Comparing Experimentally-Measured Sand's Times with Concentrated Solution Theory Predictions in a Polymer Electrolyte

We compare the electrochemically measured Sand's time, the time required for the cell potential to diverge when the applied current density exceeds the limiting current, with theoretical predictions for a 0.47 M poly(ethylene oxide) (5 kg mol(-1))/LiTFSI electrolyte. The theoretical predictions are made using concentrated solution theory which accounts for both concentration polarization and polymer motion, using independently measured parameters that depend on concentration, c: conductivity (kappa), salt diffusion coefficient (D), cationic transference number with respect to the solvent velocity ( t(+)(0) ), thermodynamic factor 1+dlnf(+/- )/ dlnc, and partial molar volume of the salt ( V ); f(+/-) is the mean molar activity coefficient of the salt. We find quantitative agreement between experimental data and theoretical predictions. We derive a generalized analytical expression for Sand's time for electrolytes based on dilute solution theory. This expression correctly predicts the divergence of the Sand's time at the limiting current, in agreement with experimental data and concentrated solution theory predictions. When the applied current is large compared to the limiting current, the analytical expression approaches the standard expression for Sand's time used in the literature.