.; Koppe, M.; Brabec, C. J. Determination of Solubility Parameters for Organic Semiconductor Formulations. Macromol. Chem. Phys. 2011, 212, 2159−2165. (5) Machui, F.; Langner, S.; Zhu, X.; Abbott, S.; Brabec, C. J. Determination of the P3HT:PCBM Solubility Parameters via a Binary Solvent Gradient Method: Impact of Solubility on the Photovoltaic Performance. Sol. Energy Mater. Sol. Cells 2012, 100, 138−146. (6) van Krevelen, D. W. Properties of Polymers, 3rd ed.; Elsevier: Amsterdam, 1990; p 861. (7) Leman, D.; Kelly, M. A.; Ness, S.; Engmann, S.; Herzing, A.; Snyder, C.; Ro, H. W.; Kline, R. J.; DeLongchamp, D. M.; Richter, L. J. In Situ Characterization of Polymer−Fullerene Bilayer Stability. Macromolecules 2015, 48, 383−392. (8) Eckert, F.; Klamt, A. COSMOtherm Version C2.1-Revision 01.07; COSMOlogic GmbH&CoKG: Leverkusen, Germany, 2007. (9) Howell, J. S.; Roesing, M.; Boucher, D. S. A Functional Approach to Solubility Parameter Computations. J. Math. Chem. 2016, under review. (10) Howell, J. S.; Boucher, D. S. Temperature Dependence of the Convex Solubility Parameters of Organic Semiconductors. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 81−88. (11) Klamt, A.; Schuurmann, G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and Its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 5, 799−805. (12) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38, 3098−3100. (13) Perdew, J. P. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 33, 8822−8824. (14) Rappoport, D.; Furche, F. Property-Optimized Gaussian Basis Sets for Molecular Response Calculations. J. Chem. Phys. 2010, 133, 134105. (15) Durand, M.; Molinier, V.; Kunz, W.; Aubry, J.-M. Classification of Organic Solvents Revisited by Using the COSMO-RS Approach. Chem. - Eur. J. 2011, 17, 5155−5164. (16) Lee, B. The Physical Origin of the Low Solubility of Nonpolar Solutes in Water. Biopolymers 1985, 24, 813−823. (17) Graziano, G. On the Cavity Size Distribution in Water and nHexane. Biophys. Chem. 2003, 104, 393−405. (18) Pohorille, A.; Pratt, L. R. Cavities in Molecular Liquids and the Theory of Hydrophobic Solubilities. J. Am. Chem. Soc. 1990, 112, 5066−5074.

4. CONCLUSIONS We investigated the solubility characteristics of C60 and PCBM using the convex hull (CSP) and solubility functions (FSP) methods. Additionally, we examined the solubility behavior using a linear solvation energy relationship (LSER) model and COSMO-RS computation. We observe reasonable agreement between the CSPs, HSPs, and previously reported Hansen solubility parameters, and our CSP and FSP results confirm the anomalously large values of the polar (δP) and hydrogenbonding (δH) solubility parameters. However, for both molecules the magnitude of these parameters, as well as the sensitivity of their FSP solubility functions to δP and δH, are at odds with structural characteristics of the molecules as well as aspects of the LSER fits and COSMO-RS computations. Therefore, contradictory results preclude a comprehensive and consistent picture of the solubility characteristics of C60 and PCBM. However, features of the FSP solubility function strongly suggest that the solubility parameters do not accurately represent the cohesive energy density properties of C60 and PCBM, as intended, but rather they manifest the solvent− solvent interactions needed to accommodate these molecules in the liquid phase. The apparent disconnect between the empirical data and the complementary methods employed in this study may be validated if the dissolution of C60 and, to a lesser extent, PCBM is treated as a problem of dispersibility rather than solubility. So, from a practical or applications standpoint, the empirical solubility parameters are suitable for solvent screening purposes, but caution may need to be exercised when using a solubility parameter analysis to rationalize the nature of the interactions between C60 and PCBM and other constituents, e.g., polymers, in blended composite materials.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b09273. (1) Tables of the Hansen solubility parameters and solvatochromic parameters of the solvents, (2) the solubility data of C60 and PCBM, (3) a brief overview of Hansen solubility parameter theory, (4) plots with different projections of the convex hulls and solubility functions of C60 and PCBM, and (5) the functional group contribution calculations (PDF) 11565


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(19) Marcus, Y.; Smith, A. L.; Korobov, M. V.; Mirakyan, A. L.; Avramenko, N. V.; Stukalin, E. B. Solubility of C60 Fullerene. J. Phys. Chem. B 2001, 105, 2499−2506. (20) Marcus, Y. The Properties of Organic Liquids That Are Relevant to Their Use as Solvating Solvents. Chem. Soc. Rev. 1993, 22, 409−416. (21) Dimroth, K.; Reichardt, C. über Pyridinium-N-phenol-betaine und ihre Verwendung zur Charakterisierung der Polarität von Lö sungsmitteln, V Erweiterung der Lö sungsmittelpolaritätsskala durch Verwendung Alkyl-substituierter Pyridinium-N-phenol-betaine. Liebigs Ann. Chem. 1969, 727, 93−105. (22) Reichardt, C. Ü ber Pyridinium-N-phenol-betaine und ihre Verwendung zur Charakterisierung der Polarität von Lösungsmitteln, VI1) Erweiterung der Lösungsmittelpolaritätsskala durch Bestimmung neuer molarer Ü bergangsenergien (ET-Werte). Liebigs Ann. Chem. 1971, 752, 64−67. (23) Reichardt, C. Solvatochromic Dyes as Solvent Polarity Indicators. Chem. Rev. 1994, 94, 2319−2358. (24) Lan, Y.; Corradini, M. G.; Liu, X.; May, T. E.; Borondics, F.; Weiss, R. G.; Rogers, M. A. Comparing and Correlating Solubility Parameters Governing the Self-Assembly of Molecular Gels Using 1,3:2,4-Dibenzylidene Sorbitol as the Gelator. Langmuir 2014, 30, 14128−14142. (25) Reichardt, C. Solvent Effects on Chemical Reactivity. Pure Appl. Chem. 1982, 54, 1867−1884. (26) Catalán, J. Toward a Generalized Treatment of the Solvent Effect Based on Four Empirical Scales: Dipolarity (SdP, a New Scale), Polarizability (SP), Acidity (SA), and Basicity (SB) of the Medium. J. Phys. Chem. B 2009, 113, 5951−5960. (27) Perea, J. D.; Langner, S.; Salvador, M.; Kontos, J.; Jarvas, G.; Winkler, F.; Machui, F.; Görling, A.; Dallos, A.; Ameri, T.; Brabec, C. J. Combined Computational Approach Based on Density Functional Theory and Artificial Neural Networks for Predicting The Solubility Parameters of Fullerenes. J. Phys. Chem. B 2016, 120, 4431−4438. (28) Duong, D. T.; Walker, B.; Lin, J.; Kim, C.; Love, J.; Purushothaman, B.; Anthony, J. E.; Nguyen, T.-Q. Molecular Solubility and Hansen Solubility Parameters for the Analysis of Phase Separation in Bulk Heterojunctions. J. Polym. Sci., Part B: Polym. Phys. 2012, 50, 1405−1413. (29) Vongsaysy, U.; Pavageau, B.; Wantz, G.; Bassani, D. M.; Servant, L.; Aziz, H. Guiding the Selection of Processing Additives for Increasing the Efficiency of Bulk Heterojunction Polymeric Solar Cells. Adv. Energy Mater. 2014, 4, 1300752. (30) Hansen, C. M. Hansen Solubility Parameters: A User’s Handbook, 2nd ed.; CRC Press: Boca Raton, FL, 2007; p 519. (31) Beerbower, A.; Wu, P. L.; Martin, A. Expanded Solubility Parameter Approach I: Naphthalene and Benzoic Acid in Individual Solvents. J. Pharm. Sci. 1984, 73, 179−188. (32) Beerbower, A.; B. Jensen, W. The HSAB Principle and Extended Solubility Theory. Inorg. Chim. Acta 1983, 75, 193−197. (33) Karger, B. L.; Snyder, L. R.; Eon, C. Expanded Solubility Parameter Treatment for Classification and Use of Chromatographic Solvents and Adsorbents. Anal. Chem. 1978, 50, 2126−2136. (34) Karger, B. L.; Snyder, L. R.; Eon, C. An Expanded Solubility Parameter Treatment for Classification and Use of Chromatographic Solvents and Adsorbents: Parameters for Dispersion, Dipole and Hydrogen Bonding Interactions. J. Chromatogr. A 1976, 125, 71−88. (35) Van Krevelen, D. W.; Hoftyzer, P. J. Properties of Polymers; Elsevier: Amsterdam, 1976; p 620. (36) Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224−2235. (37) Klamt, A.; Eckert, F.; Arlt, W. COSMO-RS: An Alternative to Simulation for Calculating Thermodynamic Properties of Liquid Mixtures. Annu. Rev. Chem. Biomol. Eng. 2010, 1, 101−122. (38) Klamt, A.; Eckert, F.; Hornig, M. COSMO-RS: A Novel View to Physiological Solvation and Partition Questions. J. Comput.-Aided Mol. Des. 2001, 15, 355−365. 11566


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