Molecular dynamics study of conductivity of ionic liquids: The Kohlrausch law

A molecular dynamics simulation study is performed on the 1-butyl-3-methyl-imidazolium hexafluorophosphate (BMIMPF6), 1-ethyl-3-methylimidazolium hexa fluorophosphate (EMIMPF6), and 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4). Self-diffusion coefficients are computed at temperatures ranging from 300 to 420 K (depending on the compound) using the Nernst-Einstein relation. The resulting ionic conductivities based on assumption of independent ion migration are compared with ionic conductivities computed from the Nernst-Einstein relation for a macroscopic current, the ratio is in the range 0.5-0.8. Therefore there is only moderate correlation in ionic motion, but no pronounced clustering. The simulated ionic conductivities are lower than experimental, especially for full-atom force fields.