Free and bound states of ions in ionic liquids, conductivity, and underscreening paradox

Free and Bound States of Ions in Ionic Liquids, Conductivity, and Underscreening Paradox Guang Feng,1,* Ming Chen,1 Sheng Bi,1 Zachary A.H. Goodwin,2,3 Eugene B. Postnikov,4 Nikolai Brilliantov,5,6* Michael Urbakh,7,* and Alexei A. Kornyshev3,8* 1State Key Laboratory of Coal Combustion, School of Energy and Power Engineering, Huazhong University of Science and Technology, Room 321, Power Building, 1037 Luoyu Road, Wuhan, Hubei 430074 China 2Department of Physics, Imperial College London, South Kensington Campus, SW7 2AZ London, United Kingdom 3Department of Chemistry, Imperial College London, Molecular Sciences Research Hub, White City Campus, W12 0BZ London, United Kingdom 4Theoretical Physics Department, Kursk State University, Radishcheva Str., 33, Kursk 305000, Russia 5Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom 6Skolkovo Institute of Science and Technology, Moscow 121205, Russia 7School of Chemistry, The Sackler Faculty of Science, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel 8Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, South Kensington Campus, SW7 2AZ London, United Kingdom *Correspondence: gfeng@hust.edu.cn (GF), urbakh@post.tau.ac.il (MU), nb144@leicester.ac.uk (NB) and a.kornyshev@imperial.ac.uk (AAK) ABSTRACT Using molecular dynamics simulations and theoretical analysis of velocity autocorrelation functions, we study ion transport mechanisms in typical room temperature ionic liquids. We show that ions may reside in two states – free and bound with an inter-state exchange; we investigate quantitatively the exchange process and reveal new qualitative features of this process. To this end we propose a dynamic criterion for free and bound ions, based on the ion trajectory density and demonstrate that this criterion is consistent with a static one, based on interionic distances. Analyzing the trajectories of individual cations and anions, we estimate the time that ions spend in bound, ‘clustered’ states, and when they move quasi-freely. From this we evaluate the average portion of ‘free’ ions as, ~15-25%, increasing with temperature in the range of 300-600 K. The ion diffusion coefficients and conductivities as a function of temperature, calculated from the velocity and electrical current autocorrelation functions, reproduce reported experimental data very well. The experimental data for the direct current conductivity (constant ionic current) is in good agreement with theoretical predictions of Nernst-Einstein equation, based on the concentrations and diffusion coefficients of free ions, obtained in our MD simulations. In analogy with electronic semiconductors, we scrutinize an ‘ionic semiconductor’ model for ionic liquids, with valence and conduction ‘bands’ for ions, separated by an energy gap. The obtained band gap for the ionic liquid is small, ~26 meV, allowing for easy interchange between the two dynamic states. Moreover, we discuss the underscreening paradox in the context of amount of free charge carriers, showing that the obtained results do not yet approve its simplistic resolution. Keywords: ionic liquid; ion transfer dynamics; ionic semiconductor; Nernst-Einstein relationshi