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Statistical–mechanical derivation of transport equations for glass-forming ionic liquids under a weak electric field based on time-convolutionless mode-coupling theory

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  • Tokuyama, Michio
  • Takekawa, Reiji
  • Kawamura, Junichi

Abstract

The transport equations for ionic liquids near the glass transition are derived under a weak electric field from a statistical–mechanical point of view based on the time-convolutionless mode-coupling theory recently proposed. The analytic form of ionic conductivity σ(T) is thus found as σ(T)=ρeff(T)e2DeL(T)∕kBT, where ρeff is an effective ion density, e an elementary charge, and DeL a long-time ion-diffusion coefficient. This result is quite different from the well-known Nernst–Einstein relation because ρeff(T) depends on temperature and also because DeL(T) is not just the summation of the cationic and anionic self-diffusion coefficients. The analytic function of ρeff(T) suggests that it increases drastically near the glass transition as temperature decreases. This behavior is checked by experiments. The physical origin of such a behavior is also discussed.

Suggested Citation

  • Tokuyama, Michio & Takekawa, Reiji & Kawamura, Junichi, 2019. "Statistical–mechanical derivation of transport equations for glass-forming ionic liquids under a weak electric field based on time-convolutionless mode-coupling theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 529(C).
    • Handle: RePEc:eee:phsmap:v:529:y:2019:i:c:s0378437119309057
    DOI: 10.1016/j.physa.2019.121541
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