Knowing the crossover rate of acid and base through membrane and the energy required for pH recovery, the energy efficiency was calculated when using different pH pairs. We used 3 Ω cm 2 as cell resistance, experimentally determined net crossover flux, and the theoretical energy cost (0.83 V) for BPM 1M acid-base recovery to calculate the round-trip energy efficiency. Mass transport, kinetic and other efficiency losses are not included in this calculation. Efficiency loss from resistance penalty is linear with current density. The non-linear portion of the curves in Figure (at relatively low current density) are explained by acid-base crossover energy penalty. For example, pH 0 introduces severe proton crossover, with a large penalty to the energy efficiency (only 50 % efficiency at 10 mA cm -2 , Fig. ). At lower current density, more time will be spent on each cycle, increasing the amount of crossover (or, crossover current is a larger fraction of charge/discharge current) over the course of a given cycle. As an example of "crossover current (Icrossover)", 200 nmol cm -2 s -1 is equivalent to about 19. Voltage-capacity curve with recovery (Fig. )