Abstract
The solution of the Poisson-Nernst-Planck (PNP) equation does not exist in the region of extremely high applied voltages in which a bulk electric field remains, even for a steady-state. Thus, we propose an expanded ion-conserving Poisson-Boltzmann theory at the high voltages and show that it predicts steady PNP solutions precisely at the high applied voltages. Furthermore, the bulk electric fields and appropriate zeta potential are provided through this theory. We believe that our solution opens a new way to improve the various theories on the diffused charge dynamics and their applications at high applied voltages.
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