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Onsager’s Wien effect on a lattice

Nature Materials volume 12, pages 1033–1037 (2013)Cite this article

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Abstract

The second Wien effect describes the nonlinear, non-equilibrium response of a weak electrolyte in moderate to high electric fields. Onsager’s 1934 electrodiffusion theory1, along with various extensions2,3,4, has been invoked for systems and phenomena as diverse as solar cells5,6, surfactant solutions7, water splitting reactions8,9, dielectric liquids10, electrohydrodynamic flow11, water and ice physics12, electrical double layers13, non-ohmic conduction in semiconductors14 and oxide glasses15, biochemical nerve response16 and magnetic monopoles in spin ice17. In view of this technological importance and the experimental ubiquity of such phenomena, it is surprising that Onsager’s Wien effect has never been studied by numerical simulation. Here we present simulations of a lattice Coulomb gas, treating the widely applicable case of a double equilibrium for free charge generation. We obtain detailed characterization of the Wien effect and confirm the accuracy of the analytical theories as regards the field evolution of the free charge density and correlations. We also demonstrate that simulations can uncover further corrections, such as how the field-dependent conductivity may be influenced by details of microscopic dynamics. We conclude that lattice simulation offers a powerful means by which to model and investigate system-specific corrections to the Onsager theory, and thus constitutes a valuable tool for detailed theoretical studies of the numerous practical applications of the second Wien effect.

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Figure 1: Scope of numerical simulations of the second Wien effect.
Figure 2: Second Wien effect (|μ*| = 1.45).
Figure 3: Relative mobility change with field (μ* = −1.45, T* = 0.155).
Figure 4: Charge correlations (μ* = −1.45, T* = 0.140).

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References

  1. Onsager, L. Deviations from Ohm’s law in weak electrolytes. J. Chem. Phys. 2, 599–615 (1934).

    Article  CAS  Google Scholar 

  2. Hong, K. M. & Noolandi, J. Solution of the time-dependent Onsager problem. J. Chem. Phys. 69, 5026–5039 (1978).

    Article  CAS  Google Scholar 

  3. Braun, C. L. Electric field assisted dissociation of charge transfer states as a mechanism of photocarrier production. J. Chem. Phys. 80, 4157–4161 (1984).

    Article  CAS  Google Scholar 

  4. Noolandi, J. & Hong, K. M. Theory of photogeneration and fluorescence quenching. J. Chem. Phys. 70, 3230–3236 (1979).

    Article  CAS  Google Scholar 

  5. Koster, L. J. A., Smits, E. C. P., Mihailetchi, V. D. & Blom, P. W. M. Device model for the operation of polymer/fullerene bulk heterojunction solar cells. Phys. Rev. B 72, 085205 (2005).

    Article  Google Scholar 

  6. Yuan, Y. et al. Efficiency enhancement in organic solar cells with ferroelectric polymers. Nature Mater. 10, 296–302 (2011).

    Article  CAS  Google Scholar 

  7. Randriamalala, Z., Denat, A., Gosse, J. P. & Gosse, B. Field-enhanced dissociation, the validity of Onsager’s theory in surfactant solutions. IEEE Trans. Elect. Insul. 20, 167–176 (1985).

    Article  Google Scholar 

  8. Strathmann, H., Krol, J. J., Rapp, H.-J. & Eigenberger, G. Limiting current density and water dissociation in bipolar membranes. J. Membr. Sci. 125, 123–142 (1997).

    Article  CAS  Google Scholar 

  9. Mafé, S., Manzanares, J. A. & Ramírez, P. Model for ion transport in bipolar membranes. Phys. Rev. A 42, 6245–6248 (1990).

    Article  Google Scholar 

  10. Park, J. K., Ryu, J. C., Kim, W. K. & Kang, K. H. Effect of electric field on electrical conductivity of dielectric liquids mixed with polar additives: DC conductivity. J. Phys. Chem. B 113, 12271–12276 (2009).

    Article  CAS  Google Scholar 

  11. Ryu, J. C., Park, H. J., Park, J. K. & Kang, K. H. New electrohydrodynamic flow caused by the Onsager effect. Phys. Rev. Lett. 104, 104502 (2010).

    Article  CAS  Google Scholar 

  12. Eigen, M. & Demaeyer, L. Self-dissociation and protonic charge transport in water and ice. Proc. R. Soc. Lond. A 247, 505–533 (1958).

    Article  CAS  Google Scholar 

  13. Brüesch, P. & Christen, T. The electrical double layer at a metal electrode in pure water. J. Appl. Phys. 95, 2846–2856 (2004).

    Article  Google Scholar 

  14. Pai, D. M. Electric-field-enhanced conductivity in solids. J. Appl. Phys. 46, 5122–5126 (1975).

    Article  Google Scholar 

  15. Tomozawa, M., Cordaro, J. F. & Singh, M. Applicability of weak electrolyte theory to glasses. J. Non Cryst. Solids 40, 189–196 (1980).

    Article  CAS  Google Scholar 

  16. Tsong, T. Y. & Astumian, R. D. Electroconformational coupling and membrane protein function. Prog. Biophys. Mol. Biol. 50, 1–15 (1987).

    Article  CAS  Google Scholar 

  17. Bramwell, S. T. et al. Measurement of the charge and current of magnetic monopoles in spin ice. Nature 461, 956–959 (2009).

    Article  CAS  Google Scholar 

  18. Mason, D. P. & McIlroy, D. K. Gauss’s divergence theorem in the theory of Wien dissociation of weak electrolytes. J. Chem. Soc. Faraday Trans. II 74, 2019–2026 (1978).

    Article  CAS  Google Scholar 

  19. Liu, C. T. PhD thesis. Yale Univ. (1965).

  20. Fuoss, R. M. & Onsager, L. The conductance of symmetrical electrolytes. II. The relaxation field. J. Phys. Chem. 67, 621–628 (1963).

    Article  CAS  Google Scholar 

  21. Castelnovo, C., Moessner, R. & Sondhi, S. L. Magnetic monopoles in spin ice. Nature 451, 42–45 (2008).

    Article  CAS  Google Scholar 

  22. Jaubert, L. D. C. & Holdsworth, P. C. W. Signature of magnetic monopole and Dirac string dynamics in spin ice. Nature Phys. 5, 258–261 (2009).

    Article  CAS  Google Scholar 

  23. Fulde, P., Penc, K. & Shannon, N. Fractional charges in pyrochlore lattices. Ann. Phys. (Leipz.) 11, 892–900 (2002).

    Article  CAS  Google Scholar 

  24. Vilciauskas, L., Tuckerman, M. E., Bester, G., Paddison, S. J. & Kreuer, K. D. The mechanism of proton conduction in phosphoric acid. Nature Chem. 4, 461–566 (2012).

    Article  CAS  Google Scholar 

  25. Ryzhkin, I. A. Magnetic relaxation in rare-earth oxide pyrochlores. J. Exp. Theoret. Phys. 101, 481–486 (2005).

    Article  CAS  Google Scholar 

  26. Wang, R. F. et al. Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature 439, 303–306 (2006).

    Article  CAS  Google Scholar 

  27. Ladak, S., Read, D. E., Perkins, G. K., Cohen, L. F. & Branford, W. R. Direct observation of magnetic monopole defects in an artificial spin-ice system. Nature Phys. 6, 359–363 (2010).

    Article  CAS  Google Scholar 

  28. Dunsiger, S. R. et al. Spin ice: Magnetic excitations without monopole signatures using muon spin rotation. Phys. Rev. Lett. 107, 207207 (2011).

    Article  CAS  Google Scholar 

  29. Revell, H. M. et al. Evidence of impurity and boundary effects on magnetic monopole dynamics in spin ice. Nature Phys. 9, 34–37 (2013).

    Article  CAS  Google Scholar 

  30. Ryzhkin, I. A. & Petrenko, V. F. Violation of ice rules near the surface: A theory for the quasiliquid layer. Phys. Rev. B 65, 012205 (2001).

    Article  Google Scholar 

  31. Dukhin, A. & Parlia, S. Ions, ion pairs and inverse micelles in non-polar media. Curr. Opin. Colloid Interface Sci. 18, 93115 (2013).

    Article  Google Scholar 

  32. Ingram, M. D., Moynihan, C. T. & Lesikar, A. V. Ionic conductivity and the weak electrolyte theory of glass. J. Non-Cryst. Solids 38 and 39, 371–376 (1980).

    Article  Google Scholar 

  33. Persoons, A. P. Field dissociation effect and chemical relaxation in electrolyte solutions of low polarity. J. Phys. Chem. 78, 1210–1217 (1974).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank L. D. C. Jaubert for generously sharing and discussing his numerical code with us. P.C.W.H. thanks L. Bocquet for useful discussions. R.M. thanks C. Castelnovo and S. Sondhi for many discussions and related collaborations. S.T.B. thanks S. R. Giblin for related collaborations. P.C.W.H. thanks the Institut Universitaire de France for financial support. The work of S.T.B. was supported by EPSRC grant EP/I034599/1.

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Authors and Affiliations

  1. Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany

    V. Kaiser & R. Moessner

  2. Université de Lyon, Laboratoire de Physique, École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon CEDEX 07, France

    V. Kaiser & P. C. W. Holdsworth

  3. London Centre for Nanotechnology and Department of Physics and Astronomy, University College London, London WC1H 0AJ, 17–19 Gordon Street, UK

    S. T. Bramwell

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  1. V. Kaiser
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  4. R. Moessner
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Contributions

V.K. conducted the simulations. All four authors contributed equally to the formulation and development of the project, as well as to the text of the paper.

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Correspondence to V. Kaiser.

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Kaiser, V., Bramwell, S., Holdsworth, P. et al. Onsager’s Wien effect on a lattice. Nature Mater 12, 1033–1037 (2013). https://doi.org/10.1038/nmat3729

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