Solubility of C60 and PCBM in Organic Solvents

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
quantitiesin contrast to the more often employed, static onesmay 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 shella tiny
(angstrom-sized) structured region of solvent molecules encompassing a fullerene particlehas 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
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DOI: 10.1021/acs.jpcb.5b07399
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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
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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
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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 orientationor structured statewithin 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
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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
aggregationwhich, conceptually, represents the reverse process of solvationof 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
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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 judgedbut 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 penaltyis 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 shellpresently characterized
by the half-life time t1/2 of the solvent molecules within the
shelland 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
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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 diffusivityand 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.
■
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)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
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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