Transmission line model of mixed ionic and electronic conductor: the case of hydrous ruthenium oxide

Composite membranes made of RuO₂·xH₂O dispersed in an insulating polymer matrix were prepared and used as separators in a conductivity cell filled with H₂SO₄ electrolyte solution. The volume fraction of RuO₂·xH₂O was varied between 7 and 18 % and x between 0 and 2.4. The total capacitance of the composite membranes was determined either from galvanostatic charging using a four-electrode configuration or potential cycling using a three-electrode configuration. In the first case, protons are the only charge carriers at the boundaries of the composite membranes. In the four-electrode configuration, a transmission line that accounts for the pseudocapacitive nature of RuO₂·xH₂O was used to describe successfully the voltage–time profiles of composite membranes with active material contents above 10?V _f%. The total capacitance determined with both setups increases for 0?≤?x?≤?0.6, and the values are identical in this interval of x. However, the trends diverge afterwards, and the capacitance values measured in the four-electrode configuration are higher by a factor of 2 for x?=?2.4. Unlike in the three-electrode configuration, charge storage in the four-electrode configuration is not limited to the sites accessible to both electrons and protons.