Clusters and Their Contributions to Ionic Conductivity in NaOTf-DME Electrolytes

Electrolytes serve as critical components in batteries and electrolytic cells. This study proposes a framework to assess the contributions of clusters to electric conductivity. Within this framework, clusters are first identified, and their molarities are calculated by integrating excess infrared spectroscopy with density functional theory (DFT). Subsequently, the self-diffusion coefficients of these clusters are estimated through the Stokes-Einstein relation. Finally, the conductivities of charged clusters are evaluated using the Nernst-Einstein equation. By combining these steps, the percentage contribution of charged clusters to overall electric conductivity is quantitatively determined. Taking the binary system of sodium trifluoromethanesulfonate (NaOTf) and 1,2-dimethoxyethane (DME) as a model electrolyte, liquid clusters, namely, Na⁺(DME)₃, Na⁺(DME)₂, OTf^-(DME)₄, Na(OTf)₂^-(DME)₄, (Na)₂OTf⁺(DME)₄, NaOTf(DME)₂, NaOTf(DME)₃, as well as DME monomer, dimer, trimer, and tetramer, were identified in the binary mixtures. Contributions from charged clusters to the overall conductivity at each experimental concentration were derived. It was found that, at low salt concentrations, Na⁺(DME)₃ plays the dominant role, while at high concentrations, the biggest contributor is OTf^-(DME)₄. Together with other techniques including nuclear magnetic resonance and molecular dynamics, DME was found to interact strongly with Na⁺, in a mode of bidentate to make a coordination number of six. On the contrary, the interaction between DME and OTf^- is weak, with negligible hydrogen bonds. The present work addresses the conductivity properties of electrolytes at the cluster level, providing physical insights into the concerned topic. It may also shed light on the design of new electrolytes to meet the needs of vigorously developing battery industries.