Probing transference and field-induced polymer velocity in block copolymer electrolytes

Concentration polarization in an electrolyte comprising dissociated ions and a solvent is often modeled using concentrated solution theory developed by Newman. This theory is built upon two differential equations for electrolyte concentration and solvent velocity fields. We characterize the concentration and solvent velocity fields in a polystyrene-block-polyethylene oxide (SEO) block copolymer electrolyte using operando X-ray transmission measurements and X-ray photon correlation spectroscopy, respectively. Using calculations based on the assumption that the SEO chain behaves as a single species, we show that the experimental data are consistent with a cation transference number, $t_{+}^0$, $\approx$ 0.7. Previously published electrochemical experiments using small polarizations led to the conclusion that $t_{+}^0$ is less than 0.3. The discrepancy indicates that the block copolymer electrolyte cannot be approximated as a three-component system (cation, anion, and a single solvent), and frictional interactions involving the glassy polystyrene cannot be lumped with those involving rubbery poly(ethylene oxide) segments.