  Using classical molecular dynamics simulations, we investigate the mobility
of ions in [Bmim][TFSI], a typical room temperature ionic liquid. Analyzing the
trajectories of individual cations and anions, we estimate the time that ions
spend in bound, clustered states, and when the ions move quasi-freely. Using
this information, we evaluate the average portion of free ions that dominate
conductivity. The amount of thus defined free ions comprises 15-25%,
monotonically increasing with temperature in the range of 300-600 K, with the
rest of the ions being temporarily bound, moving rather in local potentials.
The conductivities as a function of temperature, calculated from electric
current autocorrelation functions, reproduce reported experimental data well.
Interestingly, for free ions the Nernst-Einstein relationship between the
mobility and diffusion coefficient holds fairly well. In analogy with
electronic semiconductors, one can speak about an ionic semiconductor model for
ionic liquids with valence (or excitonic) and conduction band states for ions,
separated by an energy gap. The obtained band gap for the ionic liquid is,
however, very small, about 0.026 eV, allowing for easy interchanges between the
two dynamic states.
