Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Accelerating charging dynamics in subnanometre pores

An Erratum to this article was published on 22 April 2014

This article has been updated

Abstract

Supercapacitors have exceptional power density and cyclability but smaller energy density than batteries. Their energy density can be increased using ionic liquids and electrodes with subnanometre pores, but this tends to reduce their power density and compromise the key advantage of supercapacitors. To help address this issue through material optimization, here we unravel the mechanisms of charging subnanometre pores with ionic liquids using molecular dynamics simulations, navigated by a phenomenological model. We show that charging of ionophilic pores is a diffusive process, often accompanied by overfilling followed by de-filling. In sharp contrast to conventional expectations, charging is fast because ion diffusion during charging can be an order of magnitude faster than in the bulk, and charging itself is accelerated by the onset of collective modes. Further acceleration can be achieved using ionophobic pores by eliminating overfilling/de-filling and thus leading to charging behaviour qualitatively different from that in conventional, ionophilic pores.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Charging of narrow electrode pores with room-temperature ionic liquids.
Figure 2: Charging of nanopores predicted by the mean field model.
Figure 3: Ion self-diffusion during charging of ionophilic pores.
Figure 4: Charging of ionophilic pores obtained from molecular dynamics simulations.
Figure 5: Self-diffusion and charging in ionophobic pores.

Similar content being viewed by others

Change history

  • 25 March 2014

    In the version of this Article originally published, the e-mail address of Svyatoslav Kondrat was misspelt; it should have read ‘s.kondrat@fz-juelich.de’. This error has now been corrected in the online versions of the Article.

References

  1. Conway, B. E. Electrochemical Capacitors: Scientific Fundamentals and Technological Applications (Kluwer, (1999).

    Google Scholar 

  2. Miller, J. R. & Simon, P. Materials science electrochemical capacitors for energy management. Science 321, 651–652 (2008).

    Article  CAS  Google Scholar 

  3. Simon, P. & Gogotsi, Y. Materials for electrochemical capacitors. Nature Mater. 7, 845–854 (2008).

    Article  CAS  Google Scholar 

  4. Chmiola, J. et al. Anomalous increase in carbon capacitance at pore sizes less than 1 nanometre. Science 313, 1760–1763 (2006).

    Article  CAS  Google Scholar 

  5. Largeot, C. et al. Relation between the ion size and pore size for an electric double-layer capacitor. J. Am. Chem. Soc. 130, 2730–2731 (2008).

    Article  CAS  Google Scholar 

  6. Lin, R. et al. Solvent effect on the ion adsorption from ionic liquid electrolyte into sub-nanometre carbon pores. Electrochim. Acta 54, 7025–7032 (2009).

    Article  CAS  Google Scholar 

  7. Kondrat, S., P’erez, C. R., Presser, V., Gogotsi, Y. & Kornyshev, A. A. Effect of pore size and its dispersity on the energy storage in nanoporous supercapacitors. Energy Environ. Sci. 5, 6474–6479 (2012).

    Article  CAS  Google Scholar 

  8. Simon, P. & Gogotsi, Y. Capacitive energy storage in nanostructured carbon electrolyte systems. Acc. Chem. Res. 46, 1094–1103 (2013).

    Article  CAS  Google Scholar 

  9. Wang, H. et al. Interconnected carbon nanosheets derived from hemp for ultrafast supercapacitors with high energy. ACS Nano 7, 5131–5141 (2013).

    Article  CAS  Google Scholar 

  10. Yoo, J. J. et al. Ultrathin planar graphene supercapacitors. Nano Lett. 11, 1423–1427 (2011).

    Article  CAS  Google Scholar 

  11. Zhu, Y. et al. Carbon-based supercapacitors produced by activation of graphene. Science 332, 1537–1541 (2011).

    Article  CAS  Google Scholar 

  12. Yang, X., Cheng, C., Wang, Y., Qiu, L. & Li, D. Liquid-mediated dense integration of graphene materials for compact capacitive energy storage. Science 341, 534–537 (2013).

    Article  CAS  Google Scholar 

  13. Lukatskaya, M. R. et al. Cation intercalation and high volumetric capacitance of two-dimensional titanium carbide. Science 341, 1502–1505 (2013).

    Article  CAS  Google Scholar 

  14. Huang, J., Sumpter, B. G. & Meunier, V. Theoretical model for nanoporous carbon supercapacitors. Angew. Chem. Int. Ed. 47, 520–524 (2008).

    Article  CAS  Google Scholar 

  15. Shim, Y. & Kim, H. J. Nanoporous carbon supercapacitors in an ionic liquid: A computer simulation study. ACS Nano 4, 2345–2355 (2010).

    Article  CAS  Google Scholar 

  16. Skinner, B., Chen, T., Loth, M. S. & Shklovskii, B. I. Theory of volumetric capacitance of an electric double-layer supercapacitor. Phys. Rev. E 83, 056102 (2011).

    Article  Google Scholar 

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

    CAS  Google Scholar 

  18. Kondrat, S. & Kornyshev, A. Corrigendum: Superionic state in double-layer capacitors with nanoporous electrodes. J. Phys.: Condens. Matter 25, 119501 (2013).

    CAS  Google Scholar 

  19. Wu, P., Huang, J., Meunier, V., Sumpter, B. G. & Qiao, R. Complex capacitance scaling in ionic liquids-filled nanopores. ACS Nano 5, 9044–9051 (2011).

    Article  CAS  Google Scholar 

  20. Feng, G. & Cummings, P. T. Supercapacitor capacitance exhibits oscillatory behaviour as a function of nanopore size. J. Phys. Chem. Lett. 2, 2859–2864 (2011).

    Article  CAS  Google Scholar 

  21. Jiang, D. E., Jin, Z. H. & Wu, J. Z. Oscillation of capacitance inside nanopores. Nano Lett. 11, 5373–5377 (2011).

    Article  CAS  Google Scholar 

  22. Merlet, C. et al. On the molecular origin of supercapacitance in nanoporous carbon electrodes. Nature Mater. 11, 306–310 (2012).

    Article  CAS  Google Scholar 

  23. Xing, L., Vatamanu, J., Borodin, O. & Bedrov, D. On the atomistic nature of capacitance enhancement generated by ionic liquid electrolyte confined in subnanometre pores. J. Phys. Chem. Lett. 4, 132–140 (2013).

    Article  CAS  Google Scholar 

  24. Merlet, C. et al. Highly confined ions store charge more efficiently in supercapacitors. Nature Commun. 4, 2701 (2013).

    Article  CAS  Google Scholar 

  25. Brandt, A., Pohlmann, S., Varzi, A., Balducci, A. & Passerini, S. Ionic liquids in supercapacitors. MRS Bull. 38, 554–559 (2013).

    Article  CAS  Google Scholar 

  26. Monk, J., Singh, R. & Hung, F. R. Effects of pore size and pore loading on the properties of ionic liquids confined inside nanoporous CMK-3 carbon materials. J. Phys. Chem. C 115, 3034–3042 (2011).

    Article  CAS  Google Scholar 

  27. Rajput, N. N., Monk, J. & Hung, F. R. Structure and dynamics of an ionic liquid confined inside a charged slit graphitic nanopore. J. Phys. Chem. C 116, 14504–14513 (2012).

    Article  CAS  Google Scholar 

  28. Perkin, S. Ionic liquids in confined geometries. Phys. Chem. Chem. Phys. 14, 5052–5062 (2012).

    Article  CAS  Google Scholar 

  29. Bazant, M. Z., Thornton, K. & Ajdari, A. Diffuse-charge dynamics in electrochemical systems. Phys. Rev. E 70, 021506 (2004).

    Article  Google Scholar 

  30. Biesheuvel, P. M. & Bazant, M. Z. Nonlinear dynamics of capacitive charging and desalination by porous electrodes. Phys. Rev. E 81, 031502 (2010).

    Article  CAS  Google Scholar 

  31. Kondrat, S. & Kornyshev, A. Charging dynamics and optimization of nanoporous supercapacitors. J. Phys. Chem. C 117, 12399–12406 (2013).

    Article  CAS  Google Scholar 

  32. Taberna, P. L., Simon, P. & Fauvarque, J. F. Electrochemical characteristics and impedance spectroscopy studies of carbon–carbon supercapacitors. J. Electrochem. Soc. 150, A292–A300 (2003).

    Article  CAS  Google Scholar 

  33. Whitaker, S. Fundamental Principles of Heat Transfer (Pergamon Press, 1977).

    Google Scholar 

  34. Galantini, L. & Pavel, N. V. Collective diffusion and self-diffusion coefficients comparison to separate interactions and micellar size effects on ionic micelle diffusivities: Cylindrical micelles of sodium taurodeoxycholate. J. Chem. Phys. 118, 2865–2872 (2003).

    Article  CAS  Google Scholar 

  35. Kilic, M. S., Bazant, M. Z. & Ajdari, A. Steric effects in the dynamics of electrolytes at large applied voltages ii modified Poisson–Nernst–Planck equations. Phys. Rev. E 75, 021503 (2007).

    Article  Google Scholar 

  36. Iacob, C. et al. Enhanced charge transport in nano-confined ionic liquids. Soft Matter 8, 289–293 (2012).

    Article  CAS  Google Scholar 

  37. Klahn, M., Seduraman, A. & Wu, P. A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study. J. Phys. Chem. B 112, 13849–13861 (2008).

    Article  CAS  Google Scholar 

  38. Tsai, W-Y. et al. Outstanding performance of activated graphene based supercapacitors in ionic liquid electrolyte from 50 to 80 C. Nano Energy 2, 403–411 (2013).

    Article  CAS  Google Scholar 

  39. Fic, K., Lot, G. & Frackowiak, E. Effect of surfactants on capacitance properties of carbon electrodes. Electrochim. Acta 60, 206–212 (2011).

    Article  Google Scholar 

  40. Mattia, D. & Gogotsi, Y. Review: Static and dynamic behaviour of liquids inside carbon nanotubes. Microfluid. Nanofluid. 5, 289–305 (2008).

    Article  CAS  Google Scholar 

  41. Borukhov, I., Andelman, D. & Orland, H. Steric effects in electrolytes: A modified Poisson–Boltzmann equation. Phys. Rev. Lett. 79, 435–438 (1997).

    Article  CAS  Google Scholar 

  42. Kondrat, S., Kornyshev, A., Stoeckli, F. & Centeno, T.A. The effect of dielectric permittivity on the capacitance of nanoporous electrodes. Electrochem. Comm. 34, 348–350 (2013).

    Article  CAS  Google Scholar 

  43. Kornyshev, A. A., Ulstrup, J. & Vorotyntsev, M. A. The effect of the spatial dispersion of the dielectric permittivity on the capacitance of thin insulating films: Nonlinear dependence of the inverse capacitance on film thickness. Thin Solid Films 75, 105–118 (1981).

    Article  CAS  Google Scholar 

  44. GNU Scientific Library. http://www.gnu.org/software/gsl/

  45. Lindahl, E., Hess, B. & van der Spoel, D. Gromacs 3.0: A package for molecular simulation and trajectory analysis. J. Mol. Modell. 7, 306–331 (2001).

    Article  CAS  Google Scholar 

  46. Raghunathan, A. V. & Aluru, N. R. Self-consistent molecular dynamics formulation for electric-field-mediated electrolyte transport through nanochannels. Phys. Rev. E 76, 011202 (2007).

    Article  CAS  Google Scholar 

  47. Wu, P., Huang, J. S., Meunier, V., Sumpter, B. G. & Qiao, R. Voltage dependent charge storage modes and capacity in sub-nanometre pores. J. Phys. Chem. Lett. 3, 1732–1737 (2012).

    Article  CAS  Google Scholar 

  48. Merlet, C. et al. Simulating supercapacitors: Can we model electrodes as constant charge surfaces? J. Phys. Chem. Lett. 4, 264–268 (2013).

    Article  CAS  Google Scholar 

  49. Bussi, G., Donadio, D. & Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 126, 014101 (2007).

    Article  Google Scholar 

  50. Frenkel, D. & Smith, B. Understanding Molecular Simulations (Academic, (1996).

    Google Scholar 

Download references

Acknowledgements

We thank the Clemson-CCIT office and E. Duffy for providing computer facilities. R.Q. acknowledges the support of the NSF (CBET-1264578). S.K. and A.K. were supported by the Engineering and Physical Science Research Council via Grant EP/H004319/1. We are grateful to Y. Gogotsi, P. Simon, C. Pérez, J. Griffin, G. Oshanin and F. Stoeckli for fruitful discussions, and X. Jiang for technical assistance.

Author information

Authors and Affiliations

Authors

Contributions

A.A.K., R.Q. and S.K. designed the research. P.W. performed MD simulations and S.K. performed MFT calculations. The results were analysed jointly by R.Q., S.K., A.A.K. and P.W., and all participated in writing the paper.

Corresponding authors

Correspondence to Svyatoslav Kondrat, Rui Qiao or Alexei A. Kornyshev.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 499 kb)

Supplementary Information

Supplementary Movie 1 (MOV 488 kb)

Supplementary Information

Supplementary Movie 2 (MOV 30531 kb)

Supplementary Information

Supplementary Movie 3 (MOV 15960 kb)

Supplementary Information

Supplementary Movie 4 (MOV 29748 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kondrat, S., Wu, P., Qiao, R. et al. Accelerating charging dynamics in subnanometre pores. Nature Mater 13, 387–393 (2014). https://doi.org/10.1038/nmat3916

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3916

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing