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

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 sigma(T) is thus found as sigma(T) = rho(eff)(T)e(2)D(e)(L)(T)/k(B)T, where rho(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 rho(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 rho(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. (C) 2019 Elsevier B.V. All rights reserved.