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

Michio Tokuyama, Reiji Takekawa, Junichi Kawamura

Research output: Contribution to journalArticlepeer-review

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)e2De L(T)∕kBT, where ρeff is an effective ion density, e an elementary charge, and De L 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 De L(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.

Original languageEnglish
Article number121541
JournalPhysica A: Statistical Mechanics and its Applications
Volume529
DOIs
Publication statusPublished - 2019 Sep 1

Keywords

  • Effective ion density
  • Ion-diffusion coefficient
  • Ionic conductivity
  • Ionic liquid
  • Time-convolutionless mode-coupling theory
  • Weak electric field

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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