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Onsager’s Wien effect on a lattice


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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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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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).

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