Article pubs.acs.org/JPCB
Solubility of C60 and PCBM in Organic Solvents Chun I Wang and Chi C. Hua* Department of Chemical Engineering, National Chung Cheng University, Chia-Yi 62102, Taiwan R.O.C. S Supporting Information *
ABSTRACT: The ability to correlate fullerene solubility with experimentally or computationally accessible parameters can significantly facilitate nanotechnology nowadays for a wide range of applications, while providing crucial insight into optimum design of future fullerene species. To date, there has been no single relationship that satisfactorily describes the existing data clearly manifesting the effects of solvent species, system temperature, and isomer. Using atomistic molecular dynamics simulations on two standard fullerene species, C60 and PCBM ([6,6]-phenyl-C61-butyric acid methyl ester), in a representative series of organic solvent media (i.e., chloroform, toluene, chlorobenzene, 1,3-dichlorobenzene, and 1,2-dichlorobenzene), we show that a single time constant characterizing the dynamic stability of a tiny (angstrom-sized) solvation shell encompassing the fullerene particle can be utilized to effectively capture the known trends of fullerene solubility as reported in the literature. The underlying physics differs substantially between the two fullerene species, however. Although C60 was previously shown to be dictated by a diffusion-limited aggregation mechanism, the side-chain-substituted PCBM is demonstrated herein to proceed with an analogous reaction-limited aggregation with the “reaction rate” set by the fullerene rotational diffusivity in the medium. The present results suggest that dynamic quantitiesin contrast to the more often employed, static onesmay provide an excellent means to characterize the complex (entropic and enthalpic) interplay between fullerene species and the solvent medium, shed light on the factors determining the solvent quality of a nanoparticle solution, and, in particular, offer a practical pathway to foreseeing optimum fullerene design and fullerene−solvent interactions.
1. INTRODUCTION
relates the fullerene solubility to experimentally or computationally accessible parameters. Recently, the notion of (static) solvation shella tiny (angstrom-sized) structured region of solvent molecules encompassing a fullerene particlehas proven fruitful in revealing key molecular factors dictating fullerene solubility and aggregation behavior in a wide range of solvent media including water,31,33,39−45 organic solvents,46−50 ionic liquids,51−55 and metal-ammonia solutions.56−58 We demonstrated in prior work that computationally quantifiable relaxation behavior of a solvation shell can be employed to fathom C60 solubility under conditions of varying solvent species or system temperature.59 Herein, we discuss computational evidence suggesting that whereas the unmodified (C60) fullerene species forms aggregate via a diffusion-limited mechanism, the side-chain-substituted PCBM proceeds with reaction-limited aggregation as controlled by its rotational diffusivity in the medium. In both cases, we show that the known trends of fullerene solubility in a representative series of organic solvent media can be well captured by a single time constant characterizing the dynamic stability of the solvation shell. Thus, the phenomenal effects of
Buckminsterfullerene (C60) and its derivatives, such as [6,6]phenyl-C61-butyric acid methyl ester (PCBM), have currently served as promising materials for pharmaceutical and nanotechnological applications via solution-processing techniques that imperatively demand tolerable solubility of the fullerene species in specific solvent media.1,2 A number of schemes have been proposed to molecularly improve the fullerene solubility by means of functionalization,3−6 hydroxylation,7,8 and doping a metal atom.9,10 From thermodynamic perspectives, solubility of fullerenes was suggested to correlate with the cohesive energy densities (Hansen solubility parameters), the so-called “like dissolving/seeking like” concept.11−14 Quantitative structure−property relationship (QSPR) methods further invoked a detailed account of the solvent attributes including topology, geometry, and electronic properties.15−21 Alternatively, the notion of “fullerene solvate” was utilized to explain the interesting phenomenon that fullerene solubility often exhibits a maximum with increasing system temperature.22−26 Modern computer simulations, on the other hand, shed light on the origin of solvent-induced repulsion between C60 molecules,27−29 the hydrophobic attribute of fullerene particles,30−34 and essential features of fullerene aggregates.14,35−38 To date, however, there has been no single relationship that satisfactorily © 2015 American Chemical Society
Received: July 31, 2015 Revised: October 21, 2015 Published: October 21, 2015 14496
DOI: 10.1021/acs.jpcb.5b07399 J. Phys. Chem. B 2015, 119, 14496−14504
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The Journal of Physical Chemistry B solvent type, system temperature (which has so far been evaluated for some C60 solutions59), and isomers seem to be well explained in this context.
2. METHODOLOGY Using atomistic molecular dynamics (AMD) simulations of two standard fullerene species (i.e., C60 and PCBM), we have systematically explored the dynamic as well as static behavior of single fullerene particle in various organic solvent media including chloroform (CF), toluene (T), chlorobenzene (CB), 1,3-dichlorobenzene (mDCB), and 1,2-dichlorobenzene (oDCB). These solvent media, among the few that bear known solubility for both fullerene species, have now been commonly employed for solution-processing fullerene species in the fabrication of organic electronic devices. Focus is on the solvent−molecule relaxation within the first solvation shell, as well as the fullerene (translational and rotational) diffusivities that, together, will be shown to correlate intimately with the solvation and aggregation phenomena of fullerene molecules. This work requires some substantial analysis of a vast variety of experimental and simulation data, as described below. Evaluation of Force Field. The force fields and parameter values employed in the AMD simulations have been thoroughly evaluated against known system density, self-diffusion coefficient, and viscosity of each of the solvent media investigated, along with the structural and dynamic features of C60 and PCBM as had been known from early experiments or simulations (see Section SI of the Supporting Information). During this process, the effect of different force fields was also scrutinized, leading to the present choice that modifies the previous one used for C60 solutions59 only in some quantitative aspect. Thus, for the C60 and PCBM solutions reported herein, atomic interactions are described by the OPLS united-atom force field60,61 along with partial atomic charges obtained from the CM4 charge model,62 with an exception for chloroform molecule which apparently requires an all-atom description;59 see chemical structures and charge distributions in Figure 1. Besides, we follow the recent work by Huang et al.63 and by Cheung et al.64 who utilized the equilibrium bond lengths of fullerene carbon as taken from gas-phase electron diffraction data.65 Electronic polarizations on the carbon ball as effected by the surrounding polar solvent molecules44,45,66,67 were not considered. Simulation Details. All simulations were performed with the DL_POLY simulation package (version 4.02).68 The general procedure of the AMD simulation is as follows: A single C60 or PCBM molecule was fixed at the center of a cubic box consisting of an appropriate number of solvent molecules as listed in Table 1. Each system was equilibrated using Nosé−Hoover NPT ensemble (with a coupling constant of 0.1 ps for both thermostat and barostat) at 1 atm and 300 K for a duration of 2 ns with a time step of 1 fs. Periodic boundary conditions in all three directions were enforced. Long-range electrostatic interactions were calculated using the smoothedparticle-mesh-Ewald (SPME) technique with a real space cutoff of 12 Å. The same cutoff distance was used for the truncation of Lennard-Jones interactions, where standard Lorentz−Berthelot combining rules were adopted for any pair of unlike atoms. After the system equilibration, statistical data were collected every 0.25 ps for another duration of 5 ns, which results in fairly convergent results for the static features (e.g., radial distribution function, orientation profile, and spatial distribution function) as well as for the occupation time correlation function (OTCF).
Figure 1. Chemical structures of buckminsterfullerene (C60), [6,6]phenyl-C61-butyric acid methyl ester (PCBM), chloroform (CF), toluene (T), chlorobenzene (CB), 1,3-dichlorobenzene (mDCB), and 1,2-dichlorobenzene (oDCB), along with the distribution of partial atomic charges in unit of elementary charge (e) on each solvent molecule.
Table 1. Description of the AMD Simulation Systems C60
PCBM
solvent medium
no. solvent
no. solute
no. solvent
no. solute
CF T CB mDCB oDCB
2185 1916 1916 2556 2565
1 1 1 1 1
4032 2565 2565 2556 2565
1 1 1 1 1
Note, in particular, that the time interval (0.25 ps) has been confirmed to yield accurate results on OTCF described below, as compared with those obtained using a much shorter time interval (i.e., 0.02 ps). Finally, the C60 or PCBM was released to undergo free diffusion for a duration of 1.25 ns, and the trajectories were recorded every 0.05 ps for evaluating the translational and rotational diffusivities of C60 or PCBM in each solvent system, as detailed in Section SII of the Supporting Information. Assessment of Dynamic Quantities. To assess the relaxation behavior of solvent molecules within a solvation shell that determines the dynamic stability of the shell encompassing a single, fixed (see additional remarks in Section SIII of the Supporting Information) fullerene particle, we utilized the OTCF,31,32,47,69 which reflects the way a solvent molecule is escaping from a solvation shell where it initially resided: N
R (t ) =
∑i = 1 θi(t0)θi(t + t0) N
∑i = 1 θi(t0)θi(t0)
(1)
where θi = 1 if the mass center of the ith solvent molecule remains in a specific shell at the elapsed time t (t0 being the starting time) and is set to be zero otherwise; N denotes the total number of solvent molecules in a shell; the angular 14497
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Table 2. Solubility (s), Half-Life Time (t1/2), Translational Diffusivity (Dt), Rotational Diffusivity (Dr), and Rotational Time Constant (τ2) at 300 K in Various C60 and PCBM Solutions C60
PCBM
Dr
Dt
τ2
t1/2a
sb
[10−2 ps−1]
[10−10 m2/s]
[ps]
[ps]
[mg/mL]
± ± ± ± ±
4.2 4.0 4.5 6.2 5.5
44 ± 12 51 ± 14 68 ± 18 105 ± 31 130 ± 30
0.28 2.40 6.45 3.70 22.9
4.00 4.18 3.74 2.70 3.02
6.5 7.4 6.8 5.6 4.3
0.8 1.1 0.8 0.2 1.3
solvent medium CF T CB mDCB oDCB
sc
t1/2
τ2
Dt
Dr
[mg/mL]
[ps]
[ps]
[10−10 m2/s]
[10−2 ps−1]
19 45 180
49 ± 12 51 ± 13 72 ± 19 108 ± 31 124 ± 33
32 29 47 36 74
± ± ± ± ±
0.52 0.58 0.35 0.46 0.22
7.6 6.9 3.8 4.8 3.9
0.7 0.7 0.6 0.4 0.2
a The half-life time, t1/2, is defined as the elapsed time when half of the initial solvent population has already fled from the first solvation shell, i.e., R(t1/2) = 0.5; see also ref 59 for more detailed discussion. bThe solubility of C60 at 298 K as reported in ref 76. cThe solubility of PCBM at 298 K as reported in ref 77.
Figure 2. Spatial distribution functions of solvent molecules encompassing a C60 particle (top) or PCBM (bottom) in (a, f) chloroform, (b, g) toluene, (c, h) chlorobenzene, (d, i) 1,3-dichlorbenzene, and (e, j) 1,2-dichlorobenzene media, where the arrows indicate the first solvation shell. The various colors shown in the inset represent the corresponding values of SDF, which describes the local solvent density normalized by the bulk density of solvent medium.
brackets denote averaging over 16 000 independent time blocks. On the other hand, the dynamic attributes of the fullerene particle itself can be fully characterized by its translational and rotational diffusion coefficients. Due to the sluggish motion, the translational diffusivity (Dt) of fullerene in a solvent medium can be more readily assessed via time integration of the velocity autocorrelation function.70 The retrieval of the rotational diffusivity (Dr) is more complex and consists of two main steps: first, the AMD data were used to obtain the orientational correlation function. The result was then fitted using rotational Brownian dynamics formulated in terms of the second-order Legendre polynomial71,72 (see details in ref 72 as well as in Section SII of the Supporting Information). In relation to the rotational time constant (τ2), as often measured in nuclear magnetic resonance (NMR) experiments,73 the rotational diffusivity Dr so extracted was used in a typical transformation τ2 = 1/(6 Dr). All results are gathered in Table 2, and we noticed that the order magnitudes of Dt and Dr (or τ2) are in good agreement with a limited amount of data reported in the literature.48,74,75
Figure 3. RDFs of C60−solvent pair (gray line), PCBM−solvent pair locating in the hemisphere without side chains (blue line), and PCBM−solvent pair locating in the hemisphere with side chains (orange line) in (a) CF, (b) T, (c) CB, (d) mDCB, or (e) oDCB medium. The RDFs of PCBM−solvent pair locating in the hemisphere with side chains, in general, bear a lower peak height than those of C60−solvent pair, indicative of the steric hindrance effect. Otherwise, the results are basically no different for the two fullerene solutions.
3. RESULTS AND DISCUSSION We begin with the static aspect of solvation shells, as illustrated in Figure 2. Due to the asymmetry of PCBM molecule, the twodimensional spatial distribution function (SDF) is introduced. In the vicinity of a fullerene particle, the first and second solvation shells can be clearly identified with a thickness, a, of ∼3.7 and ∼4.5 Å, respectively; see also the radial distribution function (RDF) in Figure 3, where the minima were used to define the solvation shells. It can also be seen that the sidechain substitutes of PCBM play a role of steric hindrance that 14498
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Figure 4. Mean static orientation profiles of solvent molecules surrounding a C60 (blue line) or PCBM (red line) molecule in (a) CF, (b) T, (c) CB, (d) mDCB, or (e) oDCB medium, where r denotes the distance between the mass center of fullerene ball and the mapping center (e.g., the geometrical center of a phenyl ring) of the solvent molecule. As depicted in the figure, the angle was measured by the vector defining the dipole moment of the solvent molecule and that connecting the mass center of fullerene ball and the mapping center of the solvent molecule. The circle in each case marks the region of pronounced anisotropic orientationor structured statewithin the first solvation shell.
notably affects the solvent molecule distribution in the first solvation shell. Evidence of this hindrance effect can be more clearly seen in Figure 3, where the RDF of PCBM-solvent pair locating in the hemisphere with side chains, in general, bears a considerably lower peak height than the corresponding C60-solvent pair without altering the peak position. Moreover, the warm color of the first solvation shell in Figure 2 and a pronounced peak of RDF in Figure 3 are reminiscent of the strong van der Waals (vdW) interactions between fullerene and solvent molecules. More important, it seems the solvent molecules within the first solvation shell have organized themselves to form highly anisotropic orientation profiles, as shown in Figure 4. This phenomenon for organic solvent media is similar to the configurational ordering as had been reported for C60 in ionic liquids53−55 and water,7,33,42,43 as well as for fulleride anion (C60n−) in metal-ammonia solutions.56−58 In fact, some of these early reports suggested that this (anisotropic) feature of the (first) solvation shell might have an effect of impeding fullerene aggregation.53−58 Still, the generally slight disparities as observed in Figure 2 cannot explain the conspicuous effects of varying solvent species or the drastic difference between C60 and PCBM in view of the phenomenal solvation behavior. Thus, it seems necessary to delve into the dynamic aspect of the solvation shell. In prior work, we showed that the dynamic stability of the first solvation shell bears an intimate correlation with the solvation behavior of C60 in five different solvent media (i.e., CF, T, CB, water, ethanol) and a range of system temperatures (i.e., T = 250−330 K).59 It was further demonstrated that solvent−solvent interactions, aside from fullerene−solvent interactions, play an important role dictating the shell stability. Accordingly, we had proposed a physical parameter (ξ) defined as the ratio of two fundamental time constants representing, respectively, the solvent molecule relaxation time within the
Figure 5. Correlation between the solubility of PCBM and the parameter ξ for T, CB, or oDCB as the solvent medium. The correlation, for instance, incorrectly predicts a notably higher solubility (i.e., a larger value of ξ) for PCBM/T solution compared with PCBM/CB solution.
first solvation shell (t1/2) and the characteristic time required for the fullerene particle to diffuse a distance comparable to the shell thickness (a2/Dt). This parameter, bearing the physical significance of the permanence of a solvation shell with respect to the attempting time of fullerene particles to form aggregate, was found to describe excellently the known trends of C60 solubility under conditions of varying solvent species or system temperature. Surprisingly, however, as a similar relationship for PCBM solutions was evaluated, we found generally poor correlation as shown in Figure 5 suggesting that different physics must be at work. Intriguingly, Figure 6a illustrates there is a remarkably high correlation between the half-life time of solvation shell (t1/2) and the solubility for both C60 and PCBM solutions. In general, PCBM is known to bear a substantially higher solubility in organic solvents as compared with C60. The correlation presently 14499
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Figure 6. Correlations between the fullerene solubility and the characteristic relaxation time for T, CF, CB, mDCB, or oDCB as the solvent medium: (a) The computed half-life time in relation to the reported solubility of C60 (square symbols) and PCBM (circle symbols) solutions with the linear regressions described by t1/2 = 3.82s + 42.68 and t1/2 = 0.43s + 42.28, respectively, where s denotes solubility; the data point for C60 in mDCB (whose anomalously high melting point posed yet unknown challenge to the force field presently utilized) was excluded in the prior regression. (b) The halflife time (circle symbols) and the rotational time constant (triangle symbols) in relation to the known solubility of PCBM solutions with the linear regressions described by t1/2 = 0.43s + 42.28 and τ2 = 0.26s + 29.00, respectively.
found between C60 solubility and the half-life time of the solvation shell for an extended series of organic solvent media can be rationalized by a similar argument as given above, noting that the values of a2/Dt for the solvent media investigated vary only slightly and thus the effect of t1/2 would dominate in determining the parameter value of ξ. In contrast, the following analysis strongly suggests that the solvent relaxation time within the first solvation shell, t1/2, impacts the PCBM solubility through a distinctively different mechanism. To perceive the similarity as well as disparity between C60 and PCBM in view of the solvation behavior, it is instructive to examine the vdW interactions that govern the aggregationwhich, conceptually, represents the reverse process of solvationof a pair of fullerene molecules. Figure 7 demonstrates that both C60 and PCBM pairs possess a binding energy as large as about 10 kBTref when in close contact. As the pair of molecules are separated by their individual (first) solvation shells, as the cartoons illustrate, the vdW attraction drops abruptly to below 2 kBTref comparable with their thermal energy. If one regards the solvation shell as an additional, albeit temporal, excluded-volume of a fullerene molecule, the features above appear to explain why the stability of the solvation shell helps control the aggregation of diffusional C60 molecules. In contrast, it should be clear that the steric hindrance of sidechain-substituted PCBM would prevent a close contact in general, noticing that two of the four representative pair alignments depicted in Figure 7 are entirely forbidden in the region defined by their first solvation shells. Under this circumstance, PCBM molecules must invoke the rotational motion in order to find proper mutual alignments that would allow for a closer contact and, hence, the chance to form an aggregate. In this perspective, PCBM may be regarded as proceeding with
Figure 7. Sum of Lennard-Jones interaction energy for C60 (the dashed line) or PCBM (solid lines) pairs (Tref = 300 K) as a function of the separation distance of their carbon ball centers, where three representative configurations of the PCBM pair can be categorized: close contact (C60−C60 and C60−90 side), separated by one of the substituents (C60−side), and separated by two substituents (side− side). The yellow and blue regions mark that two fullerenes may be kept separated and, hence, nonaggregated in solution by the effect of the first or the second solvation shell.
“reaction-limited” aggregation as controlled by its rotational diffusivity. Further evidence supporting this assertion is discussed below. In Table 2, it can be seen that the values of t1/2 for C60 and PCBM are about the same for the same solvent medium. A closer inspection also revealed nearly identical relaxation pattern of OTCFs for the two cases, as can be seen in Figure 8. These observations, somewhat unexpected, suggest that the side-chain substitutes of PCBM have little influence on the dynamic stability of a solvation shell. In fact, having nearly identical solvent−shell stability while bearing distinct solubility 14500
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shows no similar correlation with its known solubility. These central observations indicate there is an intimate correlation between the rotational rate of PCBM and the relaxation rate of the solvation shell and lend support to the scenario depicted in Figure 7, suggesting that PCBM is dictated by a rotation-limited aggregation. In future perspectives, the availability of a more extensive set of (thermodynamic) solubility data on fullerene species, especially for PCBM, should help appraise the correlation relationships presently established in Figure 6. The scarcity of such data, in general, and the difficulty to obtain them in rigorous ways, in particular, clearly demonstrate the indispensability of theoretical insights that might lead to more accurate predictions on fullerene solubility. Due to scarce data currently reported on PCBM solubility, the solvation power (or solvent quality) may alternatively be judgedbut only qualitatively by the morphological feature of PCBM in solvent-cast PCBM/ polymer thin film,78 or by the size of PCBM aggregates as observed in recent simulation of PCBM/polymer solutions.79 In this way, the PCBM solubility in various solvent media appears to follow the trend: oDCB > CB > CF > T, as captured by the predicted rotational time constants shown in Table 2. The same table also implies PCBM enjoys a substantially higher solubility in oDCB than in mDCB, in agreement with the experimental observation.80 Before concluding this work, it is worth noting that the solvation behaviors of nanoparticle solutions have often been addressed in light of entropy−enthalpy interplay during the aggregation process. Given that a larger value of the half-life time t1/2 has been associated herein with a more stable solvation shell, it appears that as the (ordered) solvent molecules within the shell are being released to the (disordered) bulk medium during the aggregation process, there will be more entropy gain and, on the other hand, higher enthalpy penalty (the penalty arises from a general weakening in both fullerene−solvent and solvent−solvent interactions for the released solvent molecules) for organic solvent medium with a larger value of t1/2.Thus, the trend noticed in Figure 6 seems to imply that the latter the enthalpy penaltyis the dominant factor determining the relative solvation power of an organic solvent medium, because only the (increased-with-t1/2) enthalpy penalty would act (more strongly) to oppose the aggregation process and, presumably, lead to higher fullerene solubility. Similar enthalpic stabilization (entropy−enthalpy compensation) had been reported for some nanoscopic hydrophobic solutes.81−85 In contrast, entropy-driven aggregation had long been predicted86,87 and observed88−91 for different nanoparticle solutions. Essential features of the dynamic solvation shells in between two closely contacted fullerene particles and the detailed free-energy profile are under exploration.
Figure 8. Occupation time correlation functions of solvent molecules in the first and second solvation shells for C60 (dashed line) and PCBM (solid line) in (a) CF, (b) T, (c) CB, (d) mDCB, or (e) oDCB medium. These results demonstrate nearly identical relaxation pattern of OTCFs for the two fullerene species in the same solvent medium.
for C60 and PCBM for the same solvent medium is a significant feature, clearly suggestive of distinctive physics underlying their solvation behaviors. From the perspective of fullerene molecules, the data gathered in Table 2 indicate that the translational diffusivities of C60 and PCBM are very similar too and bear a value around 10−10 m2/s in agreement with the reported data.48,75 This feature, along with nearly identical solvent−shell stability as noted above, suggests that PCBM cannot be dictated by a similar diffusion-limited aggregation mechanism as previously found for C60 solutions. In contrast, the rotational diffusivity (or rotational time constant) differs substantially between the two species. The rotation of PCBM molecule represents a remarkably slower process than that of C60 molecule, as can be better visualized by the video of AMD trajectories provided in the Supporting Information. This slow-down in particle rotation can be ascribed to the rising frictional drag the PCBM encounters in the first solvation shell due to the presence of side-chain substitutes. On the basis of Debye−Stokes−Einstein relation, the rotational drag coefficient for PCBM was found to be at least 10 times larger than that for C60 (see Section SIV of the Supporting Information). Finally, Figure 6b shows that the rotational time constant bears an as good correlation with the known solubility of PCBM as previously found for the solvent half-life time shown in Figure 6a. In contrast, the rotational time constant of C60
4. CONCLUSIONS This study systematically explored the correlations between the dynamic stability of a solvation shellpresently characterized by the half-life time t1/2 of the solvent molecules within the shelland the solubility of two standard fullerene species, C60 and PCBM, in a representative series of organic solvent media. The results clearly suggested that the relaxation time of a solvation shell as can be readily retrieved from AMD simulations provides a simple and adequate means to predict fullerene solubility. The underlying physics differs substantially between the two fullerene species, however. We showed previously that C60 solutions are basically described by a 14501
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(8) Prylutskyy, Y. I.; Petrenko, V. I.; Ivankov, O. I.; Kyzyma, O. A.; Bulavin, L. A.; Litsis, O. O.; Evstigneev, M. P.; Cherepanov, V. V.; Naumovets, A. G.; Ritter, U. On the Origin of C60 Fullerene Solubility in Aqueous Solution. Langmuir 2014, 30, 3967−3970. (9) Xie, Q.; Perez-Cordero, E.; Echegoyen, L. Electrochemical detection of C606‑ and C706‑: Enhanced Stability of Fullerides in Solution. J. Am. Chem. Soc. 1992, 114, 3978−3980. (10) Fullagar, W. K.; Gentle, I. R.; Heath, G. A.; White, J. W. Reversible Alkali-metal Reduction of C60 in Liquid Ammonia; First Observation of Near-Infrared Spectrum of C5‑60. J. Chem. Soc., Chem. Commun. 1993, 525−527. (11) 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. (12) 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. (13) 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. (14) Tummala, N. R.; Mehraeen, S.; Fu, Y.-T.; Risko, C.; Brédas, J.-L. Materials-Scale Implications of Solvent and Temperature on [6,6]Phenyl-C61-butyric Acid Methyl Ester (PCBM): A Theoretical Perspective. Adv. Funct. Mater. 2013, 23, 5800−5813. (15) Murray, J. S.; Gagarin, S. G.; Politzer, P. Representation of C60 Solubilities in Terms of Computed Molecular Surface Electrostatic Potentials and Areas. J. Phys. Chem. 1995, 99, 12081−12083. (16) Marcus, Y. Solubilities of Buckminsterfullerene and Sulfur Hexafluoride in Various Solvents. J. Phys. Chem. B 1997, 101, 8617− 8623. (17) Abraham, M. H.; Green, C. E.; Acree, W. E., Jr. Correlation and Prediction of the Solubility of Buckminsterfullerene in Organic Solvents; Estimation of Some Physicochemical Properties. J. Chem. Soc., Perkin Trans. 2 2000, 281−286. (18) Sivaraman, N.; Srinivasan, T. G.; Vasudeva Rao, P. R.; Natarajan, R. QSPR Modeling for Solubility of Fullerene (C60) in Organic Solvents. J. Chem. Inf. Model. 2001, 41, 1067−1074. (19) Danauskas, S. M.; Jurs, P. C. Prediction of C60 Solubilities from Solvent Molecular Structures. J. Chem. Inf. Model. 2001, 41, 419−424. (20) Toropova, A. P.; Toropov, A. A.; Benfenati, E.; Gini, G.; Leszczynska, D.; Leszczynski, J. CORAL: QSPR Models for Solubility of [C60] and [C70] Fullerene Derivatives. Mol. Diversity 2011, 15, 249− 256. (21) Petrova, T.; Rasulev, B. F.; Toropov, A. A.; Leszczynska, D.; Leszczynski, J. Improved Model for Fullerene C60 Solubility in Organic Solvents Based on Quantum-Chemical and Topological Descriptors. J. Nanopart. Res. 2011, 13, 3235−3247. (22) Smith, A. L.; Walter, E.; Korobov, M. V.; Gurvich, O. L. Some Enthalpies of Solution of C60 and C70. Thermodynamics of the Temperature Dependence of Fullerene Solubility. J. Phys. Chem. 1996, 100, 6775−6780. (23) Avramenko, N. V.; Mirakyan, A. L.; Korobov, M. V. Thermal Behaviour of the Crystals Formed in the BuckminsterfullereneToluene, o-Xylene and Bromobenzene systems. Thermochim. Acta 1997, 299, 141−144. (24) Korobov, M. V.; Mirakian, A. L.; Avramenko, N. V.; Valeev, E. F.; Neretin, I. S.; Slovokhotov, Y. L.; Smith, A. L.; Olofsson, G.; Ruoff, R. S. C60·Bromobenzene Solvate: Crystallographic and Thermochemical Studies and Their Relationship to C60 Solubility in Bromobenzene. J. Phys. Chem. B 1998, 102, 3712−3717. (25) Korobov, M. V.; Mirakyan, A. L.; Avramenko, N. V.; Olofsson, G.; Smith, A. L.; Ruoff, R. S. Calorimetric Studies of Solvates of C60 and C70 with Aromatic Solvents. J. Phys. Chem. B 1999, 103, 1339− 1346. (26) Sawamura, S.; Fujita, N. High-Pressure Solubility of Fullerene C60 in Toluene. Carbon 2007, 45, 965−970.
diffusion-limited aggregation, controlled in addition by the dynamic stability of the solvation shell serving as a (temporal) protection layer. The side-chain-substituted PCBM, on the other hand, was demonstrated herein to be dictated by an analogous reaction-limited aggregation, where the solvation shell directly controls the rotational diffusivityand thus the “reaction rate”of two PCBM molecules that desperately seek for proper mutual alignments to form aggregate. In both cases, the dynamic parameter of t1/2 was explicated to reflect the (competing) entropy−enthalpy interplay of the solvent molecules during fullerene aggregation process. The physics so unveiled should help provide guideline for future molecular designs of fullerene and, perhaps, other carbon-based materials, such as carbon nanotubes and graphenes, that imperatively demand tolerable solubility in organic solvent media for a wide range of nanotechnological applications.
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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.5b07399. Validation of force field, evaluation of diffusion coefficients, simulation results based on fixed or freemotion fullerene particles, data on viscosity and drag force (PDF) Video of fullerene trajectories in chlorobenzene medium (MPG)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is sponsored by the Ministry of Science and Technology of R.O.C. Resources provided by the National Center for High-Performance Computing of ROC are acknowledged.
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REFERENCES
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