Correlation Between Free Volume and Ionic Conductivity of Non-Aqueous Lithium Battery Electrolyte Solutions over a Wide Concentration Range

Abstract

There is little known about the transport behavior of ions in electrolyte solutions at very high concentration and there is currently no satisfactory theory/equation to describe it [1,2]. In this work electrolyte solutions of lithium salts of various anions: [(CF3SO2)2N]°¥, (TFSI), [PF6]°¥ and [BF4]°¥ dissolved in polar solvents and solvent mixtures up to saturation have been prepared. The solvents are propylene carbonate (PC), acetonitrile (ACN), adiponitrile (ADN) and ethylene carbonate:dimethyl carbonate (1:1 v/v) (EC:DMC). The Ionic conductivity and density of the electrolyte solutions have been measured over a wide concentration range (up to 5.4 M). The specific ionic conductivity (κ) vs. C plots show a non-ideal behavior with very strong dependence on concentration (a typical Gaussian-like function) while the molar conductivity (Λ) vs. C plots show an exponential decrease similar to the behavior of weak electrolyte solutions. The conductivity vs. concentration data were fitted to various equations of known models (Debye-Hückel-Onsager’s square-rate law: Λ vs. C^1/2, Cubic-root law: Λ vs. C^3, Casteel-Amis equation: κ/κmax vs. C/Cmax , or the corresponding state-law equation based on the pseudo-lattice theory: κ/κmax vs. C/Cmax .The models show good fit only in the low concentration, with the last two models fail to show universal behavior beyond the concentration of maximum conductivity, Cmax. However, we have derived a new, semi-empirical equation that shows a very good fit over the whole concentration range and can correlate molar ionic conductivity to changes in free volume within the liquid solution: Λ = A' exp [-B C], B =-γ Vo/Vf, and Vf = V-Vo Where Vƒ is the free volume which can be calculated from the difference between the measured volume, V, of the liquid (from density measurements) and the Van der Waal “molecular “volume, Vo, which can be obtained from XRD data at low temperatures or calculated using chemical models. C is concentration, A’ is a pre-exponential factor that can be related to limiting molar conductivity and square root of temerature. γ is a correction factor for overlapping holes with a value between 0.5 and 1. These preliminary results are encouraging in bringing us closer to a free volume-based approach to explain the behavior of ionic conductivity of electrolyte solutions at very high concentrations. However, more work is underway to study more solutions with different chemical and physical properties, including aqueous solutions, to test the validity of this approach. [1] S. I. Smedley, The Interpretation of Ionic Conductivity in Liquids, Springer, 1980 [2] C.A. Angell, J. Phys. Chem., 70, 1966, 3988