Graphene in Ionic Liquids: Collective van der Waals Interaction and

Article pubs.acs.org/JPCB

Graphene in Ionic Liquids: Collective van der Waals Interaction and Hindrance of Self-Assembly Pathway Yinghe Zhao and Zhonghan Hu* State Key Laboratory of Supramolecular Structure and Materials and Institute of Theoretical Chemistry, Jilin University, Changchun, 130012, P. R. China S Supporting Information *

ABSTRACT: Over the past decade, there has been much controversy regarding the microscopic mechanism by which the π-electron-rich carbon nanomaterials such as graphene and carbon nanotubes can be dispersed in ionic liquids. Through a combination of a quantum mechanical calculation on the level of density functional theory, an extensive molecular dynamics study on the time scale of microseconds, and a kinetic analysis at the experimental time scale, we have demonstrated that collective van der Waals forces between ionic liquids and graphene are able to describe both the shortranged cation−π interaction and the long-ranged dispersion interaction and this microscopic interaction drives two graphene plates trapped in their metastable state while two graphene plates easily self-assemble into graphite in water.

is crucial to resolve the current debate in the field and might be helpful to advance the design and use of carbon nanomaterials in the future. In order to understand the mechanism of graphene dispersion, we carry out multiscale calculation for a variety of systems. We first perform quantum mechanics study of gas phase system consisting of one π-electron-rich molecule and one pair of cation 1-octyl-3-methylimidazolium ([C8MIM+]) and anion hexafluorophosphate ([PF6−], see Figure 1). From the result of quantum mechanical calculation, we illustrate that it is reasonable to use standard van der Waals (VDW) parameters to model the interaction between graphene and ionic liquids. We further carry out extensive molecular dynamics study for model graphene plates consisting of 77 carbon atoms in various solvents such as water, ionic liquids [C8MIM+][PF6−], 1-butyl-3-methylimidazolium hexafluorophosphate [C4MIM+][PF6−], 1-ethyl-3-methylimidazolium hexafluorophosphate [C2MIM+][PF6−] (see Figure S1 in the Supporting Information), and pesudo-ILs [C8MIM+][PF6−] with the atomic charges reduced to 10 or 50%. The effects of alkyl chain length and the charges are illustrated by comparing the results from various types of systems. Through the computed free energy curves from molecular dynamics simulations, we are able to estimate macroscopic kinetics in the experimental time scale.

1. INTRODUCTION Noncovalent dispersion of carbon nanomaterials such as carbon nanotubes and graphene in solvents is a crucial step to carbon nanotechnology, as it increases the applicability of these nanomaterials while still maintaining their intrinsic properties. In the past decade, many experimentalists have been devoted to dispersion of graphene or carbon nanotubes in room temperature ionic liquids (ILs).1−18 Aida and co-workers have discovered the formation of “bulky gel” composed of single wall carbon nanotubes and imidazolium ion-based ILs.9−11 Inspired by the successful dispersion of carbon nanotubes in ILs, Han and co-workers reported highly dispersed graphene sheets in ILs using a non-covalent approach12,13 and the gels formed by ILs and graphene have been studied as potential electrolytes for dye sensitized solar cells by Ahmad et al.14 Because ILs bestow great thermal stability and green chemistry solvent properties, dispersion of carbon nanomaterials in ILs may provide a sustainable solution for energy and environmental issues.15−18 However, there has been much controversy about how and why ILs can disperse π-electron-rich carbon materials. As carbon nanotubes and graphene are rich in π-electrons, it was suspected that strong cation−π interaction between carbon nanomaterials and ILs may be responsible for the mechanism of dispersion of carbon materials in ILs. 19 In contrast, spectroscopic evidence in the experiment by Li and co-workers has suggested that there might not be electronic interaction between carbon materials and ILs.20 In order to understand how typical carbon materials can be dispersed in ILs from molecular details, we now model the system from a quantum mechanical level and directly simulate the behavior of graphene in ILs with comparison to that in water. Understanding the intrinsic mechanism underlying the dispersion of the graphene © XXXX American Chemical Society

Received: June 7, 2013 Revised: August 13, 2013

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dx.doi.org/10.1021/jp405660d | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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Figure 1. Schematic plots of two types of model graphene plates77 carbon atoms model plate (a) and nine-phenyl-ring molecule (b), two configurations of the strongest cation−π effect (c and d) in the gas phase between a nine-phenyl-ring molecule and anion [PF6−] (e), cation [C8MIM+] (f). To simpify the quantum mechanical computation of the cation−π effect in the gas phase, we have used a smaller plate consisting of nine phenyl rings (shown as b). In the molecular dynamics simulation of the liquid phase, we use larger graphene plates consisting of 77 carbon atoms (shown as a). Rectangular boxes in e and f indicate the anionic polar group, cationic polar headgroup, and nonpolar tail group, respectively.

2. RESULTS AND DISCUSSION 2.1. Cation−π Interaction and van der Waals Interaction. In this work, we aim to directly simulate the behavior of model graphene plates (see Figure 1a and b) in water and in a series of ILs such as [C8MIM+][PF6−]. It is nontrivial to develop a force field to characterize the complex interactions between graphene and ILs. Previous theoretical studies on graphene in solution take VDW parameters for graphene from a standard force field which correctly catches the long-ranged weak interaction between graphene and water or organic molecules.21−23 The VDW parameters are usually used for characterizing the interaction between neutral molecule and π-electron-rich molecule, as was successfully applied in the study of graphene in water and several traditional organic solvents.21−23 One might wonder whether the same VDW parameter set is still valid in the presence of cation−π interaction especially when graphene is close to a cation of IL. Instead of using a large graphene sheet, we chose to study a molecule with nine phenyl rings (Figure 1b) possessing πelectron similar to the interaction center of a large graphene plate. Figure 2 shows results of energy and charge transfer from a quantum mechanical calculation based on the B3PW91/6311+g(d,p) level of theory24−26 at a series of separation distances. As has been verified by Lopes and co-workers,27 this density functional B3PW91 has been successful in describing the intermolecular interaction for polymorphs. We have verified that results of interaction energies are very similar when using a larger graphene model (see Figure S1e, Supporting Information) or using a different DFT method B3LYP. We have chosen two cases where the cation−π interaction is supposed to be the largest (Figure 1c and d). Surprisingly, the VDW interaction energy is able to mimic that of the quantum mechanical calculation for the configuration where strong cation−π interaction exists. At a close distance of about 0.3 nm, the large effect of electron transfer is about 0.3 e and the electron transfer effect approaches 0 at a relatively larger distance of 0.5 nm, which is typical in the liquid phase. This finding agrees with the experimental result from Li and co-workers that the electron transfer effect is rarely observed in the liquid phase.20 A test simulation of two positively charged graphenes in water

Figure 2. Interaction energies (a and b) and charges (c and d) for the model graphene plates and ions at a series of distances. The distance r is defined in Figure 1c (for a and c) and in Figure 1d (for b and d). The calculations using force field parameters are indicated by VDW or VDW+Coul. 9 phe and 14 phe stand for graphene models of 9-phenylring molecule and 14-phenyl-ring molecules, respectively.

has confirmed that the repulsion between model graphene plates will not be able to significantly affect the time scale of collapse (see Figure S2 in the Supporting Information). Therefore, the effect of charge transfer will be neglected in our next molecular dynamics simulation. This part of the quantum mechanical study assures us that modeling the graphene plates using VDW parameters from the standard force field is reasonable for both short-ranged cation−π interaction and long-ranged dispersion interaction between graphene and typical ILs. Throughout this article, the longranged interaction stands for interactions beyond a few angstroms where the cation−π interaction is relatively less effective. It has to be noted that VDW interaction, which is effective at distances as large as our cutoff distance 1.3 nm, is often classified as short-ranged when compared with longerranged electrostatic interaction in molecular dynamics study. 2.2. Thermodynamics and Structure. Before we investigate the dispersion of graphene in solution, we carry out a tutorial simulation for motion of two graphene plates (Figure 1a) in water and in a typical IL. The slides in Figure S3 (in the Supporting Information) show a short-time behavior of the two graphene sheets in the IL [C8MIM+][PF6−] with B



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comparison to water in the time scale of nanoseconds. Clearly collapse of graphene sheets happens in the time scale of nanoseconds in water, while it remains separated in ILs. It is challenging to directly simulate the system to experimental time scales of minutes and hours. Instead, we compute the minimal (reversible) work needed to bring two graphene sheets together from an infinity large distance to their closest distance (about 0.34 nm) in graphite to provide an alternative way to interpret the thermodynamics of graphene dispersion in this IL (see Figure 3). We simulate molecular systems consisting of two

ΔG(r ) =

∫r

∞

Feq(z) dz

(1)

This methodology of computing the potential of mean force was first developed in as early as 1986 by Andersen,28 and has been recently used to investigate the effect of solvents on the thermodynamics of graphene sheets.21−23 Berne and coworkers have shown that urea can destabilize the hydrophobic interaction between two graphene plates by watching the difference of potential of mean force due to addition of urea into water. Notably, calculation of potential of mean force between two graphene sheets covered by surfactant or placed in different polar organic solvents by Blankschtein and coworkers22,23 confirmed the existence of a metastable bilayer graphene structure if appropriate solvents are chosen. Undertaking a similar calculation of the free energy difference as a function of distances for two graphene sheets in ILs has its own significance and challenge. The purpose of this calculation is threefold. First, cation−π interactions have been regarded as the basic interaction between particles with positive charges and molecules rich in π-electron and have been commonly used to interpret experimental results, although the underlying connection is not clear. It is of great interest to understand whether a molecular model taking only the VDW interaction to respresent both short-ranged strong cation−π interaction and long-ranged weak dispersion interaction is able to explain experimental observation. Second, ILs have been used as potential substitutes for traditional organic solvents because of its diversity and green chemistry properties. Understanding the graphene dispersion in ILs at varying temperatures, charges, and chain lengths provides a comprehensive survey for the effect of various ionic solvents on the properties of graphene. Third, due to existence of unique spatial and energetic heterogeneity in ILs first observed by Voth and co-worker and Lopes and co-workers,29−32 it is much more challenging to simulate systems of ILs than any other solvents. Because of the slow dynamics of ILs, simulation results starting from different initial configurations often differ significantly.33 It is much more challenging to get convergent results for properties of ILs than those of traditional organic solvents. Our calculation by undertaking the temperature annealing procedure and checking results from simulations of independent groups provides an example of how to get convincing results for difficult properties. A plot of the free energy difference ΔG as a function of the separation distance r is shown as the solid lines in Figure 4a for graphene sheets in water and in ILs at T = 300 K. Clearly, the thermodynamically stable state for graphene sheets in either water or ILs is identically located at a separation of about 0.34 nm. However, the metastable state for graphene sheets in ILs at a distance of 0.75 nm can exist in a well as deep as 100 kJ/mol. In contrast, for the system of graphene sheets in water, only shallow wells as deep as one-fifth of that of graphene sheets in ILs exist. These states are not stable, and thermo-fluctuation can drive the unstable state to the global minima at a distance of 0.34 nm. However, graphene sheets trapped in the well as deep as 100 kJ/mol are quite stable. The underlying mechanism for the formation of metastable deep wells can be understood if we carefully examine the force exerted on the graphene sheets by the surrounding media and the corresponding local structure of solvents around graphene sheets. A very strong peak at the distance of around 0.75 nm (the black line in Figure 4b) indicates that the local ILs around the graphene sheets provide

Figure 3. A scheme showing that the self-assembly pathway for graphene plates in ILs is hindered due to the formation of the metastable state while graphene plates can easily self-assemble into graphite in water. The cross symbol means that the process is hindered due to a high free energy barrier. The free energy cost for the formation of each state is evaluated using simulations with graphene plates fixed at various distances; it is shown in Figure 4.

graphene sheets separated at a series of distances surrounded by the IL [C8MIM+][PF6−] at temperatures of T = 300, 400, 500, and 600 K. For the IL system at each temperature, we have created eight independent configurations annealed from configurations at a higher temperature. A total of 1−5 μs simulations are done at each temperature. Results from independent simulations converge, indicating that our microsecond simulations are enough to reproduce experimental results at equilibrium conditions which usually requires relaxation at time scales of hours and minutes. Similar systems of two graphene sheets in water at T = 300 K, in two other ILs, and in charge-reduced pseudo-ILs are also simulated for comparison. The simulations of graphene in water are reproduced from a previous study by Berne and co-workers.21 Only VDW interactions between each atom of graphene and each atom of ILs or water are considered, and in our modeling, the cation−π interaction is a result of the combination of the VDW interaction. We use the usual 12−6 Lennard-Jones (LJ) potential to describe the VDW interaction. The LJ parameters for the carbon atom of graphene are σ = 0.32 nm and ε = 0.236 kJ/mol. Details of modeling and simulation setup are found in the section Methods. The free energy difference between a system of two graphene sheets separated at a distance of r and a system of graphene separated at a distance of infinity (ΔG(r) = G(r) − G(∞)) is equivalent to the reversible work needed to bring the two graphene sheets from infinity to the distance of r. We compute ΔG by evaluating the accumulated equilibrium force exerted on the graphene sheets along the route of bringing two graphene sheets together: C



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Figure 4. Free energy difference, strength of forces exerted on the two graphene plates, and the corresponding local structures in ILs where the forces reach the maxima at the distance around 0.65 nm. The free energy difference (a) and the strength of the forces (b) are plotted as a function of the separation r for the two graphene plates in water at T = 300 K (solid green curve), in ILs at different temperatures T = 300 K (solid black curve), 400 K (dashed black curve), 500 K (dashed red curve), and 600 K (dash green curve), and in charge reduced ILs at T = 300 K (solid red curve, 10% means the charges are reduced to 10% of the origin). View of graphene plates in ILs (c) and charge reduced ILs (d) is visualized by the VDW software.40 For the system of ILs (c), only nonpolar tail groups into the middle of the graphene plates. As the charges are reduced to 10% (d), the head groups of the ILs start to enter into the middle of the region and further hinder the collapse of graphene plates.

a strong force preventing the escape of graphene sheets from the deep well. It is commonly known that heterogeneous polar and nonpolar domains exist in ILs which give rise to specific properties29−39 different from traditional organic solvents. As the imidazolium ring and the anion are spatially correlated in the polar domain, only the nonpolar tails insert into the middle of the graphene sheets (Figure 4c) and provide strong collective VDW forces to prevent the escape of the graphene sheets from its metastable state. However, the observation that only nonpolar tail groups exist between the two graphene sheets is limited to the case where the two graphene plates are separated at a small distance of around 0.65 nm where the peak of the force reaches the maxima (Figure 4b). As shown by previous work of ILs confined between graphene plates separated at more than 6 nm, both anions and head groups of cations can be close to the graphene plates.41−44 Experimentalists have argued that there might not be electronic interaction between ILs and π-electron-rich carbon nanomaterials.20 To further understand whether the charges of the ILs are deterministic factors for the formation of the metastable state, we simulate charge reduced IL systems with the charges of atoms reduced to 10% of the origin. As the charges are significantly reduced, the strong correlation between the anion and the cation head polar group disappears (see changes from black solid line to red solid line in Figure 5). In the chargereduced pseudo-IL, the correlation between the anion and the cation headgroup is almost identical to that between the anion

Figure 5. Radial distribution function between anion and cation polar headgroup (solid lines) and between anion and cation nonpolar tail group (dash lines) for the system of [C8MIM+][PF6−] and the charge reduced pseudo-IL (10% means the charges of atoms are reduced 10% of the origin, and the definition of cation head and tail groups is shown in Figure 1).

and the cation tail group (see red solid line and red dashed line in Figure 5). This model pseudo-IL is similar to branched alkyl compounds with collective VDW forces and less electrostatic interactions. Comparison between the pseudo-IL and the corresponding original IL enables us to further illustrate how the collective VDW forces may disperse graphene efficiently. The corresponding results of free energies and forces are shown as solid red lines in Figure 4a and b, respectively, and the surrounding local structures are shown in Figure 4d. Surprisingly, we find that the wells formed in Figure 4a are D



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water (green lines) and ILs (black lines). Clearly, the positions of peaks and bottoms of ΔH resemble those of ΔG curves (black and green lines in Figure 4). −TΔS contributes negatively and is relatively negligible. From the view of thermodynamics, the dispersion process is driven by enthalpy instead of entropy. 2.3. Kinetics. So far, we have presented structural and thermodynamics analysis for systems of two graphene sheets in water and different ILs at different temperatures. Although it is clear that formation of a deep well is crucial to trap graphene sheets in its metastable state, it might be interesting to see how differences in free energies determine the time scale of kinetics for the dispersion of graphene sheets. Blankschtein and coworker have formulated the kinetics of graphene plates using colloid theory.22 We now apply the classical theory of Kramers for barrier crossing problems45,46 to estimate the time scale for the self-assembly process from the two graphene plates in the metastable state to the two graphene plates in its global minima state (r = 0.34 nm). In the limit of large friction, the relative stochastic motion of two graphene plates in an external field ΔG follows:

even deeper than that of the original ILs when comparing the red line and black line in Figure 4a and b. As shown in Figure 4d, because no strong correlation between cation and anion exists anymore, cation head rings can enter into the middle of graphene sheets and provide even stronger collective VDW force to trap the graphene sheets in their metastable state. This gives us a clue that the charges of the ILs are not necessary to separate the graphene, which directly supports that the charge transfer effect is not responsible for the dispersion of graphene plates in ILs. Indeed, Blankschtein and co-workers have found that surfactant can separate graphene too in their experiment.23 We have also simulated similar systems for ILs with much shorter nonpolar chains at T = 600 K (see Figure S4 in the Supporting Information). Obviously, as the chain length becomes shorter, less nonpolar atoms will stay in the middle of the two plates, providing relatively smaller VDW force. Both results from the charged reduced pseudo-IL and ILs with different chain lengths support that domain formation in ILs and the corresponding collective VDW interaction are crucial for the dispersion of graphene sheets. As gels formed by graphene in ILs have also been applied to batteries which may require a working temperature as high as T = 600 K,14 we simulate a high temperature system and similar results are found and shown by dashed lines in Figure 4. As the metastable states are persistent up to T = 600 K, we are confident that these systems are applicable in environments at high temperatures such as solar cells. It might also provide further insight when we consider the role of enthalpy and entropy in driving the dispersion of graphene sheets in ILs, as the free energy can be simply expressed as ΔG = ΔH − TΔS. Figure 6 shows the computed ΔH and −TΔS for solvents of

∂β ΔG(r ) dr = −D + dt ∂r

2D ξ(t )

(2)

where r is the distance between the two plates and ΔG(r) is the curve calculated in MD simulation, as shown in Figure 4. D is the diffusion constant for free Brownian motion of a graphene plate in water or in ILs. β is inversely proportional to temperature (β = 1/kbT, kb is Boltzmann constant). ξ satisfies the white noise condition: ⟨ξ(t )ξ(t ′)⟩ = δ(t − t ′)

(3)

Assuming the two plates are initially located at the metastable state with the separation r = r0 (location of the well, see Table 1), the probability of finding the two plates with separation r at a later time t satisfies the Smoluchowski equation: ∂f ∂ ⎡ ∂β ΔG(r ) ∂⎤ =D ⎢ + ⎥f ∂t ∂r ⎣ ∂r ∂r ⎦

(4)

subject to the initial condition and the absorbing boundary condition: ⎧ ⎪ f (r , 0) = δ(r − r0) ⎨ ⎪ ⎩ f (b , t ) = 0

Figure 6. Analysis of the driving thermodynamic functions. Changes of entropy and enthalpy are shown as a function of the separation r for the solvents of ILs at T = 300 K (black curves) and water at T = 300 K (green curves). The enthalpy term is directly evaluated as ΔH = ΔE + PΔV. ΔE and PΔV are the standard output of MD, and −TΔS is obtained by subtracting enthalpy from the free energy.

for

0 ≤ t < +∞ (5)

where b is the position of the local maximum between the global minima state and the metastable state. In eqs 4 and 5, the physical meaning of f(r, t) is that f(r, t) dr gives the probability of finding the two graphene plates in the vicinity of a certain

Table 1. Experimental Values of Viscosities from ref 52 and Computed Values of k from eq 8a systems water [c8MIN+][PF6−]

condition T T T T T T

= = = = = =

300 300 400 500 600 300

K K K K K K,10%

viscosity (cP)52

k (s−1)

0.8615 625.62795 10.4643 1.9555 0.78462 0.001 (gas)

× × × × × ×

1.00 1.63 1.55 8.13 8.45 4.92

9

10 10−7 10−1 103 106 10−12

b (nm)

r0 (nm)

0.604 0.633 0.642 0.652 0.661 0.612

0.932 0.766 0.786 0.797 0.812 0.724

a

The value for water at T = 300 K is estimated from direct simulation of aggregation of two model graphene sheets. The prefactor in eq 8 is thus obtained from the ratio of solvent viscosity to water viscosity. The input ΔG(r) in eq 8 are obtained from molecular dynamics simulation shown in Figure 4a. The viscosity of the pseudo-IL is taken as a small gas phase value for illustration. E



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separation r after a time t when they were at r0 at t = 0. The concentration of the dispersed graphene plates in their metastable states is proportional to the survival probability for graphene plates not passing over the barrier b defined as S(t ) =

∫b

Current simulations are not able to capture graphene systems at this scale. Nonetheless, the significantly increased time scale for the model graphene systems in various IL solutions strongly indicates that ILs are in much favor of graphene dispersion than water, which is in agreement with experimental observation.

+∞

f (r , t ) d r

(6)

3. CONCLUSIONS In conclusion, we have described the consistence between the cation−π interaction and the VDW interaction. On the basis of the model of VDW interaction, we have successfully simulated the process of graphene dispersion in various ILs with different chain lengths and charges and at different temperatures. Much larger barriers exist due to a formation of metastable states when graphene plates aggregate from large separation to their closest distance of 0.34 nm in ILs than in water. The formation of the metastable state in ILs purely originates from the microscopic collective VDW interaction between the graphene and ILs. By analyzing the underlying thermodynamic and structural origin, we have found that the domain formation in ILs is directly correlated to the height of the barrier. Our kinetic model further shows that the aggregation rate of two graphene plates in solvents is dramatically affected by the height of the barrier through exponents. As the collapse of the graphene plates will naturally induce the self-assembly of graphene into graphite, our study has also explained why the self-assembly process is hindered in solvents of ILs. Recently, Tian and coworkers have introduced the term “cassemblyst” to describe the role of a substance in the process of self-assembly, which is the analogue of a catalyst in the process of chemical reaction.53 From the point view of cassemblyst, our study sheds light on the microscopic reason why a cassemblyst can change the rate of self-assembly.

This problem is a typical diffusion-controlled reactive process, as has been studied in the case of a biological rupture experiment.47−49 Assuming first order reaction kinetics for the process from graphene dispersed in solution to graphene collapsed: dS = −kS(t ) dt

The classical work of Krammers k−1 =

1 D

(7) 45,50,51

states that

∫barrier e βΔG(r) dr∫well e−βΔG(r) dr

(8)

The integration over the barrier is approximately proportional to an exponential factor:

∫barrier e βΔG(r) dr ∼ e βΔG(r)

(9)

Clearly, the average time of escape from the metastable well k−1 is inversely proportional to the diffusion constant and the difference in ΔG dramatically changes the value of k−1 through the exponent in eq 9. Direct simulation shows that collapse of graphene plates in water, as shown in Figure S3 (in the Supporting Information), happens in nanoseconds. We estimate the value of k−1 for the average time from a metastable state (r0 = 1.0 nm) to a global minima state (r0 = 0.34 nm) as k−1 (water) = 1 ns. We assume that the diffusion constant appearing here is inversely proportional to the viscosity satisfying the Stokes−Einstein relation. Taking the experimental values of solvent viscosities for water and ILs at different temperatures, as shown in Table 1, we find that the prefactor 1/ D in eq 8 contributes 3 orders of magnitude at T = 300 K for the ration of k(ILs)/k(water). Complete results of the rate of collapse by evaluating eq 8 numerically using the free energy profile ΔG in Figure 4 are shown in Table 1. Computed values of S(t) are plotted in Figure 7 for various systems studied. Clearly, for our model systems of nanoscale graphene plates, the relaxation time scale can be as large as 250 h in ILs at T = 300 K. Realistic systems of graphene in solutions could be column-shaped, and their size might be as large as micrometers.

4. METHODS Details of Quantum Mechanical Calculation. The calculation is done at the level of B3PW91/6-311+g(d,p) using Gaussian software for gas phase systems of one graphene molecule, one cation [C8MIM+], and one anion [PF6−].54 The atomic charges are fitted using the CHELPG method.55 To investigate the cation−π interaction between a graphene plate and the cation efficiently, we use a smaller π-electron-rich molecule consisting of nine phenyl rings (shown in Figure 1b) as a representation for the graphene plate. We have scanned many possible configurations for the gas phase systems of cation and the π-electron-rich nine-phenyl-ring molecule, among which two cases with the strongest cation−π effect are studied at a series of separation distances, as shown in Figure 1c and d. We have verified that using a different DFT method B3LYP gives almost identical results to that of B3PW91. Also, we have verified that using a larger πelectron-rich molecule consisting of 14 phenyl rings gives similar results as well. The two verifications give us confidence that it is quite reasonable to study the cation−π interaction between graphene and the cation by using the smaller ninephenyl-ring molecule as a representation of the graphene plate. Results of these two verifications are shown in Figure 2a. Molecular Dynamics Simulation Details. Our simulation is carried out by using the software GROMACS version 4.56 Force field parameters for ILs are the same as those in the previous work of Canongia Lopes and co-workers57 and have been used in our previous publication.39 The VDW parameters

Figure 7. Survival probability for two graphene plates in water at T = 300 K (solid green curve), in ILs at different temperatures T = 300 K (solid black curve), 400 K (dashed black curve), 500 K (dashed red curve), and 600 K (dashed green curve), and in charge reduced ILs at T = 300 K (solid red curve, 10% means the charges are reduced to 10% of the origin). F



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the State Key Laboratory of Theoretical and Computational Chemistry and the Jilin University Supercomputing Center for providing resources for our work. We thank Prof. Claudio Margulis for helpful remarks.

of atoms in graphene are taken from the work of Berne and coworkers.21 The system of graphene in an IL ([C8MIM+][PF6−], see Figure 1) has two graphene plates and 309 pairs of ions. The two graphene plates are placed at a distance varying from 0.27 to 2.00 nm. The distance between the two plates is always maintained in each individual simulation. The interval of the separation is not uniform. We primarily use a smaller interval at distances where the free energy profile changes more dramatically and use a larger interval at distances where the free energy profile varies slowly. For each separation, we run a 6 ns simulation at T = 600 K with the later 4 ns trajectory for data collection. We choose eight configurations with an interval of 0.5 ns from the 4 ns trajectory and perform temperature annealing from 600 to 500 K with further simulation of 4 ns for systems at T = 500 K. Similar temperature annealing processes have been performed from 500 to 400 K with further simulation of 6 ns for systems at T = 400 K, and from 400 to 300 K with further simulation of 6 ns for systems at T = 300 K. For all simulations carried out, the former 2 ns are enough for equilibration and the later 2−4 ns are for data collection. To view the effect of charges and chain length, we have also simulated systems of two graphene plates in the pseudo-IL with its atomic charges reduced to 50 or 10% of the origin and in ILs ([C4MIM+][PF6−]) or ([C2MIM+][PF6−]). Simulations of the charge reduced pseudo-IL system are done for T = 300 K only, and the simulations for systems of [C4MIM+][PF6−] or [C2MIM+][PF6−] are done for T = 600 K. The simulations of graphene in water separated at the series of distances are performed for comparison at T = 300 K. We have used the water model tip4p. The number of water molecules is 1577. The distances between the two graphene plates are a total of 91 from 0.26 to 1.76 nm. We run a 10 ns simulation and take the later 8 ns for data collection. We have uploaded a simulation setup file and a typical system configuration file as the Supporting Information. More electronic files can be sent to readers of interest via email upon request ([email protected]).

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ASSOCIATED CONTENT

S Supporting Information *

More chemical structures and results about [C2MIM+][PF6−], [C4MIM+][PF6−], and [C8MIM+][PF6−] with the atomic charges reduced to 50% of the origin. Moreover, a direct simulation of aggregation of model graphene sheets in water and in ionic liquids is also included. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by NSFC grant no. 21103063 and no. 91127015 (Z.H.), the innovation project from the State Key Laboratory of Supramolecular Structure and Materials (Z.H.), the open project from the State Key Laboratory of Theoretical and Computation Chemistry at Jilin University (Z.H.), and Graduate Innovation Fund of Jilin University (project no. 20121060). We gratefully acknowledge the computing center in G



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