Effective Polarization in Pair-Wise Potentials at the Graphene-Electrolyte Interface

Christopher D. Williams*1, James Dix1, Alessandro Troisi2 and Paola Carbone1

1School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, M13 9PL, United Kingdom.

2Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom.

Abstract

At the graphene-electrolyte interface the polarizability of both the surface and the solution play a major role in defining the interfacial structure and dynamics of the ions. Current molecular models predict different ion adsorption behavior at the interface depending on whether surface or solution polarization is included in the model. Here, we propose a simple method to parameterize the ion-carbon interaction from density functional theory, implicitly modeling the solution using the conductor-like polarizable continuum model. The new model simultaneously takes into account the polarizability of both the graphene sheet and the solution without the need to use time-consuming polarizable potentials and can predict the ion adsorption trend so far only achievable using first-principles simulations. Simulations performed with 1 M electrolyte solutions of different ions show that cations are strongly adsorbed onto the graphene surface with a trend (Li+ < Na+ < K+) opposite to that predicted by the gas phase calculations and different to that obtained from the single ion simulations.

TOC Graphic

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Technological developments in many disciplines are underpinned by a fundamental physical understanding of ion adsorption onto metallic or semimetallic surfaces.1-2 Specifically for graphene-based technologies, examples of new emerging applications include analytical chemistry,3 water filtration,4-7 energy storage8-10 and electrochemical sensing11-12. All of these novel applications require a precise understanding of the relative stability of ions at the graphene-electrolyte interface. Simple continuum theories,13 which account only for the size and magnitude of the charge on the ion, predict that ions are repelled by hydrophobic surfaces, due to their preference to be fully hydrated in bulk solution. However, experimental studies suggest that large anions can be attracted to electrolyte-air interface,14-15 with a propensity that follows the Hofmeister series (Cl− < Br− < I−).16 The driving force for this ion-specific interfacial adsorption is a rather complex mix of enthalpic and entropic contributions,17 but molecular dynamics (MD) simulations of the electrolyte interface with both air and unstructured hydrophobic surfaces have demonstrated that it is mainly related to the stability of the ion’s solvation shell and its propensity to dehydrate.18-19 In particular, monovalent anions such as the heavier halides are characterized by weakly bound water molecules in their primary solvation shell and adsorption is due to interactions with a local electric field caused by the orientation of water molecules at the interface.20 For a metallic or semimetallic surface, the proximity of an ion induces a further effect associated with polarization of the surface itself, which strongly affects the interfacial attraction/repulsion of the ions.21

In order to capture these important phenomena, molecular models employed to simulate interfacial systems need to include the polarizability of all the species involved. In the majority of classical simulations, however, only the polarizability of the electrolyte is included in the model, assuming that surface polarization has a negligible effect on ion adsorption.12, 22-23 In the case of metallic/semimetallic surfaces, such as graphene or carbon nanotubes (CNT), which have an abundance of aromatic rings with delocalized π-electrons, this assumption is questionable. Recently, several authors have shown that the attraction of ions toward such surfaces can be grossly underestimated if the model does not account for the polarizability of the surface. This important effect has recently been highlighted by Kulik et al.24, who, using first-principles MD simulations, showed that cations such as Na+ preferably reside at the interface when confined in a CNT. This is in contrast to their behavior at unstructured, non-polarizable surfaces, in which cations are repelled. More recently, Pham et al.25 have also proved, again using first-principles MD, that including only the polarizability of the ions in the model predicts the wrong adsorption tendency between Na+ and K+ on the surface of a CNT. Finally, Shi et al.26 have shown that cations do have a strong attractive interaction with the graphene surface, and that such an interaction is essential in describing the concentration of ions at the interface.

These recent results show that an accurate model of the graphene-electrolyte interface should simultaneously consider polarization of the ions, water and surface to properly take into account mutual electronic structure effects. To avoid the time and length scale restrictions of first-principles MD, one can employ polarizable classical force fields.27 However, these are still more computationally demanding than standard classical force fields and, especially for metallic surfaces, difficult to parameterize. In the specific case of aromatic surfaces such as graphene, while much effort has been spent on the development of accurate parameters for ion-water28-31 and graphene-water32-34 potentials (including polarization), relatively little attention has been paid to surface-ion potentials.35 In this letter, we propose a novel and relatively quick method to parameterize a classical potential that includes these highly specific effects for

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various ubiquitous ions (Li+, Na+, K+, Mg2+, Ca2+ and Cl−). The new model takes into account the polarizability of the water, ions and graphene using a simple pairwise potential, avoiding the need to implement computationally expensive polarizable models or perform first-principle MD simulations.

To obtain the new parameters, we considered the adsorption of a single ion onto a 54 C graphene flake. Density functional theory (DFT) calculations were firstly used to optimize the position of each ion on the graphene flake (Figure 1a) and then to calculate benchmark graphene-ion adsorption energies, Eads, from the equation,

(1)where Egi, Eg and Ei are the DFT energies of the ion adsorbed on graphene, isolated ion and isolated graphene flake, respectively. This procedure was repeated for both gas and aqueous phase adsorption. In the latter, water was implicitly accounted for using the conductor-like polarizable continuum model (CPCM).36-37

The final, optimized, position for all the ions was above the ‘hollow’ of a six-carbon ring at the centre of the graphene flake, consistent with previously published results.38-39 The calculated gas phase adsorption energies, provided in the supplementary information, are in good general agreement with previously published results. Gas and aqueous phase adsorption energies are shown in Figure 1b) and 1c), respectively. In all cases, ion adsorption is favourable (Eads < 0). In the gas phase there is a trend, most evident for the monovalent cations of the group 1 elements, of decreasing magnitude of adsorption energy down the group (Li+ > Na+ > K+). The energies for divalent species are significantly larger than their monovalent counterparts. Both of these trends can be explained by surface polarization. Small and highly charged ions polarize the delocalized electrons in the graphene flake to a much greater degree than large, less highly charged ions.

Adsorption in the aqueous phase is still favorable, but the magnitude of the adsorption energy is decreased relative to the gas phase because the ion is stabilized in bulk solution by hydration effects. Since aqueous phase adsorption is a fine balance between this stabilization and polarization of the graphene flake, there is no obvious trend in the resulting energies (Figure 1c). The DFT adsorption energy for Na+

calculated with the CPCM method can be compared with the value obtained by Shi et al.,26 who instead used a small number of explicit water molecules around the ion to account for hydration. The adsorption energy these authors reported is vastly in excess of our calculated value of −13.8 kJ mol−1. However, the authors also noted that the magnitude of the adsorption energy was strongly dependent on the number of water molecules included in the DFT calculations and they observed a decrease from −78.7 kJ mol−1 to −68.6 kJ mol−1 when the number of water molecules was increased from 6 to 9. It is extremely difficult to evaluate the hydration free energy of an ion, and therefore is adsorption energy, extrapolating from a model containing only a small number of water molecules. According to classical electrostatics, if the dielectric medium around an ion is replaced by a finite sphere of radius, r, the hydration free energy approaches the bulk value with increasing r but only very slowly as ~1/r or, approximately, as 1/n1/3 where n is the number of molecules.40 We therefore believe that many more water molecules would be required to properly account for the stabilization of the ion in bulk solution, explaining the difference between our Na+ adsorption energy and that obtained by Shi et al.

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Figure 1. a) The geometry of the 54 C graphene flake used in the calculations, b) DFT ion adsorption energies in b) the gas phase and c) aqueous solution.

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Considering that the adsorption energies obtained with the CPCM method are free energies, the parameterization of the ion-carbon interaction was carried out by optimizing the potential parameters until the free energy of the classical system matched the corresponding CPCM energy. MD simulations and the umbrella sampling technique were used to obtain a potential of mean force (PMF)41 for each ion adsorbing to the centre of the graphene flake (z = 0) from bulk solution (z = 1.4 nm). The adsorption free energies were then taken to be equal to the energy minimum along the PMF profile, after shifting to zero at z = 1.4 nm. Adsorption energies were first calculated using the original values of the parameters in the Lennard-Jones 12-6 potential, εi-c and σi-c, determined from the Lorentz-Berthelot combining rules. In the new potential, only εi-c was modified to account for polarization, overriding the standard combining rules, until agreement was reached with the aqueous DFT adsorption energies to within 0.7 kJ mol−1. A detailed explanation of the practical implementation of this parameterization scheme is provided in the supplementary information. This approach to parameterization ensures that the new potential simultaneously captures the polarization due to graphene, water and the ions at the interface. By directly modifying εi-c, the approach incorporates polarization at the interface directly into the model whilst modeling all other pair-wise interactions using the original parameter set. This feature of our approach is important because it avoids modifying the ion-water and graphene-water parameters, which are known to reproduce key experimental properties such as ion hydration free energies and the interfacial water droplet contact angle, respectively. It also yields parameters that capture the effect of polarization at the surface whilst simultaneously avoiding the need for computationally expensive fully polarizable potentials, and could potentially be exploited to simulate other examples of ion adsorption where surface polarization is known to be important.

Table 1. Comparison of aqueous ion-graphene adsorption energies (kJ mol−1) obtained from DFT and MD simulations and εi-c (kJ mol−1) calculated either using the Lorentz-Berthelot (LB) combining rules or adjusted (ion-π) to reproduce the DFT adsorption energies.

Ion Eads (DFT) LB ion-πεi-c Eads εi-c Eads

Li+ −10.4 0.831 −4.5 4.000 −10.7Na+ −13.8 0.850 1.7 3.000 −14.5K+ −12.6 0.939 2.9 2.200 −12.3

Mg2+ −16.5 0.538 −2.9 14.250 −16.3Ca2+ −15.7 0.679 −3.9 5.000 −16.3Cl− −6.9 0.162 n/a 0.600 −7.0

The PMF profiles obtained using the original and optimized values of εi-c are compared in Figure 2 and the adsorption energies are summarized in Table 1. It is clear that ion adsorption energies are significantly underestimated using the original parameters, in which the important ion-π interactions are unaccounted for, and εi-c had to be increased by a factor between 2 and 26, depending on the ion. The newly optimized potential now allows for appreciable differences in the ion adsorption energies that were not predicted by the original force field. There are typically two or three distinct minima and maxima along the PMF, and these correspond to the successive partial dehydration of the ion hydration shells. For two of the cations, Na+

and K+, the position of the global minimum shifts to a much shorter distance upon

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optimizing εi-c, from 0.57 to 0.31 nm and 0.76 to 0.30 nm, respectively. From the calculation of the hydration number for the first and second hydration shell (Figure 2), it appears that these two cations lose waters from the first hydration shell upon adsorption, whereas the other ions adsorb preserving their first hydration shells. This result is explained by the relatively small hydration free energy of these cations. In contrast to the other cations, Na+ and K+ have weak enough ion-water interactions that the energy penalty associated with their partial dehydration is compensated by the cation-π interaction that the model now accounts for. The distinction between ions that adsorb with or without their hydration shells is most obvious when comparing K+

to Mg2+. For Mg2+, the first hydration number is always exactly 6.0, regardless of whether the ion is adsorbed or desorbed. For K+, however, the first hydration number decreases from 7.2 to 5.7 upon adsorption. This distinction is not apparent when the cation-π interaction is ignored (original εi-c) and, in that case, the primary hydration number of K+ is 7.6 at the minimum in the PMF. Figure 3 shows the typical hydrated structure of the Mg2+ and K+ ions at the position of the minimum along the PMF. Simulation snapshots for the other ions at their minima are provided in the supplementary information. For Cl−, the individual minima and maxima in the PMF profile are less well defined but this ion also prefers to adsorb to the surface with its first hydration shell intact.

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Figure 2. Potential of mean force (w) for ion adsorption using the original (dashed lines) and newly optimized (solid lines) parameters and coordination numbers (nw) for the first (circle) and second (squares) hydration shells for a) Li+, b) Na+, c) K+, d) Mg2+, e) Ca2+ and f) Cl−. The hydrated structures of the ions at the minima are provided in the supplementary information, as well as an explanation of how the hydration numbers were obtained.

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Figure 3. Structure of hydrated a) K+, at z = 0.31 nm, and b) Mg2+, at z = 0.43 nm, from the graphene surface. For clarity, only waters in the first hydration shell are shown.

In order to understand the interfacial behavior of realistic systems, the collective behavior of ions in aqueous solution must be studied. Hence, we simulated the propensity of ions to reside at the interface in 1.0 mol dm−3 LiCl, NaCl, KCl, MgCl2 and CaCl2 electrolyte solutions, comparing the original parameters to our newly optimized ones. In these simulations, the graphene sheet (at z = 0) was much larger (5.2 nm × 5.1 nm) and periodic in the x, y-plane. The density profiles of ions adjacent to the interface using both the original and modified εi-c, are shown in Figure 4. Apart from Li+, the concentration of ions at the interface is severely depleted relative to bulk solution using the original value of εi-c. When the ion-π interaction is included in the potential, the concentration of ions at the surface increases significantly. This once again demonstrates the unsuitability of parameters obtained using standard combining rules. In the 1:1 electrolytes, the cation is always closer to the interface than Cl− and the concentration at the surface increases down the group (Li+ < Na+ < K+). This result is analogous to that found by Pham et al.,25 who showed that K+ has a higher propensity to partially dehydrate and reside at the interface when under confinement in a CNT than Na+. Their simulations also showed that Na+ retains its first hydration shell while our simulations indicate that Na+ partially dehydrates upon adsorption. This different behavior is likely to be due to differences in surface geometry (i.e. curved vs planar). The adsorption of Na+ at the graphene surface was also observed in recent experiments,42 but not in MD simulations employing potentials that only account for the polarization of the solution and not the surface.12, 23

It is important to note that the observed ion adsorption trend is the opposite of that predicted by the gas phase DFT calculations (Li+ > Na+ > K+) and different to that obtained from the single ion PMFs (Li+ < K+ < Na+). The latter observation also emphasizes the importance of considering electrolyte solutions at realistic

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concentrations, and simulations of this size are not achievable using first-principles MD. Mg2+ and Ca2+ reside further from the interface than Cl−, enabling them to retain their first hydration shell. The area under the main peak in the density profile shows that the interfacial concentration of Cl− is approximately double that of Mg2+ and Ca2+

in the 2:1 electrolytes.In conclusion, our present study demonstrates that molecular simulations can

only yield reliable understanding of the physics of the graphene-electrolyte interface if the ion-π interaction is included in the intermolecular potential and the attraction of ions to the surface is severely underestimated if this important contribution is ignored. This novel approach to intermolecular potential parameterization simultaneously accounts for polarization of the surface and the solvent using just a single adjustable parameter, εi-c. Such an approach avoids the need to use more time-consuming and computationally expensive methods such as first-principles MD or polarizable potentials, the use of which restricts the time and length scale accessible to simulation. Our effective potential can now be used to model electrolyte solutions at realistic concentrations to design, for example, graphene-based materials for ion-exchange chromatography or electrowetting applications.43 Finally, our parameterization method could also be extended to model the interaction of any ion with graphene. This will be useful to help understand ion permeation through graphene-based membranes,5 where relative ion permeation rates depend on the strength of the interaction between ions and graphene, with significant implications for water decontamination by nanofiltration. One specific example is the recently proposed remediation of radioactive TcO4

− from solutions containing competing ions.6

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Figure 4. Cation (coloured lines) and anion (black lines) density profiles at the graphene-electrolyte interface for a 1 mol dm−3 electrolyte of a) LiCl, b) NaCl, c) KCl, d) MgCl2 and e) CaCl2 comparing the new parameters (solid lines) with the original parameters (dashed lines).

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AUTHOR INFORMATION

Corresponding Author*Email: christopher.williams@manchester.ac.uk

paola.carbone@manchester.ac.uk

NotesThe authors declare there are no competing financial interests.

ACKNOWLEDGMENTSThe authors would like to acknowledge the support of the Engineering and Physical Science Research Council (grant numbers EP/M506436 and EP/G03737X/1) and the ERC (Grant No. 615834). Computational resources were provided by the University of Manchester’s Computational Shared Facility and the N8 high-performance computing facility.

Supporting Information Available: Contains a discussion of the computational methods employed for the DFT calculations, potential of mean force calculations and force fields employed and 1 M electrolyte simulations.

REFERENCES1. Netz, R. R. Water and Ions at Interfaces. Curr. Opin. Colloid Interface Sci. 2004, 9, 192-197.2. Pounds, M.; Tazi, S.; Salanne, M.; Madden, P. A. Ion Adsorption at a Metallic Electrode: an ab initio Based Simulation Study. J. Phys. Condens. Matter 2009, 21, 424109.3. Sitko, R.; Zawisza, B.; Malicka, E. Graphene as a New Sorbent in Analytical Chemistry. TrAC, Trends Anal. Chem. 2013, 51, 33-43.4. Sun, P.; Zheng, F.; Zhu, M.; Song, Z.; Wang, K.; Zhong, M.; Wu, D.; Little, R. B.; Xu, Z.; Zhu, H. Selective Trans-Membrane Transport of Alkali and Alkaline Earth Cations through Graphene Oxide Membranes Based on Cation-pi Interactions. ACS Nano 2014, 8, 850-859.5. Joshi, R. K.; Carbone, P.; Wang, F. C.; Kravets, V. G.; Su, Y.; Grigorieva, I. V.; Wu, H. A.; Geim, A. K.; Nair, R. R. Precise and Ultrafast Molecular Sieving Through Graphene Oxide Membranes. Science 2014, 343, 752-754.6. Williams, C. D.; Carbone, P. Selective Removal of Technetium from Water Using Graphene Oxide Membranes. Environ. Sci. Technol. 2016, 50, 3875-3881.7. Dai, H.; Xu, Z.; Yang, X. Water Permeation and Ion Rejection in Layer-by-Layer Stacked Graphene Oxide Nanochannels: A Molecular Dynamics Simulation. J. Phys. Chem. C 2016, 120, 22585-22596.8. Yoo, E.; Kim, J.; Hosono, E.; Zhou, H.; Kudo, T.; Honma, I. Large Reversible Li Storage of Graphene Nanosheet Families for use in Rechargeable Lithium Ion Batteries. Nano Lett. 2008, 8, 2277-2282.9. Colherinhas, G.; Fileti, E. E.; Chaban, V. V. The Band Gap of Graphene Is Efficiently Tuned by Monovalent Ions. J. Phys. Chem. Lett. 2015, 6, 302-307.10. Stoller, M. D.; Park, S. J.; Zhu, Y. W.; An, J. H.; Ruoff, R. S. Graphene-Based Ultracapacitors. Nano Lett. 2008, 8, 3498-3502.11. Ang, P. K.; Chen, W.; Wee, A. T. S.; Loh, K. P. Solution-Gated Epitaxial Graphene as pH Sensor. J. Am. Chem. Soc. 2008, 130, 14392-14393.

11

12. Cole, D. J.; Ang, P. K.; Loh, K. P. Ion Adsorption at the Graphene/Electrolyte Interface. J. Phys. Chem. Lett. 2011, 2, 1799-1803.13. Onsager, L.; Samaras, N. N. T. The Surface Tension of Debye-Huckel Electrolytes. J. Chem. Phys. 1934, 2, 528-536.14. Jarvis, N. L.; Scheiman, M. A. Surface Potentials of Aqueous Electrolyte Solutions. J. Phys. Chem. 1968, 72, 74-78.15. Raymond, E. A.; Richmond, G. L. Probing the Molecular Structure and Bonding of the Surface of Aqueous Salt Solutions. J. Phys. Chem. B 2004, 108, 5051-5059.16. Marcus, Y. Ions in Water and Biophysical Implications: From Chaos to Cosmos; Springer: Dordrecht; 2012.17. Jungwirth, P.; Tobias, D. J. Specific Ion Effects at the Air/Water Interface. Chem. Rev. 2006, 106, 1259-1281.18. Archontis, G.; Leontidis, E.; Andreou, G. Attraction of Iodide Ions by the Free Water Surface, Revealed by Simulations with a Polarizable Force Field Based on Drude Oscillators. J. Phys. Chem. B 2005, 109, 17957-17966.19. Horinek, D.; Netz, R. R. Specific Ion Adsorption at Hydrophobic Solid Surfaces. Phys. Rev. Lett. 2007, 99, 226104.20. Horinek, D.; Herz, A.; Vrbka, L.; Sedlmeier, F.; Mamatkulov, S. I.; Netz, R. R. Specific Ion Adsorption at the Air/Water interface: The Role of Hydrophobic Solvation. Chem. Phys. Lett. 2009, 479, 173-183.21. Sunner, J.; Nishizawa, K.; Kebarle, P. Ion-Solvent Molecule Interactions in the Gas Phase. The Potassium Ion and Benzene. J. Phys. Chem. 1981, 85, 1814-1820.22. Chialvo, A. A.; Cummings, P. T. Aqua Ions-Graphene Interfacial and Confinement Behavior: Insights from Isobaric-Isothermal Molecular Dynamics. J. Phys. Chem. A 2011, 115, 5918-5927.23. Sala, J.; Guardia, E.; Marti, J. Specific Ion Effects in Aqueous Electrolyte Solutions Confined within Graphene Sheets at the Nanometric Scale. Phys. Chem. Chem. Phys. 2012, 14, 10799-10808.24. Kulik, H. J.; Schwegler, E.; Galli, G. Probing the Structure of Salt Water under Confinement with First-Principles Molecular Dynamics and Theoretical X-ray Absorption Spectroscopy. J. Phys. Chem. Lett. 2012, 3, 2653-2658.25. Pham, T. A.; Mortuza, S. M. G.; Wood, B. C.; Lau, E. Y.; Ogitsu, T.; Buchsbaum, S. F.; Siwy, Z. S.; Fornasiero, F.; Schwegler, E. Salt Solutions in Carbon Nanotubes: The Role of Cation-pi Interactions. J. Phys. Chem. C 2016, 120, 7332-7338.26. Shi, G.; Liu, J.; Wang, C.; Song, B.; Tu, Y.; Hu, J.; Fang, H. Ion Enrichment on the Hydrophobic Carbon-based Surface in Aqueous Salt Solutions due to Cation-pi Interactions. Sci. Rep. 2013, 3, 3436.27. Halgren, T. A.; Damm, W. Polarizable Force Fields. Curr. Opin. Struct. Biol. 2001, 11, 236-242.28. Joung, I. S.; Cheatham, T. E., III. Determination of Alkali and Halide Monovalent Ion Parameters for use in Explicitly Solvated Biomolecular Simulations. J. Phys. Chem. B 2008, 112, 9020-9041.29. Horinek, D.; Mamatkulov, S. I.; Netz, R. R. Rational Design of Ion Force Fields based on Thermodynamic Solvation Properties. J. Chem. Phys. 2009, 130, 124507.

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30. Williams, C. D.; Carbone, P. A Classical Force Field for Tetrahedral Oxyanions Developed using Hydration Properties: the Examples of Pertechnetate (TcO4-) and Sulfate (SO42-). J. Chem. Phys. 2015, 143, 174502.31. Mamatkulov, S.; Fyta, M.; Netz, R. R. Force Fields for Divalent Cations Based on Single-Ion and Ion-Pair Properties. J. Chem. Phys. 2013, 138, 024505.32. Werder, T.; Walther, J. H.; Jaffe, R. L.; Halicioglu, T.; Koumoutsakos, P. On the Water-Carbon Interaction for use in Molecular Dynamics Simulations of Graphite and Carbon Nanotubes. J. Phys. Chem. B 2003, 107, 1345-1352.33. Ho, T. A.; Striolo, A. Polarizability Effects in Molecular Dynamics Simulations of the Graphene-Water Interface. J. Chem. Phys. 2013, 138, 054117.34. Ma, J.; Michaelides, A.; Alfe, D.; Schimka, L.; Kresse, G.; Wang, E. Adsorption and Diffusion of Water on Graphene from First Principles. Phys. Rev. B 2011, 84, 033402.35. Striolo, A.; Michaelides, A.; Joly, L. The Carbon-Water Interface: Modeling Challenges and Opportunities for the Water-Energy Nexus. Annu. Rev. Chem. Biomol. Eng. 2016, 7, 533-556.36. Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999-3093.37. Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comput. Chem. 2003, 24, 669-681.38. Peles-Lemli, B.; Kannar, D.; Nie, J. C.; Li, H.; Kunsagi-Mate, S. Some Unexpected Behavior of the Adsorption of Alkali Metal Ions onto the Graphene Surface under the Effect of External Electric Field. J. Phys. Chem. C 2013, 117, 21509-21515.39. Zheng, J.; Ren, Z.; Guo, P.; Fang, L.; Fan, J. Diffusion of Li+ Ion on Graphene: A DFT Study. Appl. Surf. Sci. 2011, 258, 1651-1655.40. Noyes, R. M. Thermodynamics of Ion Hydration as a Measure of Effective Dielectric Properties of Water. J. Am. Chem. Soc. 1962, 84, 513-522.41. Roux, B. The Calculation of the Potential of Mean Force using Computer Simulations. Comput. Phys. Commun. 1995, 91, 275-282.42. Shi, G. S.; Shen, Y.; Liu, J.; Wang, C. L.; Wang, Y.; Song, B.; Hu, J.; Fang, H. P. Molecular-Scale Hydrophilicity Induced by Solute: Molecular-Thick Charged Pancakes of Aqueous Salt Solution on Hydrophobic Carbon-Based Surfaces. Sci. Rep. 2014, 4, 6793.43. Ashraf, A.; Wu, Y. B.; Wang, M. C.; Yong, K.; Sun, T.; Jing, Y. H.; Haasch, R. T.; Aluru, N. R.; Nam, S. Doping-Induced Tunable Wettability and Adhesion of Graphene. Nano Lett. 2016, 16, 4708-4712.

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