Spatial-decomposition analysis of electrical conductivity in concentrated electrolyte solution.

A framework for analyzing the electrical conductivity is proposed on the basis of the Green-Kubo formula. The conductivity is decomposed into the contributions from the ionic species in the electrolyte solution to enable the determination of the transport number, and is further expressed as a sum of the autocorrelation term of the Nernst-Einstein form and the cross-correlation term describing the two-body motions of ions. The spatial decomposition is then conducted for the cross-correlation term by formulating an integral expression over the ion-pair distance to bridge the static picture of ion pairing and the dynamic picture of correlated motions. The present framework is applied to 1 m aqueous solution of NaCl using molecular dynamics simulation. The electrical conductivity and the transport number are computed in agreement with the experimental, and the cross-correlation term is seen to cancel the Nernst-Einstein term by 40%. The spatial decomposition of the time correlation functions for ion motions shows that the Na(+)-Cl(-) pair in the first coordination shell moves together and that the like-ion pairs also have positive correlations due to the bridging effect by counter ions. The extent of localization is further analyzed for the cross-correlation effect on the conductivity by introducing a cutoff to the integral expression of spatial decomposition over the ion-pair distance. It is found that the contribution from the cross correlation is localized in the first coordination shell of the Na(+)-Cl(-) pair.