Theoretical Study on the Solvation of C60 Fullerene by Ionic Liquids

Sep 3, 2014 - The solvation of C60 fullerene by 24 different ionic liquids belonging to the imidazolium, piperazinium, and cholinium families was anal...
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Theoretical Study on the Solvation of C60 Fullerene by Ionic Liquids Gregorio García,† Mert Atilhan,‡ and Santiago Aparicio*,† †

Department of Chemistry, University of Burgos, 09001 Burgos, Spain Department of Chemical Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

‡

S Supporting Information *

ABSTRACT: The solvation of C60 fullerene by 24 different ionic liquids belonging to the imidazolium, piperazinium, and cholinium families was analyzed from a nanoscopic viewpoint using classic molecular dynamics simulations and Density Functional Theory (DFT) methods. Charge transfer between the ions and fullerene were computed by DFT. Force field parametrization used in molecular dynamics simulations was corrected to reproduce DFT ion−C60 interaction mechanism. Structural, dynamic, and energetic factors were analyzed to infer the role of the studied ions on the behavior of fullerenes in ionic liquids. The intermolecular ion−C60 interaction energy controls the behavior of these fluids, leading to prevailing roles by interaction mechanism through the π system of C60 nanoparticle, both for anions and cations.

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INTRODUCTION Ionic liquids, ILs, have attracted great attention in industry and academia for many possible technological applications, relevant areas such as energy,1 carbon capture,2 lubrication,3 electrochemistry,4 separation methods,5 catalysis,6 analytical chemistry,7 synthesis,8 or pharmaceutical applications.9 This wide interest may be justified considering (i) the large number of ion combinations leading to ILs10 and (ii) the possibility of controlling and tuning ILs properties through the choice of ions, leading to task-specific ionic liquids.11 The property of ILs as designer solvents is a remarkable advantage in comparison with traditional solvents and may lead to technological applications not available with common fluids. Moreover, the properties of ILs may be even enhanced or modified through suitable combinations with traditional molecular solvents.12 Among the fields being the subject of studies, the behavior of ILs with regard to carbon nanostructures (e.g., graphene, fullerenes, and nanotubes),13 have been considered using both experimental and computational approaches.14−17 The interests of these ILs/carbon nanosystems stand on their applications in fields such as electrochemistry,18 heat transfer,19 biosensors,20 or lubrication.21 The solvation of carbon nanostructures, specially using molecular dynamics simulations,22−24 and the confinement of ILs in carbon nanostructures has also been studied, showing the appearance of ILs crystal-like phases inside carbon nanotubes25−27 or in the vicinity of graphene sheets.13,28−31 In a recent study, Ohba and Chaban32 showed through a combined X-ray diffraction and theoretical study the adsorption of highly viscous ionic liquids in the inner walls of carbon nanotubes, and the role of the nanotube on the ionic motion inside the nanotube in comparison with the bulk fluid, suggesting the use of ionic liquids confinement as a way to modify the phase behavior of ionic liquids. © 2014 American Chemical Society

A very useful application of ILs stands on their use for the dispersion of carbon nanostructures. Fukushima et al.33,34 proposed for the first time the use of imidazolium-based ILs for the successful dispersion of carbon nanotubes. Moreover, ILs have also been applied successfully for the dispersion of graphene sheets14 and recently by Chaban et al. for C60 fullerene.35 The particular case of developing methods for obtaining fullerene solutions in suitable solvents has been widely studied in the literature. Experimental measurements of C60 solubility in common solvents range from 0.01 mg mL−1 in methanol36 to 53.28 mg mL−1 in piperidine.37 Nevertheless, fullerenes are sparingly soluble in most solvents,36,38 which hinders the industrial applications of fullerenes in many processes. Therefore, although some molecular properties of the considered solvents are known to increase fullerenes solubility, such as methylation,38 halogenation,38 or aromaticity,39 and high solubilities may be obtained in certain solvents (“good solvents”), such as piperidine or pyrrolidine,37 these solvents tend to react with the fullerene. Likewise, the poor fullerene solubility in polar solvents, leading even to the development of colloidal systems, tends to complicate the analysis of the properties of fullerenes in solvents and their technological applications. In a recent review work, Mchedlov-Petrossyan40 analyzed the behavior of fullerenes in liquid media, remarking how solubility is characterized by negative entropy of solvation, solvophobic solvation, and the role of supramolecular size of fullerenes on their behavior in solution. Therefore, all these available studies of fullerenes solvation point to the need of developing new methods for the dispersion of fullerenes. Received: July 17, 2014 Revised: September 2, 2014 Published: September 3, 2014 11330

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Table 1. Ions Considered in This Worka

a

anions/cations

1-butyl-3-methylimidazolium [BMIM]

cholinium [CH]

methylpiperazinium [MP]

benzoate [BE] tetrafluoroborate [BF4] lactate [LA] methylsulfate [MS] hexafluorophosphate [PF6] salicylate [SA] propanoate [PR] bis(trifluoromethylsulfonyl)imide [Tf2N]

[BMIM][BE] [BMIM][BF4] [BMIM][LA] [BMIM][MS] [BMIM][PF6] [BMIM][SA] [BMIM][PR] [BMIM][Tf2N]

[CH][BE] [CH][BF4] [CH][LA] [CH][MS] [CH][PF6] [CH][SA] [CH][PR] [CH][Tf2N]

[MP][BE] [MP][BF4] [MP][LA] [MP][MS] [MP][PF6] [MP][SA] [MP][PR] [MP][Tf2N]

All cation−anion combinations, leading to 24 pure ILs, were studied for the C60 solvation. Acronym for each ion is also reported in square brackets.

Chaban et al.35 proposed in a recent work the use of 1-butyl-3methylimidazolium tetrafluoroborate, [BMIM][BF4], ionic liquid for C60 dispersion, leading to solubilities, predicted using molecular dynamics simulations, as high as 66 g L−1 at 333 K. Results by Chaban et al.35 showed a strong charge transfer between the C60 and its solvation shell for imidazolium and pyridinium ILs, whereas this behavior is not present in the cases of ammonium and phosphonium ILs. Additional molecular dynamics simulation studies by Fileti and Chaban41 confirmed the stability of supersaturated C60 solutions in [BMIM][BF4] in the microsecond range and at several temperatures. Likewise, Fileti and Chaban42 also showed the ability of [BMIM][BF4] to enhance the dispersion of C60 in water solutions, which is of remarkable relevance for applications in the biomedical field. Maciel et al.43 used molecular dynamics simulations to analyze the properties of the solvation sphere around C60 for imidazolium and ammonium ILs, showing the weakening of ion−ion interactions in the first solvation shell in comparison with the bulk ILs. Highly structured solvation layers are inferred around C60 fullerene, and the calculated free energies of solvation show the solvophobic character of the solvation process, which is strongly affected by the IL polarity. Therefore, considering the very relevant initial results for the solvation and dispersion of fullerenes using ILs,35,43 a study on C60 solvation in 24 different pure ILs is reported in this work. ILs containing imidazolium, cholinium, and piperazinium cations, were paired with eight different types of anions, Table 1. Ions studied in this work were selected to infer systematically the effect of molecular structuring and electronic properties with regard to the affinity for C60 fullerene and its relationship with the structuring of solvation layers around fullerene. Likewise, C60 solvation by mixed ILs was also considered. Molecular dynamics simulations at different temperatures were carried out to infer nanoscopic behavior of the studied systems, from the viewpoint of structural, energetic and dynamic properties. Moreover, considering the results reported by Chaban et al.35 on the charge transfer between solvating ions and fullerenes, charge transfers were computed through Density Functional Theory (DFT). The main objective of this work is to infer the mechanism and properties of fullerenes solvation by ILs, obtaining a nanoscopic view, through a systematic analysis of the effects rising from the types of involved ions to advance in the most suitable ions combinations for fullerenes dispersion.

the IL and C60 fullerene. First, stage I, the systems formed by the corresponding 200 ion pairs and one C60 fullerene were initially modeled according to force field parametrizations reported in Table S1 (Supporting Information). In this stage I, uncharged C60 was considered. From the output of stage I simulations, the systems formed by the C60 molecule and the first solvation shells around it, containing 20 ions, were extracted and DFT calculations (according to the procedure reported in the next section) were carried out to quantify IL− C60 charge transfer and binding energy for all the studied ILs. To take into account this charge transfer in molecular dynamics simulations, the depth of the corresponding pairwise LennardJones potentials (ε, for cation−C60 and anion−C60) were corrected, as proposed by Chaban et al.,35 and thus, reproducing the IL−C60 binding energies obtained from DFT with the molecular dynamics simulations. Then, stage II, molecular dynamics simulations with these new parameters were carried out for production purposes. In a recent study, Choi et al.44 developed a first-principlesbased polarizable force field for ILs in the pure state in contrast with the traditional charge transfer approach. Nevertheless, although the very valuable results by Choi et al.44 are a suitable approach for describing anion−cation interactions, the objective of the current work is to describe ion−C60 interactions, and thus, as the results reported by Chaban et al.35 showed a clear ion−C60 charge transfer, this approach was used along this work. Molecular dynamics simulations were carried out using the MDynaMix v.5.2 molecular modeling package.45 A total of 200 ion pairs with one C60 fullerene molecule were considered for all the simulations. Cubic simulation boxes were considered in all the cases. All the systems were simulated in the NPT ensemble at 0.1 MPa at 323, 348, 373, or 400 K. Pressure and temperature were controlled using the Nose−Hoover thermostat. Coulombic interactions were handled with the Ewald summation method,46 with cutoff radius of 15 Å. Tuckerman− Berne double time step algorithm,47 with long and short time steps of 1 and 0.1 fs, was considered for solving the equations of motion. Lorentz−Berthelot mixing rules were used for Lennard-Jones terms in the case of stage I simulations; this was also done for stage II simulations, with the exception of ion−C60 pairwise terms, which were corrected as previously mentioned. Initial simulation boxes were built using the Packmol program.48 Heating and quenching steps were carried out between the working temperature and 500 K to ensure equilibration before starting stage I simulations. Simulations extending to 10 ns were performed for both stage I and stage II. DFT Calculations. Charge transfer and binding energy for the systems formed by one C60 fullerene and ions in its first solvation shells, containing 20 ion pairs, which were extracted

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METHODS Molecular Dynamics Simulations. These simulations were carried out in two stages according to the procedure reported by Chaban et al.35 to consider charge transfer between 11331

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Tables S2−S11, Supporting Information, gather atomic charges for selected ILs computed according Mulliken, NPA, Hirshfeld, MK, and ChelpG schemes. Average charges per atom and, thus, average ion charges are very sensitive to the method applied for charge calculation. Results reported in Figure 2 show average ion charges, whereas the total charge of the ILs cluster surrounding the C60 molecule and, thus, the charge transfer from the IL cluster to the fullerene is reported in Figure 3. For comparison purposes, results for [BMIM][BF4] show a charge on C60 being +0.1072, −0.0210, +0.3280, +0.5567, and 0.3689 using Mulliken, NPA, ChelpG, and MK schemes, respectively. NPA method leads to charge transfer from IL to C60, which is opposite to the remaining methods and to the results from Likewise, Mulliken method leads to small charge transfer, whereas ChelpG gives rise to larger values, and Hirshfeld results being in good agreement with Chaban et al.35 results using the same scheme. Small differences could be due to different DFT methods. For a fixed method, for example, MK, the ordering of charge transfer is roughly [CH] > [MP] > [BMIM] cation effect, with minor effect rising from the type of anion, which points to cation−C60 prevailing interactions in comparison with anion−C60 ones. Molecular Dynamics Results. DFT results reported in the previous section allowed to modify the force field parametrization for the considered ionic liquids, as explained in Methods. MK charges were used to define ion−C60 interactions, and thus, ε parameters, Lennard-Jones potential well depth, for cation−C60 and anion−C60 pairwise interactions were corrected to reproduce binding energies obtained from DFT calculations of clusters formed by 1 C60 + 20 ion pairs, Figure 1, as reported in the previous section. The structure of the solvation spheres around the C60 molecules was analyzed from molecular dynamics simulation results using radial (RDFs) and spatial (SDFs) distribution functions. RDFs between the center of mass of C60 and the anion and cation center of mass are reported in Figure 4. The structure of RDFs reported in Figure 4 is obviously strongly dependent on the molecular structure of the involved ions. Nevertheless, well-defined peaks corresponding to the first solvation shells around C60 are obtained in most of the cases, which shows high structuring of ILs around the C60, especially for the first shell, but extending to larger distances, with weaker second solvation shells appearing for most of the studied compounds. Likewise, density fluctuations extend up to almost 20 Å for most of the considered ILs, showing the strong effect of the presence of C60 nanoparticle on the ILs structure. Three different cations were combined in this work with eight anions, and thus, the effect of anion and cation molecular structure on the structure of the solvation shell around the C60 may be analyzed. In the first column of Figure 4, RDFs for ILs containing [BMIM] are considered. Maciel and Fileti43 molecular dynamics results for the C60 solvation in [BMIM][BF4] show strong first RDF peaks, corresponding to the first solvation shell, which are in agreement with those reported in this work, Figure 4 and Table 2, but with stronger intensities in the work by Maciel and Fileti43 than in this work, which correspond to slightly different force field parametrization. Analogous results were reported by Wang et al.56 for [BMIM][BF4], [BMIM][CH3COO], [BMIM][PF6], [BMIM][Tf2N], [BMIM][TFA] (with TFA being trifluoroacetate), and [BMIM][TfO] (with TfO being trifluoromethanesulfonate). Results by Maciel and Fileti43 and Wang et al.55 showed that for

from stage I molecular dynamics simulations. For this, single point calculation were carried out at B3LYP/6-31G* level. The Gaussian09 (Revision D.01) package49 was used for all these calculations. Aimed to obtain a deeper description about charge transfer between C60 and ILs, atomic charges (AC) were computed through five different schemes: Mulliken,50 Natural Population Analysis51 (NPA), Hirshfeld,52 Merz−Kollman53 (MK), and ChelpG.54 All these AC can be directly computed with Gaussian09. These schemes were selected according to Meister and Schawarz’s classification:55 AC obtained from wave functions (Mulliken and NPA), from partitioning of the densities (Hirshfeld) and from electrostatic potentials (MK and ChelpG). According to Meister and Schawarz’s classifications, atomic charges can also be computed from spectroscopic data. We have not computed atomic polar tensor derived charges since it requires the calculation of the vibrational frequencies, which would need very large computational resources.

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RESULTS AND DISCUSSION DFT Analysis of C60−Ionic Liquid Interaction. DFT calculations for the clusters composed of 1 C60 + 20 ion pairs, corresponding to the first solvation shell extracted from molecular dynamics simulations, allow to calculate the IL− C60 binding energies and the charge transfer between the fullerene and the surrounding ions. The study by Chaban et al.35 on the solvation of C60 by [BMIM][BF4] using B97X-D/ 6-31G* theoretical level showed a binding energy, BE, of roughly 325 kJ mol−1, calculated per mole of IL. Binding energy reported in this work for the same system and number of ion pairs, Figure 1, are larger than those calculated by Chaban et

Figure 1. Binding energy, BE, calculated at B3LYP/6-31G* for 1 C60 + 20 ionic pairs clusters.

al.,35 but if basis set superposition error is considered (∼20% according to Chaban et al.35), the difference between both data is roughly 10%, which is in good agreement considering the different theoretical level. The effect of anion and cation on binding energy may be analyzed from results reported in Figure 1 for the 24 ILs studied in this work. Calculated BE is in the range of −157.3 kJ mol−1, for [BMIM][Tf2N], to −549.8 kJ mol−1, for [MP][LA], which shows that IL−C60 affinity may be fine-tuned through suitable anion−cation selection. Nevertheless, results reported in Figure 1 do not allow to infer a direct relationship between the molecular structure of the involved ions and BE. Chaban et al.,35 using the Hirshfeld approach, showed a remarkable charge transfer in the system [BMIM][BF4]−C60, leading to a total electron charge of +0.35 on C60, with +0.85 and −0.85 average charges on cation and anion, respectively. 11332

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Figure 2. Average charge (au) value per cation (left) and anion (right calculated at B3LYP/6-31G* level using different schemes for 1 C60 + 20 ion pairs clusters.

all the studied [BMIM]-based ILs, the position of the first peak in RDF (R1), is almost equal for all the anions. The exceptions are [BMIM][PF6] in Wang et al.55 ([PF6] anion placed further for C60 than [BMIM] cation), and [BMIM][BF4] in Maciel and Fileti43 (cation further of C60 than anion) but not for Wang et al.55 There is a discrepancy for the anion and cation RDFs first peak intensity, g(R1), in the case of [BMIM][BF4], Wang et al.55 reports g(R1) larger for the cation than for the anion, whereas Maciel and Fileti43 reported the reverse behavior in agreement with results reported in this work, Figure 4 and Table 2. Moreover, Wang et al.55 reports larger g(R1) values for the cation than for the anion for all the six ILs studied. The first solvation shell is defined as the distance at which the first minimum in RDFs appears (R2), and thus, the number of ions in this shell may be calculated from the corresponding running integrals of RDFs integrating up to this distance, N(R2). In the case of [BMIM]-based ILs, N(R2) is always larger for the anion than for the cation, Table 2, and thus, a larger number of anion than of cations should be present in the first solvation shell, in agreement with Maciel and Fileti43 but in disagreement with Wang et al.,55 whose results pointed to the opposite trend. Results for RDFs in [BMIM]-based ILs reported in Figure 4 and Table 2 show R1 both for the anion in the 7−8 Å range,

with almost negligible differences between the anion and cation for each IL, which show that both ions occupy almost the same regions in the vicinity of the C60 surface. N(R2) for anion is 2− 5 times larger than for [BMIM], which shows a larger anion than cation densification close to fullerene surface. Nevertheless, the first peak in RDF for [BMIM] cation is followed in most of the cases by a second close peak in the 9−11 Å range, with almost the same intensity than the first one, whereas further anion peaks are placed at larger distances. Therefore, for [BMIM]-based ILs, the first solvation shell is richer in anion than in cations, but there is a close region rich in cations, Figure 4. For the case of [CH]-based and [MP]-based ILs, [CH] and [MP] cations are placed further on the C60 surface than [BMIM] in [BMIM]-based ILs. This behavior may be justified considering the shapes of these cations, which in the case of [BMIM] tend to approach the C60 surface to improve the interaction between the cation and C60 π systems, whereas for [CH] and [MP], their nonplanar shapes tend to larger solvation shells fitting a larger number of cations in comparison with [BMIM]. The behavior of RDFs for anions in [CH]- and [MP]-based ILs is complex. In the case of [BMIM]-based ILs, RDF shapes are weakly dependent on the type of anion, which points to a first solvation shell structuring strongly controlled 11333

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The effect of a common cation on the structuring around the C60 may be inferred from the SDFs reported in Figure 6, for [BMIM]-based ILs. In this case, [BMIM] cation and the corresponding anions occupy almost the same region around the C60 nanoparticle, in agreement with the position of the first maxima reported in Table 2, but the concentration of anions is larger than for cations in this first solvation shell. Anions such as [PF6] tend to form islands around the C60, whereas a more evenly distribution is obtained for anions such as [Tf2N]. The structuring of ions around the C60 is controlled on one side by sterical effects (size and shape of the involved ions) and on the other side by the strength and characteristics of ion− C60 intermolecular interaction energy. Considering that C60 is a nonpolar molecule, noncharged C60 is then considered in the molecular dynamics simulations carried out in this work, and thus, ion−C60 intermolecular interaction energy is only of Lennard-Jones type, Eint, which is reported in Figure 7. In the case of [BMIM]-based ILs, cation−C60 is larger than anion− C60 for all the systems, with the exception of ILs containing [BE], [SA], and [Tf2N] anions. Maciel and Fileti43 reported −205 and −49 kJ mol−1 for [BMIM]−C60 and [BF4]−C60 Eint, respectively, in [BMIM][BF4], which are in good agreement with −232 and −51 kJ mol−1 reported in this work, Figure 7. The large [BMIM]−C60 Eint is justified considering the π−π interaction mechanism between the fullerene and the imidazolium moiety in the cation, which is remarkably stronger than all the possible anion−C60 interactions, in spite of the high structuring of anions around the C60 reported in Figures 4 and 6. In the case of [BMIM]based ILs containing [BE] and [SA] anions, these anions may also develop π−π interactions with the C60, and thus, for these systems, anion−C60 and [BMIM]−C60 Eint are very similar. It should be remarked also the strong [Tf2N]−C60 Eint, which is also comparable to [BMIM]−C60 in [BMIM][C60]. In spite of the strong [BMIM]−C60 Eint, it is dependent on the type of anion, for anions weakly interacting with C60 being roughly in the 200−250 kJ mol−1 range, whereas for anions competing with [BMIM] for C60 π−π interaction sites (BE], [SA], and [Tf2N]), it decreases to the 150 kJ mol−1 range. Eint in the case of [CH]- and [MP]-based ILs shows a complex behavior in agreement with the structural properties reported in Figure 4. [CH]−C60 and [MP]−C60 interactions are roughly weaker than [BMIM]−C60, which confirms the prevailing role of π−π interactions for C60 solvation. For [CH]-based ILs containing [BE], [SA], and [Tf2N] anions, anion−C60 Eint is larger than cation−C60 ones, and larger than the corresponding anion−C60 interactions in [BMIM]-based ILs. This behavior shows that when the cation is not able to develop π−π interactions with the C60, anion−C60 interactions are reinforced, especially when anions are able to develop π−π interactions. The behavior of [MP]-based ILs with regard to Eint is very similar to that in [CH]-based ones, with [MP]−C60 Eint being slightly larger. A parameter that may be used to analyze the structuring of ions around the C60 is the residence time, tres, which is defined as the time that an ion remains inside the first solvation sphere around the nanoparticle, being limited by the first minima for RDFs reported in Table 2. The calculation of tres is carried out from the exponential decay of the conditional probability for the center of mass, P(t), of the corresponding ions to remain inside the first solvation sphere around the C60 nanoparticle, Figure 8. The dynamic of ions inside the first solvation sphere around the C60 analyzed through P(t) show strong depend-

Figure 3. Total charge (au) for the cluster of ILs surrounding C60 calculated at B3LYP/6-31G* level using different schemes for 1 C60 + 20 ion pair clusters. For C60 same values (with opposite sign) are obtained.

by the cation, which is justified considering the aromatic structure of the [BMIM] anion, but for [CH]- and [MP]-based ILs, the type of anion determines not only the anion RDF, but also the cation one. [CH]-based ILs show RDFs for the cation with a first narrow peak in the 7−8.5 Å range, with the exception of [CH][LA], for which a broad band is obtained, whereas anion RDFs show a first peak closer to the C60 surface, with the exception of [Tf2N]-ILs. N(R2) is slightly larger for anions than for cations, with some exceptions. Results reported in Table 2 and Figure 4 show that the structure of an ion around C60 is strongly dependent on the corresponding counterion in the IL. This is analyzed in Figures 5 and 6 from the corresponding SDFs. Figure 5 show SDFs for ILs with a common [BE] anion and [BMIM], [CH], and [MP] cations. In the case of [BMIM][BE], [BE] anions are evenly distributed close to the C60, corresponding to the first peak in Figure 4, with some [BMIM] cations in the same region and with an outer [BMIM] shell formed by cation islands. For the case of [CH][BE], [BE] anions are placed close to the C60 surface with an external [CH] distribution formed by [CH] islands, even more remarkable than in the [BMIM] case. This behavior is more remarkable in the case of [MP][BE], in which both the cation and anion are distributed forming well-defined hotspots around the fullerene. 11334

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Figure 4. Radial distribution function, g(r), between the center of mass of C60 and the corresponding center of mass for anion (blue) and cation (red), obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K.

Table 2. Properties of Radial Distribution Functions between the C60 and Anions or Cations Centers of Mass Obtained from Molecular Dynamics Simulations in Ionic Liquid + C60 at 323 K (Figure 4)a anion [BMIM][BE] [BMIM][BF4] [BMIM][LA] [BMIM][MS] [BMIM][PF6] [BMIM][PR] [BMIM][SA] [BMIM][TF2N] [CH][BE] [CH][BF4] [CH][LA] [CH][MS] [CH][PF6] [CH][PR] [CH][SA] [CH][TF2N] [MP][BE] [MP][BF4] [MP][LA] [MP][MS] [MP][PF6] [MP][PR] [MP][SA] [MP][TF2N]

cation

R1 (Å)

g(R1)

R2 (Å)

N(R2)

R1 (Å)

g(R1)

R2 (Å)

N(R2)

7.26 7.72 7.74 8.03 7.99 7.58 7.24 7.45 7.03 7.65 6.89 7.99 7.79 7.68 7.26 9.13 7.46 7.85 7.88 8.02 7.78 7.38 7.04 9.12

2.18 1.96 2.70 1.84 3.71 2.77 2.51 1.13 1.55 2.89 1.57 2.40 4.89 2.62 2.58 3.81 1.71 1.31 2.45 2.18 3.51 2.52 2.29 3.14

10.60 10.21 9.66 9.51 10.76 9.84 10.47 11.36 11.05 9.54 10.06 9.59 9.87 9.88 11.00 11.32 9.60 10.93 9.37 10.03 10.18 10.06 9.17 10.90

11.12 10.53 10.55 10.89 15.45 11.47 11.42 11.67 14.99 11.83 14.20 13.16 11.09 13.99 12.39 14.04 8.98 19.36 9.76 16.44 12.05 13.61 7.17 12.57

7.55 7.65 7.63 7.75 7.50 7.83 7.43 7.52 8.16 8.18 7.05 8.22 8.06 8.38 8.39 8.46 8.22 7.13 7.92 6.97 8.14 7.08 8.07 8.42

1.11 1.33 1.81 0.95 1.41 1.68 1.59 0.95 2.94 3.79 1.77 3.75 3.65 1.73 1.95 2.39 2.41 4.09 2.47 2.85 2.45 3.09 3.16 2.67

8.44 8.24 9.73 9.75 8.09 8.74 8.37 8.13 9.60 10.16 8.98 9.54 10.31 9.82 10.00 10.23 10.33 10.17 10.28 9.42 9.83 9.41 9.34 10.76

2.84 3.54 8.88 7.86 3.97 5.57 3.21 2.05 8.50 14.72 9.57 11.67 14.07 10.18 8.50 9.47 13.15 16.02 15.65 11.07 13.37 13.18 8.91 12.71

R1 stands for the position of the first maximum, g(R1) for the RDF at R1, R2 for the position of the first minimum, and N(R2) for the running integral of RDF at R2.

a

reported in Figure 8. Likewise, [BMIM] tres is also dependent on the type of counterion, in agreement with the Eint behavior. The tres values calculated from P(t) are reported in Table S12

ence on the type of ions. In the case of anions for [BMIM]based ILs, [BE], [SA], and [Tf2N] show the slower dynamics, which is in agreement with the larger interaction energies 11335

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Figure 5. Spatial distribution functions for the ion center of mass around the center of mass of C60, for ionic liquids with a common [BE] anion, obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K.

Figure 6. Spatial distribution functions for the ion center of mass around the center of mass of C60, for ionic liquids with common [BMIM] cation, obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K.

Figure 7. Ion−C60 Lennard-Jones intermolecular interaction energy, Eint, obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K: (black) anion−C60, (red) cation−C60.

with temperature was adjusted to and Arrhenius type behavior, eq 1:

(Supporting Information) and are plotted in Figure 9 in relationship with Eint. Results reported in Figure 9 show that the ions dynamic in the first solvation shell around C60 is linearly related with Eint, both for anions and cations, the stronger the interaction between an ion and C60, the larger the ions remains around the nanoparticle. Molecular dynamics simulations for the studied ionic liquids were carried out in the 323 to 400 K temperature range, to infer the temperature effect on the solvation structuring. To quantify the temperature effect on the ion−C60 interactions, Eint change

E int = A × exp(−Ea /RT )

(1)

The Ea parameter allows quantifying the strength of ion−C60 Lennard-Jones interactions with regard to temperature, Figure 10. Ea is in the 2−3 kJ mol−1 range for most of the ions, which is in agreement with the nature of ion−C60 forces, and with similar values for anions and cations, with the exception of ILs containing [BF4] and [PF6] anions for all the cations, and for 11336

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Figure 8. Exponential decay of conditional probability P(t) for the center of mass of anions or cations to remain within a sphere of radius R + δr around the center of mass of C60 molecule, entering the sphere of radius R − δr at time t = 0. P(t) calculated from molecular dynamics simulations in ionic liquid + C60 at 323 K. All results obtained for the first solvation shell around C60 molecule.

Figure 11. Relationship among activation energy, Ea, and ion−C60 Lennard-Jones intermolecular interaction energy, Eint, obtained from molecular dynamics simulations in ionic liquid + C60. Continuous lines show linear fits for cation and anion data (R = 0.97 and 0.93 for anions and cations, respectively).

obtained for those systems presenting larger Eint values. Therefore, for those ions with large Eint, ion−C60 interactions do not change remarkably in the 323−400 K temperature range. A question rising from the molecular dynamics study is the possible effect of solvating IL structure on the properties of C60 nanoparticle. The main properties of C60 are the C−C bond distance, dC−C, and the nanoparticle radius, RC60. Molecular dynamics simulations of one C60 molecule were carried out in vacuum, for comparison purposes, leading to average values of 1.446 ± 0.002 Å and 3.579 ± 0.001 Å for dC−C and RC60, respectively. Literature experimental values for dC−C are 1.401 Å for C−C bonds fusing five and six membered rings and 1.458 Å for bonds between six membered rings,57 and thus, being in agreement with the average dC−C value obtained in this work from vacuum simulations. Upon solvation, dC−C suffers a minor change in comparison with vacuum, leading to an average value for the 24 studied ILs of 1.454 ± 0.004 Å (0.6% increase). Nanoparticle radius was also calculated in the 24 ILs, RC60 is larger in all the studied ILs than in vacuum, with an average value for the 24 ILs of 3.61 ± 0.03 Å, and thus, leading to an average 0.9% expansion upon solvation (Table S14,

Figure 9. Relationship among ion residence time in the first solvation shell around C60, tres,and ion−C60 Lennard-Jones intermolecular interaction energy, Eint, obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K. Continuous lines show linear fits for cation and anion data (R = 0.92 in both cases). Data for this figure is reported in Table S12 (Supporting Information).

[BMIM]-based ILs, for which anion−C60 Ea values are larger than cation−C60 ones in most of the cases. Moreover, there is a linear relationship, Figure 11, between the strength of ion− C60 interactions and Ea, with the lower Ea values being

Figure 10. Activation energy, Ea, for the ion−C60 Lennard-Jones intermolecular interaction energy calculated from eq 1 obtained from molecular dynamics simulations in ionic liquid + C60 in the 323 to 400 K temperature range. Ea data for this Figure in Table S13 (Supporting Information). 11337

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with the type of involved ions nor with the ion-C60 interaction energy. Nevertheless, we report in Figure 13 the Coulombic and Lennard-Jones contributions to the total anion−cation interaction energy in ionic liquid + C60 systems. Coulombic contribution is obviously large than Lennard-Jones terms considering the ionic character of the studied compounds and it is in the 2000 to 3500 kJ mol−1 range, and thus, showing the very different polarity of the studied compounds. The dynamic behavior of the whole fluid containing C60 nanoparticle was analyzed through the self-diffusion coefficients, D, obtained from the mean square displacements and the Einstein’s equation. D values for the C60 center of mass in the 24 studied ILs are reported in Table S16 (Supporting Information), with an average value of 0.11 × 10−11 m2 × s−1, and thus, this low diffusion is reasonable considering the large viscosity of most of the studied ILs, which is strongly related with the anion−cation interaction energy reported in Figure 13. Likewise, there is linear relationship between the C60 diffusion rates and the strength of the ion−C60 interactions, Figure 14, and thus, confirming the prevailing role of Eint, and its relationship with ions structure and properties, with the solvation structure and dynamics of C60 in ILs.

Supporting Information). Although these are weak changes in the C60 structural properties when solvated by ILs, they are strongly related with the strength of total ion−C60 interaction energy. Results reported in Figure 12 for the percentage

Figure 12. Percentage of C60 radius variation in ionic liquid + C60 systems, %ΔR, at 323 K in comparison with total ion-C60 interaction energy. %ΔR data for this Figure in Table S14 (Supporting Information). Continuous lines show linear fit (R = 0.91).

variation of RC60 in comparison with ion-C60 Eint show a welldefined linear relationships: the stronger the ion−C60 interactions, the larger the C60 expansion (but always lower than 1.3%). This slight C60 expansion upon IL solvation leads to a larger contact surface with solvating ions, which improves the ion−C60 interaction, but always considering the limits imposed by the nanoparticle rigidity to maintain the esphericity and dC−C into reasonable limits, and thus, to very weak changes in RC60. Dissolving C60 nanoparticles in ILs should lead to some changes in the IL properties. Maciel and Fileti43 analyzed the changes in the energetics of ion−ion interaction for [BMIM][BF4] and [ethylammonium][nitrate] with the presence of C60 molecule, showing that C60 destabilized the ionic network, especially for anion−cation interactions. Nevertheless, this C60 destabilization effect is very weak, in the case of [BMIM][BF4], results reported by Maciel and Fileti43 showed a 0.3% destabilization considering the total energy (Coulombic + Lennard-Jones), which is almost counterbalanced by the ion− C60 interaction energy. For the 24 ILs studied in this work the destabilization in the total IL ion−ion interaction energy is lower than 0.5% on average, no trend could be inferred neither

Figure 14. Self-diffusion coefficient of C60 center of mass, D, in the corresponding ionic liquid, in comparison with total ion−C60 interaction energy, obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K. Data for this figure in Table S16 (Supporting Information). Continuous lines show linear fit (R = 0.86).

Figure 13. Coulombic, EA‑C,Coul, and Lennard-Jones, EA‑C,LJ, contributions to the anion−cation intermolecular interactions energy obtained from molecular dynamics simulations in ionic liquid + C60 at 323 K. Data for this figure in Table S15 (Supporting Information). 11338

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CONCLUSIONS A DFT and molecular dynamics study on the solvation of C60 fullerene by 24 ionic liquids belonging to the imidazolium, cholinium and piperazinium families is reported in this work. The solvation shells around the C60 are characterized by strong tendency to develop π−π interactions, both for anions and cations, which lead to large ion−C60 interaction energies for those ions able to develop these intermolecular forces in comparison with ions not containing π-systems. The key parameter controlling the structure and dynamics of ions around the C60 nanoparticle is the ion−C60 Lennard-Jones interaction energy, and thus, linear relationships between this property and relevant parameters such as ion residence time in the solvation shells, of C60 self-diffusion are inferred. Likewise, very weak structural changes in C60 are obtained upon IL solvation, which lead to a slight C60 expansion in order to improve ion−C60 interactions through a small increase in C60 surface. Therefore, C60 solvation and, thus, C60 dispersion may be controlled through a selection or design of ions improving the interaction with C60 surface through π−π interactions both for anion and cation.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1 (force field parametrization), S2 (average cation Mulliken charges), S3 (average cation NPA charges), S4 (average cation Hirshfeld charges), S5 (average cation ChelpG charges), S6 (average cation MK charges), S7 (average anion Mulliken charges), S8 (average anion NPA charges), S9 (average anion Hirshfeld charges), S10 (average anion ChelpG charges), S11 (average anion MK charges), S12 (ion−C60 Lennard-Jones interaction energy), S13 (activation energy, for the ion−C60 Lennard-Jones intermolecular interaction energy), S14 (percentage of C60 radius variation), S15 (Coulombic and Lennard-Jones contributions to the anion− cation intermolecular interactions energy), and S16 (selfdiffusion coefficient of C60 center of mass). This material is available free of charge via the Internet at http://pubs.acs.org.

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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 G.G. acknowledges the funding by Junta de Castilla y León, cofunded by European Social Fund, for a postdoctoral contract. We also acknowledge The Foundation of Supercomputing Center of Castile and León (FCSCL, Spain) and Computing and Advanced Technologies Foundation of Extremadura (CénitS, LUSITANIA Supercomputer, Spain) for providing supercomputing facilities. The statements made herein are solely the responsibility of the authors.

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