Fullerenes in Aromatic Solvents: Correlation between Solvation-Shell

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Fullerenes in Aromatic Solvents: Correlation between Solvation Shell Structure, Solvate Formation, and Solubility James S Peerless, Graham Hunter Bowers, Albert L. Kwansa, and Yaroslava G Yingling J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b09386 • Publication Date (Web): 11 Nov 2015 Downloaded from http://pubs.acs.org on November 12, 2015

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The Journal of Physical Chemistry

Fullerenes in Aromatic Solvents: Correlation between Solvation Shell Structure, Solvate Formation, and Solubility James S. Peerless, G. Hunter Bowers, Albert L. Kwansa, and Yaroslava G. Yingling* Department of Materials Science and Engineering, North Carolina State University, 911 Partners Way, Raleigh, North Carolina 27695, United States

ABSTRACT. Here, an all-atom molecular dynamics simulation technique was employed to gain insight into the dynamic structure of the solvation shell formed around C60 and phenyl-C61butyric acid methyl ester (PCBM) in nine aromatic solvents. A new method was developed to visualize and quantify the distribution of solvent molecule orientation in the solvation shell. A strong positive correlation was found between the regularity of solvent molecule orientation in the solvation shell and experimentally obtained solubility limits for both C60 and PCBM. This correlation was extended to predict a solubility of 36 g/L for PCBM in 1,2,4-trimethylbenze. The relationship between solvation shell structure and solubility provided detailed insight into solvate formation of C60 and solvation in relation to solvent molecular structure and properties. The determined dependence of the solvation shell structure on the geometric shape of the solvent may allow enhanced control of fullerene solution-phase behavior during processing by chemically

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tailoring solvent molecular structure, potentially diminishing the need for costly and environmentally harmful halogenated solvents and/or additives.

KEYWORDS. Molecular Dynamics, C60, PCBM, Simulations, Structure Analysis

Introduction Fullerene, C60, and its derivatives have been the subject of study for a vast array of biological and electronic applications1 ranging from anticancer treatments2,3 and liver-protective antioxidants4 to liquid crystal materials5 and organic photovoltaic (OPV) devices6-8. The most ubiquitous fullerene derivative as an OPV material is phenyl-C61-butyric acid methyl ester (PCBM), which is considered the benchmark for electron acceptor materials in bulkheterojunction (BHJ) OPVs6-9. The primary applications of fullerenes necessitate solution-based processing; however, fullerene exhibits unusual solubility behavior due to its unique chemical structure10-13. In OPVs, for example, the solubility of the fullerene acceptor material has a direct impact on OPV device performance due to fullerene aggregation behavior during deposition of the BHJ active layer14-18. Thus, there have been a large number of experimental13,19-21, theoretical22,23, and computational24-35 studies into fullerene solvation behavior. Moreover, a variety of theoretical models have been employed to predict fullerene solubility based on solvent properties12,36-43. Although these studies have provided valuable insight into the properties of solvents that tend to produce high C60 solubility limits, it is difficult to directly relate these properties to the interactions occurring during solvation. Generally, the most accurate models for predicting C60 solubility employ advanced multivariate regression methods that provide little


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insight into the mechanism of solvation36-41. Furthermore, very few studies have been directed at the effect of substituted units24,32,34, such as those present in PCBM, on solubility mechanisms. It is well known that the majority of good solvents for C60 are aromatic10,11,21. Aromatic solvents such as 1,2-dichlorobenzene (ODCB) are commonly used as primary processing solvents of PCBM for the fabrication of OPV devices6-9. The relatively high solubility of fullerenes in aromatic solvents is presumably due to strong π-π interactions; most aromatic solvents are known to form solvation shells with a high degree of regularity during fullerene solvation as well as solid crystalline solvate complexes10,12,20,21,31,43-45. The dynamic structure of the aromatic solvation shell undoubtedly plays a large part in the solvation mechanism, yet an investigation into the role of solvation shell structure and its dependence on solvent molecular structure and properties has not been performed for organic solvents. The correlation between solubility and the mechanism of solvation taking place in the solvation shell due to specific solvent molecular properties would allow scientists and engineers to better design solvents and additives to reach desired solution-phase behavior in processing environments. Molecular dynamics (MD) simulation has emerged as a powerful tool for investigations of solvation shell structure as MD allows for precise experimental control and can provide detailed insight into molecular interactions. Previous MD investigations into the dynamics and structure of the solvation shell in fullerene systems have been performed in aqueous24-29 and nonaqueous29-33 systems. In a study by Fritsch et al.31, the solvation shell structure of toluene around C60 was described by a spherical order parameter, Q, which was calculated from an average solvent orientation angle and plotted as a function of solvent distance. Similarly, Wang et al.30 described the solvation shell of toluene, chlorobenzene, and chloroform around C60 by the average angle between the solvent dipole and distance vector plotted as a function of distance, as


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well as relating a dynamic relaxation parameter to fullerene solubility. Overall, the descriptive methods of the solvation shell have been limited and very few solvent systems have been investigated. In the present work, we have utilized all-atom MD simulation to describe in detail the structure of the aromatic solvation shell formed around C60 and PCBM in nine common aromatic solvents (Table 1). These solvents were chosen to provide a variety of substitutional units, substitutional positions, and solubility limits to allow for a detailed comparison of solvation behavior. Novel post-processing techniques based on solvent molecule 3D orientations relative to the fullerene molecule were employed to quantify the extent of structure present in the dynamic solvation shell formed around fullerenes. We demonstrate that the quantification parameter, termed the degree of order (DoO), correlates with experimental solubility limits and provides insight into solvation and solid solvate formation based on solvent molecular structure. Table 1. Aromatic solvents investigated in this study and their fullerene solubility limits at 298 K displayed as log10(x2), where x2 is the mole fraction of fullerene. Solvent

Abbr.

C60

C60 Solubility

C60 Solubility

PCBM

Solubilitya

(Low)b

(High)b

Solubility15

Benzene

Benz

-3.73

-3.96

-3.67

-2.80

Toluene

Tol

-3.45

-4.10

-3.32

-2.68

Bromobenzene

BB

-3.35

-3.39

-3.32

-2.45

Styrene

Styr

-3.21

-3.22

-3.19

-2.44

Chlorobenzene

CB

-3.05

-3.09

-3.00

-2.18

o-Xylene

oX

-2.84

-2.91

-2.80

-2.53

1,2,4-Trichlorobenzene

aTCB

-2.78

-3.08

-2.43

-1.96


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1,2,4-Trimethylbenzene

aTMB

-2.48

1,2-Dichlorobenzene

ODCB -2.45

-

-

-

-2.95

-2.37

-2.28

a

Values are those reported as the most probable by Semenov et al.21 b Low and high values reflect the lower and upper limits, respectively, of values reported by Semenov et al.21 The experimental methods employed for the determination of solubility limits vary by source, including spectrophotometric21, chromatographic21,46, and gravimetric47,48 methods. Computational and Analytical Methods All MD simulations were performed using the AMBER 14 molecular dynamics package49. The initial C60 structure was obtained from Materials Studio50 and modified to PCBM. All interaction parameters were assigned with the general AMBER force field (GAFF)51 with the exception of C60 atoms and the carbon atoms in the PCBM fullerene cage which were assigned adjusted Lennard-Jones (LJ) parameters to match those reported by Girifalco35,52,53. Data was collected from each solvent-fullerene system in a 60 ns constant pressure, constant temperature (NPT ensemble) simulation at 1 atm and 300 K with a timestep of 2 fs. Additional information on how systems were built and equilibrated prior to data-collection steps is provided in the Supporting Information (SI). Force Field Modification and Validation. Initial structures of C60 and PCBM were assigned atom types and corresponding force field parameters through the AMBER 1449 antechamber program utilizing GAFF51. The program assigns all C60 atoms and PCBM carbon atoms in the fullerene cage not bonded to the adduct (Figure S1) as the ca atom type, denoting them as carbons in a purely aromatic system. However, recent work by Monticelli35 suggests that the non-bonded LJ force field parameters originally developed by Girifalco52,53 better describe C60 interactions based on the enthalpy of sublimation (∆Hsub) and lattice parameter (a) of pure C60. Similarly, Rana et al. employed the Girifalco non-bonded parameters in an MD study describing C60 solvation behavior in liquid ammonia33. Based on these works, a new atom type, c6, was


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created in AMBER with the same angle, torsion, and dihedral parameters as ca but with LJ parameters based on the Girifalco force field (LJ parameters for both the GAFF ca atom type and Girifalco-based c6 atom types are shown in Table S3). To validate this c6 atom type for C60, calculations of ∆Hsub and a were performed using the procedure described by Monticelli35 (Table 2). Table 2. Data from force field validation simulations in AMBER 14. Simulations were performed as described by Monticelli35. In our work, the ∆Hsub values represent mean ± standard deviation over the duration of the MD simulation. LJ Parameters

Experimental35

(Source)

Girifalco

GAFF

Girifalco

(Monticelli31)

(This Work)

(This Work)

∆Hsub (kJ/mol)

180 ± 3

178.4 ± 0.3

228 ± 33.4

181 ± 33.2

a (nm)

1.417

1.417 ± 0.0004

1.380 ± 0.0002

1.391 ± 0.0002

The high error associated with the ∆Hsub values in our work are attributed to a large energy fluctuation seen in the in vacuo simulations of the fullerene; the energy did not appear to drift, but did have high RMS values. In the present work, error in ∆Hsub (σ∆H) was propagated by: ଶ ଶ ߪ∆ு = ൣߪ௚௔௦ + ߪ௦௢௟௜ௗ + ሺܴߪ் ሻଶ ൧

ଵൗ ଶ

where σgas, σsolid, and σT, are the RMS values of the total energy for the gas phase simulation, the total energy of the solid phase simulation, and temperature averaged over both simulations, respectively. The method of error propagation employed for the values reported by Monticelli et al.35 were not disclosed. Overall, the use of the Girifalco LJ parameters in our system led to a ∆Hsub value < 1% different from experiment and an a value 2% different from experiment.


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Solvation Shell Analysis: The analysis of the solvation shell structure during simulations was performed by extracting distance and angle data using AMBER’s post-processing tools54. The position and detailed orientation of solvent molecules relative to the fullerene molecule is described by three parameters: the solvent distance (d), the solvent orientation angle (θ), and the solvent plane angle (φ). These parameters are depicted below for the system of PCBM in toluene (Figure 1a,b). Values were extracted from each trajectory frame (one frame every 2 ps), for each solvent molecule in the system.

Figure 1. Schematic representation of (a) the solvent plane angle, φ, and (b) the solvent orientation angle, θ, for the case of PCBM in toluene. Distance vector, d, and plane normal vector, n, are labeled. (c) Depiction of the indicator atoms designated for all solvents, where indicator atoms are shown as a CPK ball in cyan. The distance d is defined as the magnitude of the distance vector d (Figure 1a,b) between the center of mass of the fullerene cage and the center of mass of the aromatic carbons in the solvent


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molecule. For PCBM, the center of mass for the fullerene cage is the same as for C60 and does not take into account the side group. The solvent plane angle φ is defined as the smallest angle between the distance vector d and the plane formed by the aromatic carbons in the solvent molecule (Figure 1a). To calculate φ, the plane normal vector n is first constructed from three opposite aromatic carbon atoms in the solvent molecule. The solvent plane angle φ is then calculated using φ = |90-∠nd|, where ∠nd is the angle between vectors d and n. Thus, φ is a positive number between 0 and 90°. A φ of 0° corresponds to a solvent molecule perpendicular to the fullerene surface, while a φ of 90° indicates the solvent molecule aligning parallel to the fullerene surface. A single φ value is produced from each solvent molecule at each trajectory frame regardless of solvent chemical structure. The orientation angle θ is defined as the angle between the distance vector d and a solvent orientation vector that is constructed from the center of mass of the aromatic carbons in the solvent to a singular aromatic carbon in the solvent molecule denoted as the indicator atom (Figure 1b). The indicator atom in each solvent molecule, illustrated in Figure 1c, is chosen such that the calculation of θ provides information about the position of substituted units in the solvent molecule relative to the fullerene. For benzene, which contains no substituted unit, the indicator atom is an arbitrarily chosen aromatic carbon in the solvent molecule. The indicator atom is the site of the substituted group for all monosubstituted solvents (Tol, BB, Styr, and CB). Disubstituted solvents (oX, ODCB) were quantified by producing two θ values for each solvent molecule (i.e., one for each substituted site; note that this does not affect data comparison discussed below, as all data are normalized by the number of d-θ data points counted in the first solvation shell). For


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trisubstituted solvents (aTCB, aTMB), the site of the non-symmetric substituted group is used as the indicator atom. It should be noted that in the case of benzene, a method similar to that used for oX and ODCB whereby all 6 carbons were chosen as the indicator atom, producing 6 data points for each solvent molecule, was investigated. The calculated degree of order and contour plots did not change significantly with this method, so one atom was chosen arbitrarily to reduce the resources that would be needed to process data sets containing 6 data points per solvent molecule. Each φ and θ value is coupled with the associated d value of the solvent molecule from which they were calculated, thus creating d-φ and d-θ data sets. These data sets were further evaluated by a two-dimensional histogram algorithm for visualization and analysis purposes. In the case of orientation angle data, d-θ data pairs from all solvent molecules at each trajectory frame are binned (counted and assigned to a d-θ bin). For a given range of d and θ, a solvent orientation frequency value, representing the likelihood of a solvent molecule with a d and θ within that range, may be calculated as the number of d-θ values assigned to that bin divided by the total number of d-θ values in the first solvation shell. The first solvation shell was defined as those solvent molecules with d values ≤ 10 Å. Plane angle (d-φ) data were analyzed in the same manner. These data may be conveniently visualized via three-dimensional contour plots, where a color value (or z-axis) represents the solvent orientation frequency. The choice of 10 Å as the limit of the first solvation shell becomes apparent upon investigation of the contour plots discussed below. Results and Discussion Visual Representation via Contour Plots. Contour plots generated from d-θ data of all systems are primarily considered for analysis as they contain information on the position of substituted


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units in the solvent molecule relative to the fullerene (Figure 2). Contour plots were also produced from d-φ data (Figure S2). While the combination of the plane angle (d-φ) and orientation angle (d-θ) data fully defines the most frequent solvent orientations with respect to the fullerene cage, upon inspection d-φ data for most solvents of interest (high solubility, substituted) is somewhat redundant with respect to d-θ data. However, d-φ contour plots can reveal necessary and interesting solvation shell behavior in high-symmetry solvents such as benzene.


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Figure 2. Solvent orientation angle-distance (d-θ) contour plots of (a) C60 and (b) PCBM in various aromatic solvents. The z-axis (Solvent Orientation Frequency) is the number of d-θ values in each bin (bin size is 0.1 Å x 4.5°) divided by the total number of d-θ values in the first solvation shell (d ≤ 10 Å). For each fullerene, solvents are ordered left-to-right, top-to-bottom in


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order of increasing experimental solubility with the exception of PCBM in aTMB, for which solubility limits have not been reported. Previous studies have displayed the solvent orientation of toluene and chlorobenzene in relation to C60 utilizing differing line-plot methods. Here, the solvent plane angle φ is analogous to the plane angle used to calculate the order parameter Q in the work by Fritsch et al.31 Conversely, the work by Wang et al.30 employed an angle between a distance vector and solvent dipole, which is analogous to θ in this work. Our results generally agree with these studies, namely, a highly preferential 90° orientation (θ ≈ φ ≈ 90°) at the closest distance to the fullerene center of mass (6-7 Å) and a greater variation in orientation angles (θ and φ) at larger distances from the fullerene (Figure 2 and S2). This behavior is intuitive based on the geometry of the solvent molecule; rotation of the molecule to a non-parallel orientation to the fullerene surface (φ ≠ 90°) will necessarily push the center of mass of the solvent molecule further from the fullerene. The two-dimensional representations by Fritsch et al. and Wang et al. can provide important information about the average solvent orientation at each distance and the total number of solvent molecules at each distance, yet, as in most two-dimensional representations, each x value has one associated y value. However, our three-dimensional representation supplies the total number of solvent molecules associated with all distance-solvent orientation combinations. Thus, in a three-dimensional representation, regions occurring at a similar distance (x value) but different solvent orientations (θ or φ, y values) may be identified and differentiated by frequency (z value). Furthermore, the combination of the plane angle (d-φ) and orientation angle (d-θ) data presented in this work fully defines the most likely solvent orientations at each distance (Figure 2 and S2). Thus, our method offers a more complete characterization of solvent molecular alignment within the solvation shell.


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For example, in the case of C60 in benzene, all carbon atoms on benzene are equivalent via 6fold symmetry; thus, benzene provides a useful geometric control. Four high-intensity regions can clearly be identified on the d-θ contour plot: 6.7 Å and 90°, representing a benzene molecule in near-parallel planar alignment (high φ) to the fullerene surface, and three peaks at 8.2 Å and 150°, 90°, and 30°, respectively. The high-distance peaks represent molecules closer to a perpendicular planar alignment (low φ) to the fullerene surface as shown by the d-φ contour plot for benzene reproduced below in Figure 3. With the planar alignment in mind, the values of θ for the high distance peaks correspond to orientations in which the closest C=C bond in the solvent aligns parallel to the fullerene surface (Figure S3). The three peaks correspond to the 6 potential locations for the indicator atom allowed by the hexagonal geometry. Medium frequencies occur in the transition regions from the 6.7 Å peak to the 8.2 Å peaks, yet the frequencies measured in the transition regions between the three 8.2 Å peaks are significantly lower. This may be explained by considering a benzene molecule rotating about its central axis (or plane normal vector, n) while in near-perpendicular planar alignment (low φ) to the fullerene surface (Figure S3 b-d). As benzene rotates at a low φ , the orientation angle will necessarily assume values other than 30°, 90°, and 150° (i.e. angles at which a C=C bond is no longer parallel to the fullerene surface) which are unlikely based on orientation data and thus considered unfavorable.


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Figure 3. Solvent plane angle-distance (d-φ) contour plot of C60 in benzene. The z-axis (Solvent Orientation Frequency) is the number of d-φ values in each bin (bin size is 0.1 Å x 4.5°) divided by the total number of d-φ values in the first solvation shell (d ≤ 10 Å). Aromatic solvent molecules that are parallel to the fullerene surface at short distances likely participate in π interactions with the fullerene10,43,45; these occurrences are indicated by the 6.7 Å - 90° peak seen in most contour plots (Figures 2 and S2). Similarly, two benzene molecules parallel to each other are likely to participate in solvent-solvent π interactions. The higher intensity of the three high-distance peaks in the benzene data, in which benzene molecules orient parallel to each other more so than the fullerene surface, suggests benzene-benzene πinteractions are more common than C60-benzene π-interactions. Solvents other than benzene show much lower symmetry in their orientation profiles as expected from their reduction in structural symmetry relative to benzene. All solvents, barring benzene and styrene at d > 7 Å, have higher orientation frequencies at θ < 90°. Thus the substituted unit pointing slightly towards the fullerene is preferential regardless of whether the substituted group is electron withdrawing (e.g., BB, CB, ODCB, and aTCB) or electron donating (e.g., Tol, oX, and aTMB).


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Solvation Shell Degree of Order. The plots in Figures 2 and S2 are displayed such that all zaxes for each fullerene are set to the same maximum frequency allowing for direct qualitative comparison of intensity regions between solvents. Some orientation profiles, such as those of ODCB, aTMB, and aTCB systems, exhibit high intensities localized to a particular area, indicating that a large number of solvent molecules adopted a particular d-θ combination (Figure 2). Thus, it may be said that these systems exhibit higher order in the solvation shell. When compared to solubility data in Table 1, the plots qualitatively suggest a trend in which orientation profiles that converge heavily are associated with higher solubility limits as determined by experiment. To further investigate this phenomenon, a method of analysis was designed to quantify the order of the solvation shell as a singular value termed the solvation shell degree of order (DoO). The DoO is calculated from the d-θ simulation data in Figure 2 using a scanning algorithm that determines a contiguous group of bins containing the highest density of solvent molecules throughout the simulation, referred to as the peak in the data. The DoO is then calculated as the number of solvent molecules found in this peak divided by the total number of d-θ data values in the first solvation shell. Thus, a high DoO value indicates that solvent molecules are more likely to assume a specific d-θ orientation, whereas a low DoO value indicates a more even distribution of d-θ orientations throughout the solvation shell. To increase resolution in the peak determination algorithm, the data is segmented into 500 bins in both dimensions, corresponding to a bin size of 0.008 Å x 0.36°. The peak includes 6,561 (81x81) bins, corresponding to a peak size of 0.648 Å x 29.16°. The smaller bin size, while increasing the accuracy of this calculation, does make the data harder to visualize, hence the larger bin size used for the plots in Figure 2.


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Contour plots constructed with the smaller bin size used in DoO calculations are shown in Figure S4, along with identifiers of the location of the high-density peak. To investigate whether structural order in solvation shell is correlated with solubility limits, we plotted the calculated DoO data as a function of experimental fullerene solubility limits from Table 1 (Figure 4a,b). Solvents with higher solubility limits produced larger DoO values. However, the strength of this positive correlation was higher than initial expectations, indicating a significant relation between solvation shell order and solubility. Furthermore, the method originally developed for C60 produced a positive correlation for PCBM as well. The DoO values for PCBM are, in general, lower than those of C60 even though PCBM solubility tends to be higher. This effect is presumably due to the adduct unit on PCBM disrupting the order of the solvation shell. Thus, it is difficult to directly compare DoO values between systems with different solutes. In the case of C60, the association between solvation shell order and solubility is further supported by a strong correlation between the DoO and the enthalpy of solution (∆Hsol) for systems with reported values (Figure 4c).


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Figure 4. (a,b) Degree of order (DoO) plotted as a function of experimental solubility limit for (a) C60 and (b) PCBM in aromatic solvents; the unit for experimental solubility is log10(x2), where x2 is the mole fraction of fullerene. Horizontal error bars in (a) indicate ranges of reported solubility values from Semenov et al.21 (c) DoO plotted as a function of enthalpy of solution (∆Hsol) as reported by Korobov et al.20 for C60 in solvents. (d) Degree of order plotted as a function of hypothetical solubility (log(xhyp)) for C60 in solvent. Hypothetical values calculated based on experimental solubilities reported by Semenov et al.21 and the formation of equilibrium solvates at 298 K. Vertical error bars in all plots indicate the standard deviation of DoO calculated from three 20 ns intervals of the 60 ns simulation.


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Interestingly, for both C60 and PCBM the trend of solubility increasing with the number of substituted units is reproduced by calculated DoO values. On average, trisubstituted solvents display the highest DoO, followed by disubstituted solvents with intermediate DoO, and monosubstituted solvents with the lowest DoO. This is not to suggest that the role of substituent composition is inconsequential, however, as ODCB and oX, two disubstituted solvents, show differing values of both DoO and solubility. The effect of substituents is particularly interesting when comparing aTCB and aTMB, both solvents with a high DoO value as well as high C60 solubility. PCBM exhibits high solubility in aTCB, yet solubility in aTMB has not been determined. Based on our work, the DoO of PCBM in aTMB (11.3%) predicts a solubility of -2.28 log(x) or 36 g/L. As both of these solvent molecules exhibit the same geometric configuration with chemically divergent substituents, it is likely the similarity in DoO is attributable to the ability of these molecules to assume a regular orientation around the fullerene surface due to their molecular structure, thus inhibiting fullerene-fullerene interactions and increasing solubility. Based on these results, it is likely that the geometric configuration of the aromatic solvents around the fullerene plays a larger role in solvation than previously indicated. The ability of asymmetrically trisubstituted aromatics to form a regular structure around the fullerene cage with maximum solvent-fullerene π-interaction is apparently due in part to the substituents in the optimal position to fill structural voids. Our results suggest that a regular solvation shell structure formed by the solvent is a significant factor in solubility. Perhaps commonly used halogenated solvents may be circumvented by the use of more environmentally benign solvents with optimal geometry without sacrificing solubility.


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Solvate Formation and Hypothetical Solubility. C60 is known to form crystalline solvates with most aromatic solvents, including the nine solvents investigated in this work12,20,21,55,56. For a generic solvent A, the incongruent melting of the solvate C60·nA is described by the reaction below20: C଺଴ ∙ ݊Aሺsሻ ↔ C଺଴ ሺsሻ + ݊Aሺliqሻ where n is a stoichiometric coefficient denoting the number of solvent molecules per C60 molecule present in the solvate complex. The value of n is near 2 for most of the solvents investigated in this work12,20,21,55,56 with the exception of benzene, for which n = 4 molecules20. The incongruent melting reaction above has an associated enthalpy (∆rH) and temperature (Timp). Solvate formation tends to complicate experimentally determined solubility limits as the solid precipitate at saturation is likely the solvate rather than pure solid C60. For solvents in which the temperature and enthalpy of incongruent melting of the solvate (Timp and ∆rH, respectively) are known, a hypothetical solubility limit may be calculated as shown below20 that indicates the 298 K solubility limit of pure solid C60 without the formation of solvates: ‫ݔ‬ଶ,௛௬௣ ∆௥ ‫ܪ‬ 1 1 ln ൬ ൰=൬ ൰ቆ − ቇ ‫ݔ‬ଶ ܴ 298 ܶ௜௠௣ where x2 is the experimentally determined solubility limit in mole fraction of C60 at 298 K. Incongruent melting data has been reported for all of the examined solvents except for styrene. In addition, toluene solvates exhibit a Timp value of 285 K20 and are not expected to form at simulation temperature of 300 K. Thus, styrene and toluene systems were omitted from calculations of hypothetical solubility. For the remaining solvents and C60, the hypothetical solubility was calculated using experimental data in Table 1 and the relation shown above (Table 3). The correlation between the DoO and the hypothetical solubilities of the solvents (hypothetical correlation) displayed in Figure 4d is a 4.2% improvement in terms of correlation


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coefficient (R) over the correlation with experimental solubilities (experimental correlation) shown in Figure 4a. Table 3. Enthalpy (∆rH) and temperature (Timp) of incongruent solvate melting as well as the calculated hypothetical C60 solubility limits (xhyp) for aromatic solvents. Low and high hypothetical solubility values were calculated from low and high data values reported by Semenov et al.21 Solvent ∆rHa

Timpa

log10(xhyp) log10(xhyp) log10(xhyp)

(kJ/mol C60) (K)

Low

High

Benz

41 ± 1

322 ± 1

-3.19

-3.42

-3.13

BB

42 ± 2

350 ± 1

-2.26

-2.30

-2.23

CB

18.2 ± 0.8b

301.2 ± 0.9b -3.02

-3.06

-2.97

oX

30 ± 2

322 ± 2.6

-2.44

-2.52

-2.41

aTCB

48.3 ± 1.1c

340.3 ± 2.4c -1.73

-2.03

-1.38

aTMB

38.2 ± 0.4

322

-1.98

-1.98

-1.98

ODCB

18.5 ± 2.3

322

-2.20

-2.71

-2.13

a

Data from Korobov et al.20 unless otherwise noted. b Data from Marcus et al.12 c Data from Avramenko et al.56 An interesting trend in solvents showing deviations from the hypothetical correlation was noticed in relation to the Timp of the solvate species. Solvents with lower DoO values than those which would be predicted by the hypothetical correlation (i.e., negative deviations, such as aTCB and BB) form solvates with higher values of Timp. The opposite holds true for solvents with higher than predicted DoO values, such as CB. Given this dependence of DoO deviation on Timp, a linear relation between DoO and hypothetical solubility was derived from the three solvents with an identical intermediate solvate Timp (oX, aTMB, and ODCB) and used to predict an expected DoO based on the hypothetical solubility of each solvent (DoO(Expctd)). The


20

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difference between the actual value of DoO and the DoO(Expctd) is plotted as a function of Timp below (Figure 5). The trend clearly displays that as the solvate melting temperature approaches 300 K, the DoO appears higher than expected by hypothetical solubility. This may be an artifact of the thermodynamic equilibrium at Timp between the solid crystalline solvate and purely solvated C60. Although temperature dependence of DoO has not been investigated, it is likely that the maximum DoO would occur at Timp for each solvent as the entropic penalty of the solvate-solvated C60 transition would be at a minimum. This further supports the association of high DoO and high solubility limits, as solvate-forming solvents are known to have a temperature-dependent maximum solubility at the Timp of the solvate10,20.

Figure 5. Deviation of actual C60 degree of order (DoO) from degree of order predicted by constant Timp correlation (DoO(Expctd)) as a function of incongruent melting point (Timp) of C60 solvates. It should be noted that benzene has been omitted from the discussion in the previous paragraph. A detailed explanation for this can be found in the SI, along with a thorough discussion of benzene and other solvents as outliers in Figure 3. Conclusions


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This work provides detailed insight into the importance of solvation shell structure of aromatic solvents around C60 and PCBM fullerenes based on atomistic MD simulations. The use of a distance value coupled with two angles measured from simulations permitted a complete description of the orientation of solvent molecules with respect to the fullerene cage and convenient visualization in three-dimensions. A single descriptive parameter, the degree of order (DoO), was introduced as a method to quantify the relative amount of orientation regularity present in the solvation shell. Comparison of the DoO to experimentally obtained solubility limits revealed strong positive correlations for both C60 and PCBM with R values of 0.8801 and 0.8455, respectively. This correlation was used to predict a solubility limit of 36 g/L for PCBM in 1,2,4-trimethylbenzene which has yet to be reported experimentally. Additional relationships between the DoO and experimentally obtained data such as solvation enthalpy and solvate formation properties further support a strong link between the regularity in the solvation shell and the mechanism of solvation. DoO data for solvate-forming systems of C60 suggest solvation shell order reaches a maximum, along with solubility, at the solvate melting point. These results suggest that the tendency for an aromatic solvent to form regular structures around fullerene molecules is an important factor in reducing fullerene-fullerene interactions and thus increasing solubility. Further investigation into solvation shell structures associated with high DoO values (as well as high fullerene solubility limits) suggests a relation between solvent molecular structure and degree of substitution, whereas the chemistry of the substituted units appears less impactful. Thus, the geometric shape of aromatic solvents is found to have a major influence on solvation shell order and therefore fullerene solubility. The dependence on molecular shape may allow for the use of geometrically similar but less chemically harmful (i.e. non-halogenated) solvents and/or additives in fullerene solution-phase processing, effectively reducing the


22

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environmental impact and associated cost of fullerene devices while providing structure-based guidelines for solvent or additive selection. Supporting Information. Simulation details, additional orientation contour plots, simulation snapshots, and radial distribution functions. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author * Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources US National Science Foundation Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was partially supported by the National Science Foundation Research Triangle MRSEC (DMR-1121107). The computer support was partially provided by the High Performance Computing Center at North Carolina State University.

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Fullerenes in Aromatic Solvents: Correlation between Solvation-Shell

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