Molecular Dynamic Simulations of Ionic Liquids at Graphite Surface

Dec 22, 2009 - ... theory,(21) is recovered for the γ → 0 limit for the infinite dilute electrolyte solution. ..... Snapshots of the first IL layer...
8 downloads 0 Views 477KB Size
Download PDF
990

J. Phys. Chem. C 2010, 114, 990–995

Molecular Dynamic Simulations of Ionic Liquids at Graphite Surface Shu Wang,† Shu Li,† Zhen Cao,† and Tianying Yan*,†,‡ Institute of New Energy Material Chemistry, Department of Material Chemistry, and Institute of Scientific Computing, Nankai UniVersity, Tianjin 300071, People’s Republic of China ReceiVed: March 12, 2009; ReVised Manuscript ReceiVed: NoVember 25, 2009

The interface structure between room temperature ionic liquids, 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM+/PF6-) and 1-octyl-3-methylimidazolium hexafluorophosphate (OMIM+/PF6-), and the graphite (0001) surface has been studied by classical molecular dynamic simulations. It is found that the density of IL is much enhanced at the interfacial region and the density oscillation extends to ∼15 Å into the bulk with three layers. The results also demonstrate that the polar groups tend to aggregate forming a polar network, while the nonpolar groups fill up the rest of the vacancy. The imidazolium rings and the side chains preferentially lie flat at the graphite surface with the alkyl side chains of the cations elongated at the interfacial region, and the cations are closer to the graphite surface (ca. 3.6-3.7 Å) than the anions. The surface potential drop across the interface is more profound for OMIM+/PF6- than for BMIM+/PF6-, due to relatively larger local density of the anions for OMIM+/PF6- near the graphite surface. I. Introduction A recent trend in the study of room temperature ionic liquids (ILs) has suggested eminent properties of this newly emerged class of materials. ILs are mostly at liquid state at room temperature, partially due to the fact that ILs are composed of the bulky and conformationally flexible organic ions, which enhance the entropy effect in the system and thus prevent them from crystallization.1,2 Distinct combinations of ions theoretically present countless species of ILs which will satisfy diverse chemical processes. By selecting proper anions or modulating alky chains of cations slightly, both chemical and physical properties can be altered to agree with specific demands. It is important to have a deep understanding of the microscopic properties and their relation to the functions. During the past decade, extensive studies, including experiments and computer simulations, have been devoted to this new class of liquid.3 Investigations involving the interfacial properties of ILs have been drawing more and more attention.4,5 For such complex systems, computer simulations are extremely valuable for investigating the interfacial structure. A recent comprehensive computer simulation of ILs at the SiO2 surface by Sieffert and Wipff clearly revealed that the interfacial structure is sensitive to polar or apolar surface as well as hydrophobic or hydrophilic IL components.6 The above study nicely corroborates the experimental sum frequency generation vibrational spectroscopy (SFG) studies of ILs at SiO2 substrate.7–9 Despite the detailed interfacial structure depending on the nature of substrate and ILs, a common feature shared by these simulations is the wellordered structure at the IL/solid interface.6 Such ordered interfacial structure was also found in both simulation10 and experimental SFG study11 of the IL/TiO2 interface, as well as the simulations of the IL/graphite interface by Wu et al.12 and by Kislenko et al.13 Wu’s latter study also highlights the solidation of ILs at graphite, as analogue to the findings by the * To whom correspondence should be addressed. Tel.: (86)22-2350-5382. Fax: (86)22-2350-2604. E-mail: [email protected]. † Institute of New Energy Material Chemistry and Department of Material Chemistry. ‡ Institute of Scientific Computing.

same group on the solidation of confined ILs in carbon nanotube14 as well as in graphite sheets.15 Recently, Reichert and co-workers investigated ILs interfacial ordering mechanism at the charged Al2O3 substrate via high-energy X-ray reflectivity and observed strong interfacial layering which decays exponentially into the bulk region.16 Such interfacial layering was expected to be a generic trait of ILs at charged walls. Due to their large electrochemical window (up to 5 V) and designing nature, ILs are also promising in applications as a supercapacitor.17 Recent study also highlights the importance of pore curvature in the nanoporous carbon supercapacitors.18,19 Understanding the interfacial structure, especially the electric double layer (EDL), is crucial in exploring the applications of ILs in electrochemical devices. Recently, Kornyshev proposed a mean-field theory (MFT)20 based on the Poission-Boltzmann lattice-gas model, in which a compressibility parameter γ is incorporated. It is shown by MFT that the differential capacitance (DC) is bell-shaped when γ > 1/3, and it is camel-shaped otherwise, while the U-shaped DC, predicted by the classical Couy-Chapman theory,21 is recovered for the γ f 0 limit for the infinite dilute electrolyte solution.20 The bell-shaped DC is supported by Oldham’s modification of the Couy-Chapman model for ionic liquid interface in a specific case with γ ) 1.22 The bell-shaped DC was observed experimentally on an IL/ metal electrode (platinum and gold), with similar IL ion sizes, by Ohsaka and co-workers,23 stimulated by Kornyshev’s work.20 Attempts were also made to investigate the interfacial IL/ electrode structure by capacitance, and the decrease of capacitance of IL of longer cationic alkyl was attributed to the adsorption of the alkyl group on the Hg electrode.24 The bellshaped DC was also confirmed in the molecular dynamics (MD) simulations on model systems of charged spheres,25,26 and an extended MFT incorporating the Helmholtz layer fits the DC curve qualitatively well.26 Interestingly, the potential of zero charge (PZC) may not correspond to the maximum in the DC curve for ions of asymmetric sizes.20,26 The above study highlights the compressibility of ILs and the different sizes of cations and anions.

10.1021/jp902225n  2010 American Chemical Society Published on Web 12/22/2009

Molecular Dynamic Simulations of Ionic Liquids

J. Phys. Chem. C, Vol. 114, No. 2, 2010 991

Figure 1. Structures and atomic notations of BMIM+/PF6- (above) and OMIM+/PF6- (below).

In this study, we focus on liquid-solid systems and report molecular dynamics studies at the liquid-solid interface between imidazolium-based ILs, 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM+/PF6-) and 1-octyl-3-methylimidazolium hexafluorophosphate (OMIM+/PF6-), and an apolar graphite surface. The main aim of our current study is to investigate the influence of different alkyl side chain lengths of imidazolium on the interfacial structures. It should be emphasized that the graphite surface is uncharged, and the image force effect27 is not taken into account in this study. However, some interesting properties on characterizing certain EDL features may still be deduced, such as PZC and a rough estimation of compressibility of IL with different cationic alkyl size chain lengths. The EDL structure and polarization response of IL near a charged surface will be explored in further studies. II. Simulation Methodology and Model Figure 1 shows the schematic structures and atomic notations of BMIM+/PF6- and OMIM+/PF6-. The graphite (0001) sheets were constructed out of alternative layers with a separation from each other of 3.395 Å. The total number of the graphite atoms is 29640. Each graphite layer includes 26 × 15 rectangle super cells with dimensions of 2.46 Å × 4.26 Å, resulting in a surface dimension of 63.96 Å × 63.90 Å. The PBC box was then elongated in the surface normal direction up to 147.90 Å, with the interval between the two graphite (0001) interfaces 86.79 Å. The so-constructed graphite (0001) slab was frozen during the MD simulation. The BMIM+/PF6- bulk phase contains 942 ion pairs, while the OMIM+/PF6- bulk is comprised of 709 ion pairs. The van der Waals and the real space electrostatic interaction cutoff distance is set to be 12 Å, and the particlemesh Ewald (PME) algorithm28 is applied to handle the longrange electrostatic interactions in reciprocal space. The integration time step is 2 fs with SHAKE algorithm29 applied on all the C-H bonds. After the initial annealing from 1000 K down to 298.15 K gradually within 20 ns, coupled to a Berendsen thermostat,30 the MD production run was performed with an NVE ensemble with temperature fluctuating around 298.15 K for another 20 ns, using the GROMACS package.31 A nonpolarizable force field was adopted in the simulation, with the force field parameters of ILs taken from Pa´dua’s work,32,33 and the graphite was simulated as uncharged sheets composed of carbon atoms interacting with the Lennard-Jones potential corresponding to the sp2 hybrid carbon atoms in the AMBER force field.34 The van der Waals interactions among ILs and between IL and graphite were handled by the Lorentz-Berthelot combination rule.35 Our previous study showed that the polarizable model and the nonpolarizable model gave similar interfacial structural properties.36 The ILs, BMIM+/PF6-, and OMIM+/PF6- investigated in this study are well-known for their amphiphilic property. The imidazolium ring of the cation possesses nearly unit net charge

Figure 2. Snapshots of IL/graphite simulation models: (a) BMIM+/ PF6- and (b) OMIM+/PF6- cations. The red and green colors respectively represent the polar and nonpolar groups (see text). The dimension of the PBC box (63.96 Å × 63.90 Å × 147.90 Å) is drawn as a guide for the eye, and the ILs occupy the middle 86.79 Å confined between the graphite sheets.

and the alkyl side chain is nearly charge neutral, especially as the alkyl side chain is long enough. According to the division rationale suggested by Canongia Lopes and Pa´dua,37 a 1-alkyl3-methylimidazolium cation can be divided into the polar and the nonpolar groups. The imidazolium ring, plus the methyl groups and the methylene groups bonded to the nitrogen atoms, as well as the PF6- anion, belong to the polar groups, while the rest of the groups on the long alkyl side chain on the cation represent the nonpolar groups. Two snapshots of BMIM+/PF6and OMIM+/PF6- are shown in Figure 2, which demonstrates that the polar groups aggregate to form a network of polar domains and the nonpolar groups fill up the vacancies among the polar network.38,39 Thus, the polar groups would like to approach each other because of the strong electrostatic interactions among them, leading to the nonpolar groups gathering through the collective short-range interactions.37,40,41 This phenomenon becomes conspicuous as the alkyl chains increase in length. III. Results and Discussion III.1. Density Profile. Panels a and b of Figure 3 show the number density profiles of the center of mass (COM) of ions in BMIM+/PF6- and OMIM+/PF6-, and panels c and d of Figure 3 show the density profiles of individual atoms (cf. Figure 1) of the cations, respectively. On the basis of Figure 3a, the mass density of the BMIM+/PF6- bulk region for the slab within the third density oscillation is 1.32 g/cm3, which is in good agreement with the experimental density (1.36 g/cm3).42 A striking feature is that the density of IL is much enhanced at the interfacial region and the density oscillation extends to more than 15 Å with three layers into the bulk, similar to the previous simulation of the IL (BMIM+/PF6-)/graphite study with mass density.12 Such strong interfacial oscillation of the ILs highlights the solidation of ILs at the graphite surface.12,14 For the PF6anion, there exists a region with negligible density after the first intensive layer. The relatively larger local density of the anions than the cations highlights the polar group aggregations, as has been well investigated previously.37,40,41 Specifically, the PF6anions and the imidazolium ring of the cations associate with each other due to the electrostatic interactions, and the side

992

J. Phys. Chem. C, Vol. 114, No. 2, 2010

Wang et al.

Figure 3. (a) Number density profiles of the COM of BMIM+ (black) and PF6- (red) in BMIM+/PF6-; (b) number density profiles of the COM of BMIM+ (black) and PF6- (red) in OMIM+/PF6-; (c) number density profiles of different atoms of the BMIM+ cation; and (d) number density profiles of different atoms of the OMIM+ cation. The vertical dashed lines show the graphite surface. The distances between first cation and anion peak and the graphite surface, as well as the distance between the third density minimum and the graphite surface, are marked in panels a and c.

chains of the bulky cations occupy the neighboring layers, leaving a reduced PF6- density layer. Panels c and d of Figure 3 show that the density profiles of the individual atoms coincide at the interface and there is no apparent separation of the functional group on the alkyl side chains at the interfacial region, which distinguishes it from the IL/vacuum interfacial structure.36,43 Therefore, the imidazolium rings and alkyl side chains on the cations lie rather flat at the surface. The distances between the first peak of the cations and the graphite surface, i.e. ∼3.6 Å for BMIM+ and ∼3.7 Å for OMIM+, are closer to the graphite surface than those of the anions (∼4.1 Å). In MFT of the IL/electrode system, the only adjustable parameter is the compressibility of IL, characterized by γ ) 2c0/cmax, in which c0 is the average density in the bulk, and cmax is the maximum possible local density of ions near the electrode.20 Using the density profile in Figure 3, and distinguishing cation and anion,20,26 we estimate that γ+ ) 0.38, γ- ) 0.22 for BMIM+/PF6-, and γ+ ) 0.44, γ- ) 0.24 for OMIM+/PF6-. It should be noted that the above γ values are the upper bound since ILs contact with an uncharged surface. In a recent simulation by Qiao and co-workers for the BMIM+/NO3-/ electrode system, it was shown that the ionic density increases dramatically near a charged surface as compared to an uncharged surface, especially for the anion of smaller size.44 It is of interest to note that the DC simulated in Qiao’s work is U-shaped.44 Given the above scenario of the tightly packed IL near a charged surface, and taking the γ values of BMIM+/PF6- near an uncharged surface estimated here, it is reasonable to estimate that both γ+ and γ- values are smaller than 1/3 in Qiao’s work for a slightly different IL BMIM+/NO3-.44 Therefore, the U-shaped DC in Qiao’s simulation seems to be within the framework of MFT20 for the γ < 1/3 case. The bell-shaped DC was also observed in Fedorov and Kornyshev’s simulations with a cation:anion size ratio of 1:125 and 2:125,26 with a prototypical spherical IL at electrode interfaces. Further study is needed to determine the DC curve for the IL/electrode systems investigated here, especially the OMIM+/PF6- system. III.2. Orientational Ordering. The orientational ordering parameter is defined as the ensemble average of the second

Figure 4. (a) Orientational ordering of the BMIM+ imidazolium ring normal (black), N1-N3 vector (red), and N1-C10 vector (blue); (b) orientational ordering of the OMIM+ imidazolium ring normal (black), N1-N3 vector (red), and N1-C14 vector (blue). The dashed line shows the cation COM number density profiles as in Figure 3. The vertical dashed lines show the graphite surface.

Legendre polynomial. i.e., P2(θ) )〈(3cos 2θ - 1)/2〉, in which θ is the angle between a direction vector and the surface normal. The direction vectors investigated here refer to the imidazolium ring normal direction vector, the N-N vector, the butyl vector, and the octyl vector from the N1-atom on the imidazolium ring to the methyl group on the alkyl side chain (cf. Figure 1). P2(θ) values of both the BMIM+ and OMIM+ cations are shown in panels a and b of Figure 4, respectively, in which the cation COM density profiles from Figure 3a,b are also reproduced. For both IL/graphite systems, the imidazolium rings normal are parallel to the surface normal for the peaks near the interface with P2(θ) approaching 1. Meanwhile, it is notable that the N-N

Molecular Dynamic Simulations of Ionic Liquids vectors and the alkyl side chain vectors tend to be perpendicular to the surface normal with the peak values of about -0.5. These orientational orderings are consistent with Figure 3 and reveal that the cations lie flat at the graphite sheet, in agreement with previous simulations of BMIM+/PF6-/graphite interface13,45 as well as Lynden-Bell’s work of DMIM+/Cl- near a smooth surface.46 The coincidence of the nearest to the surface peaks of P2(θ) and density profile also highlights the flatness of the cations at the graphite surface. Such orientation is different from the interfacial orientation of the cations in the IL (BMIM+/PF6-)/ vacuum interface in which the cations tend to take a slant orientation with the butyl group protruding outward to the vacuum,43 and is also different from the interfacial orientation of the IL (BMIM+/PF6-, OMIM+/PF6-)/water interface47 and IL (BMIM+/PF6-)/quartz interface8 in which the alkyl side chains point inward to the IL bulk away from the interface. Interestingly, the parallel alignment of the cations near the surface was also found in Sieffert and Wipff’s work on the simulation of IL at the ionic NaCl surface, which demonstrates apolar properties in contact with ILs.48 In the same study, they also demonstrated that the density and orientation of the IL are nearly identical on the charged and uncharged NaCl surface.48 The above study may qualitatively address the question on how important the image force effects are on the structure at the IL/electrode interface. As an ion is close to a conducting surface, the surface polarization induces a nonuniform charge distribution on the surface with opposite sign, which may be represented by a fictitious image charge behind the electrode.49 The above comparison of IL near a charged and an uncharged NaCl surface may deserve a qualitative discussion of image force effects. Since the charges are generally dispersed on the cations of ILs, the attraction between cations and the negative image charges is weak, while the anion is repelled by the bulky negative image charges. The observation on the similarity in terms of density and orientation of the IL ions near the charged and uncharged NaCl surface is reasonable, and it may suggest that the image force effects may be quite minor on the structure at the IL/ electrode interface. The present results in Figure 4 suggest that the orientation of the cations does not depend on the length of the alkyl substituent, due to the strong van der Waals interactions between IL and graphite. The parallel alignment of the bulky cations allows a tighter packing with favorable energy, while the cost of the unfavorable entropy is less at the interface than in the bulk.46 Such a feature was also in the MFT of the IL/ electrode interface,20 in which the “lattice saturation” is mainly governed by enthalpy, paid by the reduced entropy. Also, the parallel stacking of the imidazolium rings at the graphite surface, altogether with the distance of 3.6-3.7 Å of the first peak of the cations to the graphite surface as shown in Figure 3, may indicate the π-stacking interactions50 between the imidazolium ring and the graphite surface. III.3. Variations of the Average Alkyl Side Chain Length. Figure 5 shows the variations of the average alkyl side chain length along the surface normal. The alkyl side chain length is defined as the distance between N1 and C10 for BMIM+ and the distance between N1 and C14 for the OMIM+ (cf. Figure 1). A distinct feature is the elongation of the alkyl side chain near the interface. For BMIM+/PF6-, the alkyl side chain length reaches ∼5.14 Å, which is ∼0.59 Å longer than the average value for the bulk, near the graphite surface. As for OMIM+/ PF6-, the alkyl side chain length reaches ∼10.29 Å, namely 1.23 Å longer than the average value in the bulk region. Such stretched alkyl chains of the cations, along with the flat imidazolium rings, are in good agreement with the atomic force

J. Phys. Chem. C, Vol. 114, No. 2, 2010 993

Figure 5. Variations of the average alkyl side chain length from N1 to C10 for BMIM+ (solid) and from N1 to C14 for OMIM+ (dashed). The vertical dashed lines show the graphite surface.

microscopy study of 1-ethyl-3-methylimidazolium at the graphite surface.51 To visualize the above picture, two snapshots of interfacial layer for the ILs within the first minima in Figure 3a,b, along with the surface graphite sheet, are displayed in the Figure 6. It can be seen that the alkyl side chains are mostly stretched out and lie parallel to the graphite surface, especially for the OMIM+ cations. Moreover, there exist the aggregations of the polar and the nonpolar groups, as indicated by the circles in Figure 6, and this tendency is more profound for OMIM+/PF6- than BMIM+/PF6-. Such observation is in agreement with the formation of the 2D mesophases of IL on a model solid surface in a recent simulation.52 The flat conformation of the cation at the graphite surface nicely explains the enhancement of the density in the interfacial region. The stretched alkyl side chain is energetically more favorable than the gauche defect one. Therefore, the elongation of the alkyl side chains at the graphite surface is rather governed by the energy issue, due to the solidation of the ILs at the graphite surface.12 III.4. Surface Potential. For a plane interface, the surface potential φ(z) along the surface normal direction is related to the surface charge density F(z) by integrating Poisson’s equation, φ(z) ) -ε0-1∫zz0(z - z′)F(z′) dz′, in which z denotes the surface normal direction and z0 is a reference point in the middle of the graphite sheet of zero charge density. Panels a and b of Figure 7 show F(z) and φ(z), respectively, for both ILs, in which φ(z) is averaged over two sides. The enhancement of the charge density near the interfacial region can be seen, in agreement with the enhancement of the number density in Figure 3. The charge density oscillation extends to ∼13.7 Å with several layers. Specifically, the positively charged first layer due to the close contact between cations and graphite surface induces several additional layers. Thus, the double layer structure in the IL/graphite interface is thicker than just one compact layer near the zero electrode charge, in agreement with previous simulations.25,26 Comparing with the surface potential of the BMIM+/PF6-/ vacuum interface,43 the potential drop across the BMIM+/PF6-/ graphite interface is smaller. It was found that the potential drop is mainly caused by the alkyl side chains attached to imidazolium rings as they protrude outward from the IL interface with the net dipole pointing outward.53 In the IL/graphite systems, the ILs are confined within the graphite, and it is reasonable to see the smaller potential drop due to the flat conformation of the BMIM+ cations at the graphite surface. Apart from that, the larger cation, i.e., OMIM+, brings a larger potential drop than the smaller BMIM+ cation. As shown in Figure 7b, for BMIM+/PF6-, there is essentially no potential drop across the interface, while for OMIM+/PF6-, the average magnitude of the

994

J. Phys. Chem. C, Vol. 114, No. 2, 2010

Wang et al.

Figure 7. (a) Charge density profiles of BMIM+/PF6- (black) and OMIM+/PF6- (red); (b) electrostatic potential changes along the z-axis of BMIM+/PF6- (black) and OMIM+/PF6- (red). The vertical dashed lines show the graphite surface.

IV. Concluding Remarks

Figure 6. Snapshots of the first IL layer at one graphite sheet seen along the z-axis: (a) BMIM+/PF6- and (b) OMIM+/PF6-. The blue square shows the PBC box, outside which are the periodic images for better view. The red circles mark the aggregations of polar and nonpolar groups.

potential drop is about 0.15 V. The above trend of the potential drops, i.e., negative potential with increasing alkyl side chain length, is in agreement with the trend of PZC of imidazoliumbased ILs at the dropping mercury electrode54 or the glass carbon electrode.55 Since there is hardly any difference between the orientations of the cations, the segregation of the anions at the interface is thought to be the determinant factor. The influence of the anion on the potential drop due to the asymmetric sizes of cation and anion in IL is mainly caused by the smaller anion tend to pack denser near the interface.26,43 Given the same anion, PF6-, the bulky OMIM+ implies a relatively denser PF6- density layer for OMIM+/PF6- than that for BMIM+/PF6- (cf. Figure 3a,b), which results in a more negative potential drop across the OMIM+/PF6-/graphite interface.

In this study, molecular dynamics simulations of the two IL/ graphite interfaces, i.e., BMIM+/PF6-/graphite and OMIM+/ PF6-/graphite, have been performed. This study shows that ILs are highly compressible near the graphite interface. For both ILs, dense regions have emerged near the interface with three oscillation layers, highlighting the solidation of ILs at the graphite surface. Spatial heterogeneity is found in the interfacial region, in which the polar groups aggregate to form a polar network among the imidazolium ring of the cations and the PF6anions, while the alkyl side chains on the cations distribute in the voids and form nonpolar domains. The orientational preference for the two simulations is alike, i.e., the imidazolium rings with the alkyl side chains on cations tend to lie flat at the graphite surface. The variation of the alkyl side chain lengths indicates that the stretch conformation is energetically more favorable for the side chains at the graphite surface. The surface potential drop across the interfacial region is smaller for the BMIM+/PF6- than that for the OMIM+/PF6-. In the interfacial region, the anions, with relatively smaller volume, have higher density than the cations. Thus, potential drops are smaller for the imidazolium cations with shorter alkyl side chains. For further studies, we plan to investigate ion size effects on the capacitance, as well as the EDL structure, near a charged surface by using MD simulations. Acknowledgment. This research is supported by the NSFC (nos. 20503013, 20873068), the 973 Program (2009CB220100), and the 863 program (2007AA03Z225) of China. We are grateful to the Institute of Scientific Computing (NKstars HPC program) of Nankai University for the computing time. We appreciate an anonymous reviewer’s valuable comments on the early version of this manuscript, in which we made several erroneous statements of the MFT developed in ref 19 due to our limited understanding. T.Y. thanks the helpful discussions with Prof. Xueping Gao and Prof. Huabin Yang. References and Notes (1) Weinga¨rtner, H. Angew. Chem., Int. Ed. 2008, 47, 654.

Molecular Dynamic Simulations of Ionic Liquids (2) Canongia Lopes, J. N.; Shimizu, K.; Pa´dua, A. A. H.; Umebayashi, Y.; Fukuda, S.; Fujii, K.; Ishiguro, S.-i. J. Phys. Chem. B 2008, 112, 1465. (3) Rogers, R. D.; Voth, G. A. Acc. Chem. Res. 2007, 40, 1077. (4) Baldelli, S. Acc. Chem. Res. 2008, 41, 421. (5) Aliaga, C.; Santos, C. S.; Baldelli, S. Phys. Chem. Chem. Phys. 2007, 9, 3683. (6) Sieffert, N.; Wipff, G. J. Phys. Chem. C 2008, 112, 19590. (7) Fitchett, B. D.; Conboy, J. C. J. Phys. Chem. B 2004, 108, 20255. (8) Romero, C.; Baldelli, S. J. Phys. Chem. B 2006, 110, 6213. (9) Rollins, J. B.; Fitchett, B. D.; Conboy, J. C. J. Phys. Chem. B 2007, 111, 4990. (10) Liu, L.; Li, S.; Cao, Z.; Peng, Y.; Li, G.; Yan, T.; Gao, X. J. Phys. Chem. C 2007, 111, 12161. (11) Aliaga, C.; Baldelli, S. J. Phys. Chem. C 2008, 112, 3064. (12) Sha, M.; Zhang, F.; Wu, G.; Fang, H.; Wang, C.; Chen, S.; Zhang, Y.; Hu, J. J. Chem. Phys. 2008, 128, 134504. (13) Kislenko, S. A.; Samoylov, I. S.; Amirov, R. H. Phys. Chem. Chem. Phys. 2009, 11, 5584. (14) Chen, S.; Wu, G.; Sha, M.; Huang, S. J. Am. Chem. Soc. 2007, 129, 2416. (15) Sha, M.; Wu, G.; Fang, H.; Zhu, G.; Liu, Y. J. Phys. Chem. C 2008, 112, 18584. (16) Mezger, M.; Schro¨der, H.; Reichert, H.; Schramm, S.; Okasinski, J. S.; Schro¨der, S.; Honkima¨ki, V.; Deutsch, M.; Ocko, B. M.; Ralston, J.; Rohwerder, M.; Stratmann, M.; Dosch, H. Science 2008, 322, 424. (17) Simon, P.; Gogotsi, Y. Nat. Mater. 2008, 7, 845. (18) Huang, J.; Sumpter, B. G.; Meunier, V. Angew. Chem., Int. Ed. 2008, 47, 520. (19) Huang, J.; Sumpter, B. G.; Meunier, V. Chem.sEur. J. 2008, 14, 6614. (20) Kornyshev, A. A. J. Phys. Chem. B 2007, 111, 5545. (21) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamental and Applications, 2nd ed.; Wiley: New York, 2001. (22) Oldham, K. B. J. Electroanal. Chem. 2008, 613, 131. (23) Islam, M. M.; Alam, M. T.; Ohsaka, T. J. Phys. Chem. C 2008, 112, 16568. (24) Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2009, 113, 6596. (25) Fedorov, M. V.; Kornyshev, A. A. Electrochim. Acta 2008, 53, 6835. (26) Fedorov, M. V.; Kornyshev, A. A. J. Phys. Chem. B 2008, 112, 11868. (27) Torrie, G. M.; Valleau, J. P.; Patey, G. N. J. Chem. Phys. 1982, 76, 4615. (28) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. (29) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327. (30) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684.

J. Phys. Chem. C, Vol. 114, No. 2, 2010 995 (31) Lindahl, E.; Hess, B.; van der Spoel, D. J. Mol. Model. 2001, 7, 306. (32) Canongia Lopes, J. N.; Deschamps, J.; Pa´dua, A. A. H. J. Phys. Chem. B 2004, 108, 2038. (33) Canongia Lopes, J. N.; Deschamps, J.; Pa´dua, A. A. H. J. Phys. Chem. B 2004, 108, 11250. (34) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179. (35) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford: New York, 1987. (36) Yan, T.; Li, S.; Jiang, W.; Gao, X.; Xiang, B.; Voth, G. A. J. Phys. Chem. B 2006, 110, 1800. (37) Canongia Lopes, J. N.; Pa´dua, A. A. H. J. Phys. Chem. B 2006, 110, 3330. (38) Xiao, D.; Rajian, J. R.; Li, S.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2006, 110, 16174. (39) Xiao, D.; Rajian, J. R.; Cady, A.; Li, S.; Bartsch, R. A.; Quitevis, E. L. J. Phys. Chem. B 2007, 111, 4669. (40) Wang, Y.; Jiang, W.; Yan, T.; Voth, G. A. Acc. Chem. Res. 2007, 40, 1193. (41) Wang, Y.; Voth, G. A. J. Am. Chem. Soc. 2005, 127, 12192. (42) Gu, Z.; Brennecke, J. F. J. Chem. Eng. Data 2002, 47, 339. (43) Lynden-Bell, R. M.; Del Po´polo, M. G. Phys. Chem. Chem. Phys. 2006, 8, 949. (44) Feng, G.; Zhang, J. S.; Qiao, R. J. Phys. Chem. C 2009, 113, 4549. (45) Lynden-Bell, R. M.; Del Po´polo, M. G.; Youngs, T. G. A.; Kohanoff, J.; Hanke, C. G.; Harper, J. B.; Pinilla, C. C. Acc. Chem. Res. 2007, 40, 1138. (46) Pinilla, C.; Del Po´polo, M. G.; Lynden-Bell, R. M.; Kohanoff, J. J. Phys. Chem. B 2005, 109, 17922. (47) Chaumont, A.; Schurhammer, R.; Wipff, G. J. Phys. Chem. B 2005, 109, 18964. (48) Sieffert, N.; Wipff, G. J. Phys. Chem. B 2007, 111, 7253. (49) Feynman, R. P.; Leighton, R. B.; Sands, M. The Feynman Lectures on Physics; Addison-Wesley: Reading, MA, 1964; Vol. 2. (50) Tsuzuki, S.; Mikami, M.; Yamada, S. J. Am. Chem. Soc. 2007, 129, 8656. (51) Atkin, R.; Warr, G. G. J. Phys. Chem. C 2007, 111, 5162. (52) Manini, N.; Cesaratto, M.; Del Po´polo, M. G.; Ballone, P. J. Phys. Chem. B 2009, 113, 15602. (53) Lynden-Bell, R. M.; Kohanoff, J.; Del Po´polo, M. G. Faraday Discuss. 2005, 129, 57. (54) Alam, M. T.; Islam, M. M.; Okajima, T.; Ohsaka, T. J. Phys. Chem. C 2007, 111, 18326. (55) Lockett, V.; Sedev, R.; Ralston, J.; Horne, M.; Rodopoulos, T. J. Phys. Chem. C 2008, 112, 7486.

JP902225N