The rate at which rechargeable batteries can be charged
and discharged
is governed by the selective transport of the working ions through
the electrolyte. Conductivity, the parameter commonly used to characterize
ion transport in electrolytes, reflects the mobility of both cations
and anions. The transference number, a parameter introduced over a
century ago, sheds light on the relative rates of cation and anion
transport. This parameter is, not surprisingly, affected by cation–cation,
anion–anion, and cation–anion correlations. In addition,
it is affected by correlations between the ions and neutral solvent
molecules. Computer simulations have the potential to provide insights
into the nature of these correlations. We review the dominant theoretical
approaches used to predict the transference number from simulations
by using a model univalent lithium electrolyte. In electrolytes of
low concentration, one can obtain a quantitative model by assuming
that the solution is made up of discrete ion-containing clusters–neutral
ion pairs, negatively and positively charged triplets, neutral quadruplets,
and so on. These clusters can be identified in simulations using simple
algorithms, provided their lifetimes are sufficiently long. In concentrated
electrolytes, more clusters are short-lived and more rigorous approaches
that account for all correlations are necessary to quantify transference.
Elucidating the molecular origin of the transference number in this
limit remains an unmet challenge.