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Molecular dynamics simulations of the electric double layer capacitance of graphene electrodes in mono-valent aqueous electrolytes

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Abstract

Electrical double layer (EDL) capacitors based on recently emergent graphene materials have shown several folds performance improvement compared to conventional porous carbon materials, driving a wave of technology breakthrough in portable and renewable energy storage. Accordingly, much interest has been generated to pursue a comprehensive understanding of the fundamental yet elusive double layer structure at the electrode/electrolyte interface. In this paper, we carried out comprehensive molecular dynamics simulations to obtain a comprehensive picture of how ion type, solvent properties, and charging conditions affect the EDL structure at the graphene electrode surface, and thereby its contribution to capacitance. We show that different symmetrical monovalent aqueous electrolytes M+X (M+ = Na+, K+, Rb+, and Cs+; X = F, Cl, and I) indeed have distinctive EDL structures. Larger ions, such as, Rb+, Cs+, Cl, and I, undergo partial dehydration and penetrate through the first water layer next to the graphene electrode surfaces under charging. As such, the electrical potential distribution through the EDL strongly depends on the ion type. Interestingly, we further reveal that the water can play a critical role in determining the capacitance value. The change of dielectric constant of water in different electrolytes largely cancels out the variance in electric potential drop across the EDL of different ion type. Our simulation sheds new lights on how the interplay between solvent molecules and EDL structure cooperatively contributes to capacitance, which agrees with our experimental results well.

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References

  1. Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P.; Taberna, P. L. Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer. Science 2006, 313, 1760–1763.

    Article  Google Scholar 

  2. Huang, J. S.; Sumpter, B. G.; Meunier, V. A universal model for nanoporous carbon supercapacitors applicable to diverse pore regimes, carbon materials, and electrolytes. Chem.—Eur. J. 2008, 14, 6614–6626.

    Article  Google Scholar 

  3. Cagle, C.; Feng, G.; Qiao, R.; Huang, J. S.; Sumpter, B. G.; Meunier, V. Structure and charging kinetics of electrical double layers at large electrode voltages. Microfluid. Nanofluid. 2010, 8, 703–708.

    Article  Google Scholar 

  4. Feng, G.; Qiao, R.; Huang, J. S.; Sumpter, B. G.; Meunier, V. Atomistic insight on the charging energetics in subnanometer pore supercapacitors. J. Phys. Chem. C 2010, 114, 18012–18016.

    Article  Google Scholar 

  5. Jiang, D.-E.; Jin, Z. H.; Wu, J. Z. Oscillation of capacitance inside nanopores. Nano Lett. 2011, 11, 5373–5377.

    Article  Google Scholar 

  6. Wander, M. C. F.; Shuford, K. L. Electrolyte effects in a model system for mesoporous carbon electrodes. J. Phys. Chem. C 2011, 115, 4904–4908.

    Article  Google Scholar 

  7. Górniak, R.; Lamperski, S. Investigation of the electrical double layer with a graphene electrode by the grand canonical Monte Carlo simulation. J. Phys. Chem. C 2014, 118, 3156–3161.

    Article  Google Scholar 

  8. Punnathanam, S. N. A gibbs-ensemble based technique for Monte Carlo simulation of electric double layer capacitors (EDLC) at constant voltage. J. Chem. Phys. 2014, 140, 174110.

    Article  Google Scholar 

  9. Jiang, D.-E.; Wu, J. Z. Microscopic insights into the electrochemical behavior of nonaqueous electrolytes in electric double-layer capacitors. J. Phys. Chem. Lett. 2013, 4, 1260–1267.

    Article  Google Scholar 

  10. Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular insights into the potential and temperature dependences of the differential capacitance of a room-temperature ionic liquid at graphite electrodes. J. Am. Chem. Soc. 2010, 132, 14825–14833.

    Article  Google Scholar 

  11. Shim, Y.; Jung, Y.; Kim, H. J. Graphene-based supercapacitors: A computer simulation study. J. Phys. Chem. C 2011, 115, 23574–23583.

    Article  Google Scholar 

  12. Kondrat, S.; Georgi, N.; Fedorov, M. V.; Kornyshev, A. A. A superionic state in nano-porous double-layer capacitors: Insights from Monte Carlo simulations. Phys. Chem. Chem. Phys. 2011, 13, 11359–11366.

    Google Scholar 

  13. Kondrat, S.; Kornyshev, A. Superionic state in double-layer capacitors with nanoporous electrodes. J. Phys.: Condens. Matter 2011, 23, 022201.

    Google Scholar 

  14. Feng, G.; Li, S.; Presser, V.; Cummings, P. T. Molecular insights into carbon supercapacitors based on roomtemperature ionic liquids. J. Phys. Chem. Lett. 2013, 4, 3367–3376.

    Article  Google Scholar 

  15. DeYoung, A. D.; Park, S.-W.; Dhumal, N. R.; Shim, Y.; Jung, Y.; Kim, H. J. Graphene oxide supercapacitors: A computer simulation study. J. Phys. Chem. C 2014, 118, 18472–18480.

    Article  Google Scholar 

  16. Vatamanu, J.; Borodin, O.; Smith, G. D. Molecular dynamics simulation studies of the structure of a mixed carbonate/LiPF6 electrolyte near graphite surface as a function of electrode potential. J. Phys. Chem. C 2012, 116, 1114–1121.

    Article  Google Scholar 

  17. Vatamanu, J.; Cao, L. L.; Borodin, O.; Bedrov, D.; Smith, G. D. On the influence of surface topography on the electric double layer structure and differential capacitance of graphite/ ionic liquid interfaces. J. Phys. Chem. Lett. 2011, 2, 2267–2272.

    Article  Google Scholar 

  18. Helmholtz, H. Ueber einige gesetze der vertheilung elektrischer ströme in körperlichen leitern mit anwendung auf die thierisch-elektrischen versuche. Annalen der Physik 1853, 165, 211–233.

    Article  Google Scholar 

  19. Gouy, G. Constitution of the electric charge at the surface of an electrolyte. J. Phys. 1910, 9, 457–467.

    Google Scholar 

  20. Chapman, D. L. LI. A contribution to the theory of electrocapillarity. Philos. Mag. Ser. 6 1913, 25, 475–481.

    Article  Google Scholar 

  21. Stern, H. O. Zur theorie der elektrolytischen doppelschicht. Z. Anorg. Allg. Chem. 1924, 30, 508–516.

    Google Scholar 

  22. Xia, J. L.; Chen, F.; Li, J. H.; Tao, N. J. Measurement of the quantum capacitance of graphene. Nat. Nanotechnol. 2009, 4, 505–509.

    Article  Google Scholar 

  23. Wander, M. C. F.; Shuford, K. L. Molecular dynamics study of interfacial confinement effects of aqueous NaCl brines in nanoporous carbon. J. Phys. Chem. C 2010, 114, 20539–20546.

    Article  Google Scholar 

  24. Feng, G.; Cummings, P. T. Supercapacitor capacitance exhibits oscillatory behavior as a function of nanopore size. J. Phys. Chem. Lett. 2011, 2, 2859–2864.

    Article  Google Scholar 

  25. Wander, M. C. F.; Shuford, K. L. Alkali halide interfacial behavior in a sequence of charged slit pores. J. Phys. Chem. C 2011, 115, 23610–23619.

    Article  Google Scholar 

  26. Feng, G.; Jiang, D.-E.; Cummings, P. T. Curvature effect on the capacitance of electric double layers at ionic liquid/ onion-like carbon interfaces. J. Chem. Theory Comput. 2012, 8, 1058–1063.

    Article  Google Scholar 

  27. Kalluri, R. K.; Ho, T. A.; Biener, J.; Biener, M. M.; Striolo, A. Partition and structure of aqueous NaCl and CaCl2 electrolytes in carbon-slit electrodes. J. Phys. Chem. C 2013, 117, 13609–13619.

    Article  Google Scholar 

  28. Reed, S. K.; Lanning, O. J.; Madden, P. A. Electrochemical interface between an ionic liquid and a model metallic electrode. J. Chem. Phys. 2007, 126, 084704.

    Article  Google Scholar 

  29. Péan, C.; Merlet, C.; Rotenberg, B.; Madden, P. A.; Taberna, P.-L.; Daffos, B.; Salanne, M.; Simon, P. On the dynamics of charging in nanoporous carbon-based supercapacitors. ACS Nano 2014, 8, 1576–1583.

    Article  Google Scholar 

  30. Merlet, C.; Péan, C.; Rotenberg, B.; Madden, P. A.; Simon, P.; Salanne, M. Simulating supercapacitors: Can we model electrodes as constant charge surfaces? J. Phys. Chem. Lett. 2013, 4, 264–268.

    Article  Google Scholar 

  31. Wang, Z. X.; Yang, Y.; Olmsted, D. L.; Asta, M.; Laird, B. B. Evaluation of the constant potential method in simulating electric double-layer capacitors. J. Chem. Phys. 2014, 141, 184102.

    Article  Google Scholar 

  32. Jorgensen, W. L. Quantum and statistical mechanical studies of liquids. 10. Transferable intermolecular potential functions for water, alcohols, and ethers. Application to liquid water. J. Am. Chem. Soc. 1981, 103, 335–340.

    Google Scholar 

  33. Ryckaert, J.-P.; Ciccotti, G.; Berendsen, H. J. C. Numerical integration of the cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes. J. Comput. Phys. 1977, 23, 327–341.

    Article  Google Scholar 

  34. Alexiadis, A.; Kassinos, S. Molecular simulation of water in carbon nanotubes. Chem. Rev. 2008, 108, 5014–5034.

    Article  Google Scholar 

  35. MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S. et al. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 1998, 102, 3586–3616.

    Article  Google Scholar 

  36. Foloppe, N.; MacKerell, A. D. All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J. Comput. Chem. 2000, 21, 86–104.

    Article  Google Scholar 

  37. Dang, L. X. Fluoride-fluoride association in water from molecular dynamics simulations. Chem. Phys. Lett. 1992, 200, 21–25.

    Article  Google Scholar 

  38. Dang, L. X.; Garrett, B. C. Photoelectron spectra of the hydrated iodine anion from molecular dynamics simulations. J. Chem. Phys. 1993, 99, 2972–2977.

    Article  Google Scholar 

  39. Fasolino, A.; Los, J. H.; Katsnelson, M. I. Intrinsic ripples in graphene. Nat. Mater. 2007, 6, 858–861.

    Article  Google Scholar 

  40. Yang, X. W.; Zhu, J. W.; Qiu, L.; Li, D. Bioinspired effective prevention of restacking in multilayered graphene films: Towards the next generation of high-performance supercapacitors. Adv. Mater. 2011, 23, 2833–2838.

    Article  Google Scholar 

  41. Yang, X. W.; Cheng, C.; Wang, Y. F.; Qiu, L.; Li, D. Liquid-mediated dense integration of graphene materials for compact capacitive energy storage. Science 2013, 341, 534–537.

    Article  Google Scholar 

  42. Ma, M. D.; Shen, L. M.; Sheridan, J.; Liu, J. Z.; Chen, C.; Zheng, Q. S. Friction of water slipping in carbon nanotubes. Phys. Rev. E 2011, 83, 036316.

    Article  Google Scholar 

  43. Xiong, W.; Liu, J. Z.; Ma, M.; Xu, Z. P.; Sheridan, J.; Zheng, Q. S. Strain engineering water transport in graphene nanochannels. Phys. Rev. E 2011, 84, 056329.

    Article  Google Scholar 

  44. Chen, C.; Ma, M.; Jin, K.; Liu, J. Z.; Shen, L. M.; Zheng, Q. S.; Xu, Z. P. Nanoscale fluid-structure interaction: Flow resistance and energy transfer between water and carbon nanotubes. Phys. Rev. E 2011, 84, 046314.

    Article  Google Scholar 

  45. Conway, B. E. Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications (POD); Kluwer Academic/Plenum: New York, 1999.

    Book  Google Scholar 

  46. Behrens, S. H.; Borkovec, M. Exact Poisson-Boltzmann solution for the interaction of dissimilar charge-regulating surfaces. Phys. Rev. E 1999, 60, 7040–7048.

    Article  Google Scholar 

  47. Spohr, E. Molecular simulation of the electrochemical double layer. Electrochim. Acta 1999, 44, 1697–1705.

    Article  Google Scholar 

  48. Crozier, P. S.; Rowley, R. L.; Henderson, D. Molecular dynamics calculations of the electrochemical properties of electrolyte systems between charged electrodes. J. Chem. Phys. 2000, 113, 9202–9207.

    Article  Google Scholar 

  49. Wang, S.; Li, S.; Cao, Z.; Yan, T. Y. Molecular dynamic simulations of ionic liquids at graphite surface. J. Phys. Chem. C 2010, 114, 990–995.

    Article  Google Scholar 

  50. Fedorov, M. V.; Kornyshev, A. A. Towards understanding the structure and capacitance of electrical double layer in ionic liquids. Electrochim. Acta 2008, 53, 6835–6840.

    Article  Google Scholar 

  51. Bazant, M. Z.; Storey, B. D.; Kornyshev, A. A. Double layer in ionic liquids: Overscreening versus crowding. Phys. Rev. Lett. 2011, 106, 046102.

    Article  Google Scholar 

  52. Feng, G.; Huang, J. S.; Sumpter, B. G.; Meunier, V.; Qiao, R. A “counter-charge layer in generalized solvents” framework for electrical double layers in neat and hybrid ionic liquid electrolytes. Phys. Chem. Chem. Phys. 2011, 13, 14723–14734.

    Article  Google Scholar 

  53. Merlet, C.; Rotenberg, B.; Madden, P. A.; Taberna, P.-L.; Simon, P.; Gogotsi, Y.; Salanne, M. On the molecular origin of supercapacitance in nanoporous carbon electrodes. Nat. Mater. 2012, 11, 306–310.

    Article  Google Scholar 

  54. Falk, K.; Sedlmeier, F.; Joly, L.; Netz, R. R.; Bocquet, L. Molecular origin of fast water transport in carbon nanotube membranes: Superlubricity versus curvature dependent friction. Nano Lett. 2010, 10, 4067–4073.

    Article  Google Scholar 

  55. Yang, K.-L.; Yiacoumi, S.; Tsouris, C. Monte Carlo simulations of electrical double-layer formation in nanopores. J. Chem. Phys. 2002, 117, 8499–8507.

    Article  Google Scholar 

  56. Marti, J.; Nagy, G.; Gordillo, M. C.; Guà rdia, E. Molecular simulation of liquid water confined inside graphite channels: Thermodynamics and structural properties. J. Chem. Phys. 2006, 124, 094703.

    Article  Google Scholar 

  57. Cui, S. T.; Cochran, H. D. Molecular dynamics simulation of interfacial electrolyte behaviors in nanoscale cylindrical pores. J. Chem. Phys. 2002, 117, 5850–5854.

    Article  Google Scholar 

  58. Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press: New York, 1988.

    Google Scholar 

  59. Schoch, R. B.; van Lintel, H.; Renaud, P. Effect of the surface charge on ion transport through nanoslits. Phys. Fluids 2005, 17, 100604.

    Article  Google Scholar 

  60. Aaqvist, J. Ion-water interaction potentials derived from free energy perturbation simulations. J. Phys. Chem. 1990, 94, 8021–8024.

    Article  Google Scholar 

  61. Richens, D. T. The Chemistry of Aqua Ions: Synthesis, Structure and Reactivity: A Tour through the Periodic Table of the Elements; Wiley: Chichester, New York, 1997.

    Google Scholar 

  62. Rajamani, S.; Ghosh, T.; Garde, S. Size dependent ion hydration, its asymmetry, and convergence to macroscopic behavior. J. Chem. Phys. 2004, 120, 4457–4466.

    Article  Google Scholar 

  63. Mähler, J.; Persson, I. A study of the hydration of the alkali metal ions in aqueous solution. Inorg. Chem. 2012, 51, 425–438.

    Article  Google Scholar 

  64. Kalluri, R. K.; Biener, M. M.; Suss, M. E.; Merrill, M. D.; Stadermann, M.; Santiago, J. G.; Baumann, T. F.; Biener, J.; Striolo, A. Unraveling the potential and pore-size dependent capacitance of slit-shaped graphitic carbon pores in aqueous electrolytes. Phys. Chem. Chem. Phys. 2013, 15, 2309–2320.

    Article  Google Scholar 

  65. Magnussen, O. M. Ordered anion adlayers on metal electrode surfaces. Chem. Rev. 2002, 102, 679–726.

    Article  Google Scholar 

  66. Feng, G.; Huang, J. S.; Sumpter, B. G.; Meunier, V.; Qiao, R. Structure and dynamics of electrical double layers in organic electrolytes. Phys. Chem. Chem. Phys. 2010, 12, 5468–5479.

    Article  Google Scholar 

  67. Singh, R.; Rajput, N. N.; He, X. X.; Monk, J.; Hung, F. R. Molecular dynamics simulations of the ionic liquid [EMIM+][TFMSI] confined inside rutile (110) slit nanopores. Phys. Chem. Chem. Phys. 2013, 15, 16090–16103.

    Article  Google Scholar 

  68. Stoller, M. D.; Park, S.; Zhu, Y. W.; An, J.; Ruoff, R. S. Graphene-based ultracapacitors. Nano Lett. 2008, 8, 3498–3502.

    Article  Google Scholar 

  69. Zhang, Y.; Feng, H.; Wu, X. B.; Wang, L. Z.; Zhang, A. Q.; Xia, T. C.; Dong, H. C.; Li, X. F.; Zhang, L. S. Progress of electrochemical capacitor electrode materials: A review. Int. J. Hydrogen Energy 2009, 34, 4889–4899.

    Article  Google Scholar 

  70. Cheng, C.; Uhe, J.; Yang, X. W.; Wu, Y. Z.; Li, D. Multilayered graphene membrane as an experimental platform to probe nano-confined electrosorption. Prog. Nat. Sci.: Mater. Int. 2012, 22, 668–672.

    Article  Google Scholar 

  71. Dimitrov, D. I.; Raev, N. D.; Semerdzhiev, K. I. Molecular dynamics simulations of the electrical double layer at 1 M potassium halide solution/Hg electrode interfaces. Phys. Chem. Chem. Phys. 2001, 3, 448–452.

    Article  Google Scholar 

  72. Feng, G.; Qiao, R.; Huang, J. S.; Sumpter, B. G.; Meunier, V. Ion distribution in electrified micropores and its role in the anomalous enhancement of capacitance. ACS Nano 2010, 4, 2382–2390.

    Article  Google Scholar 

  73. Kondrat, S.; Kornyshev, A.; Stoeckli, F.; Centeno, T. A. The effect of dielectric permittivity on the capacitance of nanoporous electrodes. Electrochem. Commun. 2013, 34, 348–350.

    Article  Google Scholar 

  74. Fulton, R. L. The nonlinear dielectric behavior of water: Comparisons of various approaches to the nonlinear dielectric increment. J. Chem. Phys. 2009, 130, 204503–204512.

    Article  Google Scholar 

  75. Yang, L.; Fishbine, B. H.; Migliori, A.; Pratt, L. R. Dielectric saturation of liquid propylene carbonate in electrical energy storage applications. J. Chem. Phys. 2010, 132, 044701.

    Article  Google Scholar 

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Jiang, G., Cheng, C., Li, D. et al. Molecular dynamics simulations of the electric double layer capacitance of graphene electrodes in mono-valent aqueous electrolytes. Nano Res. 9, 174–186 (2016). https://doi.org/10.1007/s12274-015-0978-5

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