Unveiling the Microscopic Origin of Ion Transference Numbers in Molten Salt Systems: A Kinetic Theory Approach to an Accurate "Golden Rule".

In recent years, there has been a renewed interest in accurately quantifying the ion's transference number within molten salts. Surprisingly, despite efforts to address the severe lack of experimental data, there is still no reliable theoretical framework that establishes a clear link between the transference number and simulated phase trajectories through atomistic simulations or a dependable theoretical relationship for precise estimation. In general, overcoming limitations in both experimental and fundamental aspects, transference numbers are typically estimated by either considering the Nernst-Einstein (NE) approximation or employing the so-called "golden rules". However, it is worth noting that neither the Nernst-Einstein approximation nor the "golden rules" provide a truly accurate prediction. This work concentrates on establishing a robust theoretical framework to accurately define transference number boundaries and averages within molten salt systems. This is achieved by integrating principles from kinetic theory with an in-depth exploration of the electronic structure and local ordering of molten salts. Unlike prevailing theoretical approaches that are heavily reliant on Einstein's concept of ion mobility, which correlate with self-diffusion, the proposed theoretical framework is fundamentally grounded in the inherent mobility of ions. In summary, the introduction of this original "golden rule" showcases robust predictive capabilities, effectively addressing the scarcity of diverse observations gleaned from various experimental sources in the literature. Finally, the proposed formalism is extended to complex molten salts through a microscopic consideration of the impact of the cation associated with the anion upon its diffusional cross-section. Based on this, the cationic transference number of all divalent metal halide molten salts is predicted to be very close to that reported in the literature.