Battery capacity relation to discharge rate - Peukert's law physical reason

The physical reason Peukert's law - why the battery capacity reduces at higher discharge rates (currents).









The electrons (battery capacity or energy) don't go missing, it is just the voltage (U=Q/C) that is dragged down by the higher load.
Figure on the right shows electric potential distribution inside the electrolyte at open circuit.

Figure on the left shows the e-field distribution in the electrolyte when the load resistance is comparable to the internal resistance of the battery.

The main point: internal field will move the ions in the electrolyte in the direction opposite than required for efficient discharge half reactions.

Negative electrode: Me => Me+ + e- (e- moved on external wire)
Positive electrode: Me+ + e- => Me.
Due to voltage internal voltage drop, an electric field formed inside the electrolyte will make the negative charge drift downhill (from left to right), while the negative charge should be moving from right to left (to follow up the eletronc movement direction over the external pathway) for a high rate discharge.

This effect is caused by “polarization” of the electrolyte in the battery, which causes the voltage to be dragged down faster at high load currents compared to low.