Nonlinear voltage profiles and violation of local electroneutrality in ordinary surface reactions

It is normally assumed that ordinary surface reactions, which involve no charge transfer between the surface and electrolyte, have no effect on voltage. The present work shows, on the contrary, that nontrivial voltage profiles can be produced by ordinary surface reactions. Poisson's equation then implies a nonzero bulk charge density, so that local electroneutrality is violated. The specific system considered is a planar lead-acid cell, but the results apply more generally, so long as the electrolyte charge-carrier diffusivities are not all the same. For slow steady reactions the carrier fluxes vary linearly across the cell, which produce linearly varying electric field and density gradients. As a consequence the voltage profile varies quadratically, and the volume charge density is nonzero and uniform. This result has broad implications (e.g., to steady-state oxygen loading of high T(c) materials) and may provide a contributing mechanism for the origin of the electric fields observed during biological growth.