Continuum Description of the Role of Negative Transference Numbers on Ion Motion in Polymer Electrolytes

All-solid-state rechargeable batteries are considered to be the key solution for the development of next-generation electrical energy storage. Solid polymer electrolytes (SPEs) have gained attention due to their electrochemical stability, non-flammability and processability.[1, 2] It is widely recognized that the ionic conductivity of polymer electrolytes is significantly lower than that of conventional liquid electrolytes. Recent studies have shown that salt diffusivity as well as cation transference number in polymer electrolytes is also lower than conventional electrolytes. [3-7] In fact, the cation transference number is negative in a narrow but important salt concentration window and it coincides with the peak in conductivity with respect to salt concentration. At a fundamental level, knowledge of these transport parameters can be used to characterize ion motion in SPEs. This knowledge is essential for predicting battery performance and may serve as a foundation for designing polymers with better performance. Recently, the experimental and theoretical approaches have been performed to better understand the transport of each ionic species. New experimental techniques such as electrophoretic NMR (eNMR) are emerging as powerful methods for directly measuring ion velocities in electrolytes under applied electric fields. [8-10] The standard approach to interpret these experiments is built on the assumption that electrolyte is dilute and thermodynamically ideal.[11] Timachova et al.[11] derived modified expressions for interpreting the eNMR data using concentrated solution theory. These expressions only apply at very early times after polarization when concentration gradients and diffusive fluxes can be neglected. However, they shed no light on the time- and space-dependence of the velocities of the cations and anions. The aim of this study is to provide a deeper understanding of the transient behavior of cations and anions in polymer electrolytes. We examine the role of diffusion and migration in a poly(ethylene oxide)-based (PEO) and lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) electrolytes using concentrated solution theory. This formulation was used to investigate how these negative transference numbers influence the magnitudes and directions of ion velocities when a fixed current is imposed on the electrolyte during the passage of current. Under the constraint of electroneutrality, this study reveals the interplay between diffusion and migration by thorough examination of the local velocity, salt concentration gradient, and flux of ions within the solution. Examining the differences in ion motion when the transference number is negative and comparing it to cases when it is positive, allows us to demonstrate the dynamic nature of the system during galvanostatic conditions. The study also reveals conditions where experimental methods need to focus in order to detect unexpected species migration under negative transference conditions. [1] M. Armand, Solid State Ionics, 9-10 (1983) 745-754. [2] A.K. Shukla, T.P. Kumar, Curr Sci India, 94 (2008) 314-331. [3] R. Bouchet, S. Maria, R. Meziane, A. Aboulaich, L. Lienafa, J.P. Bonnet, T.N.T. Phan, D. Bertin, D. Gigmes, D. Devaux, R. Denoyel, M. Armand, Nat Mater, 12 (2013) 452-457. [4] C.Y. Tang, K. Hackenberg, Q. Fu, P.M. Ajayan, H. Ardebili, Nano Lett, 12 (2012) 1152-1156. [5] J.W. Park, K. Yoshida, N. Tachikawa, K. Dokko, M. Watanabe, J Power Sources, 196 (2011) 2264-2268. [6] Y.P. Ma, M. Doyle, T.F. Fuller, M.M. Doeff, L.C. Dejonghe, J. Newman, J Electrochem Soc, 142 (1995) 1859-1868. [7] D.M. Pesko, Z.G. Feng, S. Sawhney, J. Newman, V. Srinivasan, N.P. Balsara, J Electrochem Soc, 165 (2018) A3186-A3194. [8] Z.Y. Zhang, L.A. Madsen, J Chem Phys, 140 (2014). [9] M. Gouverneur, F. Schmidt, M. Schonhoff, Phys Chem Chem Phys, 20 (2018) 7470-7478. [10] M.P. Rosenwinkel, M. Schonhoff, J Electrochem Soc, 166 (2019) A1977-A1983. [11] K. Timachova, J. Newman, N.P. Balsara, J Electrochem Soc, 166 (2019) A264-A267.