Modifying Kohlrausch's Law to Describe Nonaqueous Electrolytes for Lithium-Ion Batteries

To develop next-generation lithium-ion batteries with enhanced stability and safety, it is crucial to understand the physicochemical principles of nonaqueous electrolytes. Kohlrausch's law describes a linear decrease in the molar conductivity (Λ) with respect to the square root of the molarity of strong electrolytes at lower concentrations. This empirical law explains the impeded ionic mobility at higher concentrations due to ionic interactions, i.e., relaxation and asymmetric effects. However, this law does not hold at higher concentrations due to the ionic association that alleviates the ionic interactions and retards the decrease in the Λ. Especially, the anomalously stagnant decrease in the Λ near the solubility limit has not been clearly explained, calling for the consideration of other concentration-dependent factors such as the mean activity coefficient (γ_±), viscosity (η), and dielectric constant (ε). Herein, we develop a systematic method to modify Kohlrausch's law. First, we install the ionic association constant, and the theoretical estimation is compared with the experimental results to induce the correction function that is related with the previously neglected concentration-dependent factors. Thus, the induced correction function was close to the rectified linear unit (ReLU) function, which has been widely used in the field of artificial intelligence. The modified Kohlrausch's law with the ReLU-type correction function provides a highly precise and reliable data fitting, and the fitted parameters showed clear concentration dependency and straightforward interpretability. As a result, this method effectively generalized Kohlrausch's law for nonaqueous electrolytes at higher concentrations up to the solubility limit of 3.0-3.5 M. Moreover, the modified Kohlrausch's law inspired us to discover the physical origins of the anomalously stagnant Λ profiles near the solubility limit; and the most relevant physical origin of the anomaly was the concentration dependency of the γ_± and η, which grow exponentially above a critical concentration.