Abstract

Multicarrier systems, such as car batteries and semiconductors, have surprisingly complex transport properties. Even for steady-state transport, one can find counterexamples to standard assumptions about local electroneutrality, constancy in space of the electric field, linearity in space of the voltage, and the relationship between dissipation, voltage, and current. Moreover, unless recombination processes occur, boundaries impose conditions that can disturb the response far into the bulk to remove memory of the boundaries. Because the demands of the chemical reactions at the electrodes cannot be satisfied by diffusion alone, car batteries are electrically active even when they are neither charging nor discharging. We offer practical advice on battery care for bike-riders, say, who only occasionally use their cars. For semiconductors, recombination does occur, which in transport enables partial currents to adjust from their surface to their bulk values. For mixed ionic electronic conductors, bulk recombination may be essential to an understanding of “blocking electrodes.” The voltage associated with both current-producing and non-current-producing surface reactions provides a natural explanation for the bioelectric fields observed during root and other growth processes