## 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)=ρ_{eff}(T)e^{2}D_{e} ^{L}(T)∕k_{B}T, where ρ_{eff} is an effective ion density, e an elementary charge, and D_{e} ^{L} a long-time ion-diffusion coefficient. This result is quite different from the well-known Nernst–Einstein relation because ρ_{eff}(T) depends on temperature and also because D_{e} ^{L}(T) is not just the summation of the cationic and anionic self-diffusion coefficients. The analytic function of ρ_{eff}(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 language | English |
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Article number | 121541 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 529 |

DOIs | |

Publication status | Published - 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