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:

The mechanism of proton conduction in phosphoric acid

Abstract

Neat liquid phosphoric acid (H3PO4) has the highest intrinsic proton conductivity of any known substance and is a useful model for understanding proton transport in other phosphate-based systems in biology and clean energy technologies. Here, we present an ab initio molecular dynamics study that reveals, for the first time, the microscopic mechanism of this high proton conductivity. Anomalously fast proton transport in hydrogen-bonded systems involves a structural diffusion mechanism in which intramolecular proton transfer is driven by specific hydrogen bond rearrangements in the surrounding environment. Aqueous media transport excess charge defects through local hydrogen bond rearrangements that drive individual proton transfer reactions. In contrast, strong, polarizable hydrogen bonds in phosphoric acid produce coupled proton motion and a pronounced protic dielectric response of the medium, leading to the formation of extended, polarized hydrogen-bonded chains. The interplay between these chains and a frustrated hydrogen-bond network gives rise to the high proton conductivity.

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: Characterization of the proton–proton coupling in terms of the interproton force and radial distribution function.
Figure 2: Oxygen–oxygen radial distribution functions (gOO) and integrated coordination numbers (nOO) with respect to H4PO4+, H3PO4 and H2PO4 species.
Figure 3: Proton coupling correlation function Cpc(n) as a function of connectivity n.
Figure 4: Snapshots of the elementary steps of the proton conduction mechanism in H3PO4.

Similar content being viewed by others

References

  1. DeCoursey, T. E. Voltage-gated proton channels and other proton transfer pathways. Physiol. Rev. 83, 475–579 (2003).

    Article  CAS  Google Scholar 

  2. Wraight, C. A. Chance and design — proton transfer in water, channels and bioenergetic proteins. Biochim. Biophys. Acta 1757, 886–912 (2006).

    Article  CAS  Google Scholar 

  3. Kreuer, K. D. Proton conductivity: materials and applications. Chem. Mater. 8, 610–641 (1996).

    Article  CAS  Google Scholar 

  4. Kreuer, K. D., Paddison, S. J., Spohr, E. & Schuster, M. Transport in proton conductors for fuel-cell applications: simulations, elementary reactions, and phenomenology. Chem. Rev. 104, 4637–4678 (2004).

    Article  CAS  Google Scholar 

  5. Marx, D. Proton transfer 200 years after von Grotthuss: insights from ab initio simulations. ChemPhysChem 7, 1848–1870 (2006).

    Article  CAS  Google Scholar 

  6. Marx, D., Chandra, A. & Tuckerman, M. E. Aqueous basic solutions: hydroxide solvation, structural diffusion, and comparison to the hydrated proton. Chem. Rev. 110, 2174–2216 (2010).

    Article  CAS  Google Scholar 

  7. Agmon, N. The Grotthuss mechanism. Chem. Phys. Lett. 244, 456–462 (1995).

    Article  CAS  Google Scholar 

  8. Tuckerman, M. E., Marx, D., Klein, M. L. & Parrinello, M. On the quantum nature of the shared proton in hydrogen bonds. Science 275, 817–820 (1997).

    Article  CAS  Google Scholar 

  9. Marx, D., Tuckerman, M. E., Hutter, J. & Parrinello, M. The nature of the hydrated excess proton in water. Nature 397, 601–604 (1999).

    Article  CAS  Google Scholar 

  10. Tuckerman, M. E., Marx, D. & Parrinello, M. The nature and transport mechanism of hydrated hydroxide ions in aqueous solution. Nature 417, 925–929 (2002).

    Article  CAS  Google Scholar 

  11. Vuilleumier, R. & Borgis, D. Transport and spectroscopy of the hydrated proton: a molecular dynamics study. J. Chem. Phys. 111, 4251–4266 (1999).

    Article  CAS  Google Scholar 

  12. Schmitt, U. W. & Voth, G. A. The computer simulation of proton transport in water. J. Chem. Phys. 111, 9361–9381 (1999).

    Article  CAS  Google Scholar 

  13. Markovitch, O. et al. Special pair dance and partner selection: elementary steps in proton transport in liquid water. J. Phys. Chem. B 112, 9456–9466 (2008).

    Article  CAS  Google Scholar 

  14. Berkelbach, T. C., Lee, H.-S. & Tuckerman, M. E. Concerted hydrogen-bond dynamics in the transport mechanism of the hydrated proton: a first-principles molecular dynamics study. Phys. Rev. Lett. 103, 238302 (2009).

    Article  Google Scholar 

  15. Woutersen, S. & Bakker, H. J. Ultrafast vibrational and structural dynamics of the proton in liquid water. Phys. Rev. Lett. 96, 138305 (2006).

    Article  Google Scholar 

  16. de Grotthuss, C. J. T. Sur la décomposition de l'eau et des corps qu'elle tient en dissolution à l'aide de l'électricité galvanique. Ann. Chim. (Paris) LVIII, 54–74 (1806).

    Google Scholar 

  17. Marcus, R. A. On the theory of oxidation–reduction reactions involving electron transfer. I. J. Chem. Phys. 24, 966–978 (1956).

    Article  CAS  Google Scholar 

  18. Kreuer, K. D. On the complexity of proton conduction phenomena. Solid State Ionics 136, 149–160 (2000).

    Article  Google Scholar 

  19. Dellago, C., Naor, M. & Hummer, G. Proton transport through water-filled carbon nanotubes. Phys. Rev. Lett. 90, 105902 (2003).

    Article  Google Scholar 

  20. Car, R. & Parrinello, M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985).

    Article  CAS  Google Scholar 

  21. Li, Q., Jensen, J. O., Savinell, R. F. & Bjerrum, N. J. High temperature proton exchange membranes based on polybenzimidazoles for fuel cells. Prog. Polym. Sci. 34, 449–477 (2009).

    Article  CAS  Google Scholar 

  22. Boysen, D. A., Uda, T., Chisholm, C. R. I. & Haile, S. M. High-performance solid acid fuel cells through humidity stabilization. Science 303, 68–70 (2004).

    Article  CAS  Google Scholar 

  23. Schuster, M., Rager, T., Noda, A., Kreuer, K. D. & Maier, J. About the choice of the protogenic group in PEM separator materials for intermediate temperature, low humidity operation: a critical comparison of sulfonic acid, phosphonic acid and imidazole functionalized model compounds. Fuel Cells 5, 355–365 (2005).

    Article  CAS  Google Scholar 

  24. Westheimer, F. H. Why nature chose phosphates. Science 235, 1173–1178 (1987).

    Article  CAS  Google Scholar 

  25. Heberle, J., Riesle, J., Thiedemann, G., Oesterhelt, D. & Dencher, N. A. Proton migration along the membrane-surface and retarded surface to bulk transfer. Nature 370, 379–382 (1994).

    Article  CAS  Google Scholar 

  26. Tsuchida, E. Ab initio molecular-dynamics simulation of concentrated phosphoric acid. J. Phys. Soc. Jpn 75, 054801 (2006).

    Article  Google Scholar 

  27. Vilciauskas, L., Paddison, S. J. & Kreuer, K. D. Ab initio modeling of proton transfer in phosphoric acid clusters. J. Phys. Chem. A 113, 9193–9201 (2009).

    Article  CAS  Google Scholar 

  28. Greenwood, N. N. & Thompson, A. The mechanism of electrical conduction in fused phosphoric and trideuterophosphoric acids. J. Chem. Soc. 3485–3492 (1959).

  29. Aihara, Y., Sonai, A., Hattori, M. & Hayamizu, K. Ion conduction mechanisms and thermal properties of hydrated and anhydrous phosphoric acids studied with 1H, 2H, and 31P NMR. J. Phys. Chem. B 110, 24999–25006 (2006).

    Article  CAS  Google Scholar 

  30. Dippel, T., Kreuer, K. D., Lassègues, J. C. & Rodriguez, D. Proton conductivity in fused phosphoric acid: a 1H/31P PFG-NMR and QNS study. Solid State Ionics 61, 41–46 (1993).

    Article  CAS  Google Scholar 

  31. Munson, R. A. Self-dissociative equilibria in molten phosphoric acid. J. Phys. Chem. 68, 3374–3377 (1964).

    Article  CAS  Google Scholar 

  32. Janoschek, R., Weidemann, E. G., Zundel, G. & Pfeiffer, H. Extremely high polarizability of hydrogen bonds. J. Am. Chem. Soc. 94, 2387–2396 (1972).

    Article  CAS  Google Scholar 

  33. Leuchs, M. & Zundel, G. Polarizable acid–acid and acid–water hydrogen bonds with H3PO2, H3PO3, H3PO4, and H3AsO4 . Can. J. Chem. 57, 487–493 (1979).

    Article  CAS  Google Scholar 

  34. Komatsuzaki, T. & Ohmine, I. Energetics of proton transfer in liquid water. I. Ab initio study for origin of many-body interaction and potential energy surfaces. Chem. Phys. 180, 239–269 (1994).

    Article  CAS  Google Scholar 

  35. Sharma, M., Resta, R. & Car, R. Dipolar correlations and the dielectric permittivity of water. Phys. Rev. Lett. 98, 247401 (2007).

    Article  Google Scholar 

  36. Munson, R. A. Dielectric constant of phosphoric acid. J. Chem. Phys. 40, 2044–2046 (1964).

    Article  CAS  Google Scholar 

  37. Buchner, R., Barthel, J. & Stauber, J. The dielectric relaxation of water between 0 °C and 35 °C. Chem. Phys. Lett. 306, 57–63 (1999).

    Article  CAS  Google Scholar 

  38. Geissler, P., Dellago, C., Chandler, D., Hutter, J. & Parrinello, M. Autoionization in liquid water. Science 291, 2121–2124 (2001).

    Article  CAS  Google Scholar 

  39. Blessing, R. H. New analysis of the neutron diffraction data for anhydrous orthophosphoric acid and the structure of H3PO4 molecules in crystals. Acta Cryst. B 44, 334–340 (1988).

    Article  Google Scholar 

  40. Pomès, R. & Roux, B. Molecular mechanism of H+ conduction in the single-file water chain of the gramicidin channel. Biophys. J. 82, 2304–2316 (2002).

    Article  Google Scholar 

  41. Hassanali, A., Prakash, M. K., Eshet, H. & Parrinello, M. On the recombination of hydronium and hydroxide ions in water. Proc. Natl Acad. Sci. USA 108, 20410–20415 (2011).

    Article  CAS  Google Scholar 

  42. CPMD, version 3.13 (Max-Planck-Institut für Festkörperforschung and IBM Zurich Research Laboratory, 1995–2010).

  43. Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098–3100 (1988).

    Article  CAS  Google Scholar 

  44. Lee, C., Yang, W. & Parr, R. Development of the Colle–Salvetti correlation-energy formula into a functional of the electron-density. Phys. Rev. B 37, 785–789 (1988).

    Article  CAS  Google Scholar 

  45. Troullier, N. & Martins, J. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).

    Article  CAS  Google Scholar 

  46. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).

    Article  Google Scholar 

  47. Kohn, W. & Sham, L. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1131–A1138 (1965).

    Article  Google Scholar 

  48. Spieser, S. A. H., Leeflang, B. R., Kroon-Batenburg, L. M. J. & Kroon, J. A force field for phosphoric acid: comparison of simulated with experimental data in the solid and liquid state. J. Phys. Chem. A 104, 7333–7338 (2000).

    Article  CAS  Google Scholar 

  49. Martyna, G., Klein, M. & Tuckerman, M. Nosé–Hoover chains: the canonical ensemble via continuous dynamics. J. Chem. Phys. 97, 2635–2643 (1992).

    Article  Google Scholar 

  50. Tuckerman, M. E., Berne, B. J., Martyna, G. J. & Klein, M. L. Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals. J. Chem. Phys. 99, 2796–2808 (1993).

    Article  Google Scholar 

  51. Wood, B. C. & Marzari, N. Proton dynamics in superprotonic CsHSO4 . Phys. Rev. B 76, 134301 (2007).

    Article  Google Scholar 

  52. Hayes, R. L., Paddison, S. J. & Tuckerman, M. E. Proton transport in triflic acid hydrates studied via path integral Car–Parrinello molecular dynamics. J. Phys. Chem. B 113, 16574–16589 (2009).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

L.V. acknowledges partial financial support from the EU FP6 Integrated Project ‘Autobrane’ and Stiftung Energieforschung Baden-Württemberg (FKZ A 23305). M.E.T. acknowledges support from the National Science Foundation (award no. CHE-1012545). The authors thank B. Frick (Institut Laue-Langevin, Grenoble) for valuable discussions and the Rechenzentrum Garching of the Max Planck Society for the use of computational resources.

Author information

Authors and Affiliations

Authors

Contributions

L.V., M.E.T., G.B., S.J.P. and K.D.K. designed the research. L.V., M.E.T. and G.B. performed AIMD simulations. L.V., M.E.T., G.B., S.J.P. and K.D.K carried out analysis. All authors discussed the results and contributed to preparation of the manuscript.

Corresponding authors

Correspondence to Mark E. Tuckerman or Klaus-Dieter Kreuer.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vilčiauskas, L., Tuckerman, M., Bester, G. et al. The mechanism of proton conduction in phosphoric acid. Nature Chem 4, 461–466 (2012). https://doi.org/10.1038/nchem.1329

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nchem.1329

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