On the determination of ion transport numbers in molten salts using molecular dynamics

Individual transport numbers provide a measure of the charge ratio which is carried by each ionic species of an electrolyte. However, unlike the electrical conductivity or diffusion coefficients, this quantity lacks a clear definition from the statistical mechanics point of view. In practice, it is measured via complex experimental setups, and most of the interpretation of the available data is made by using the Nernst–Einstein approximation. Here we show that this approach is not suitable in molten salts due to the large contributions of the cross-terms due to the ionic interactions in the total ionic conductivity. We propose a partition scheme that allows to attribute these cross-terms to the various ions, allowing for an estimate of the transport numbers in a series of molten salt formed by mixing NaF and AlF₃ at various compositions. The results are interpreted using the speciation of the melt, which is characterized by the formation of various AlF_x clusters. At large AlF₃, the Na⁺ ions are shown to contribute almost totally to the ionic conductivity.