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

New experimental techniques such as electrophoretic NMR (eNMR) are emerging as powerful methods for directly measuring ion velocities in electrolytes under applied electric fields. The aim of this theoretical study is to predict the spatial- and temporal-dependence of these velocities of ions as a function of the magnitude of the applied field and salt concentration. It has recently been shown that mixtures of poly(ethylene oxide)-based (PEO) and lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) electrolytes exhibit negative cation transference numbers in a certain salt concentration range. In this range, the cation motion at early times is directed to the positive electrode at all locations in the cell; ion migration dominates in this regime. As time progresses, the cation velocity in finite zones near both the electrodes changes sign. These zones grow rapidly with time, reflecting the increasing importance of diffusion, and a point in time is reached beyond which the cation velocity in the entire cell is directed toward the negative electrode. Our work reveals the limited time window over which the results of eNMR can be used to determine the transference number. More importantly, it shows how to account for the effect of diffusional flux in such experiments.