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A Perturbation Solution to the Full Poisson-Nernst-Planck Equations Yields an Asymmetric Rectified Electric Field

Abstract

We derive a perturbation solution to the one-dimensional Poisson-Nernst-Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences. Treating the applied potential as the perturbation parameter, we show that the second-order solution yields a nonzero time-average electric field at large distances from the electrodes, corroborating the recent discovery of Asymmetric Rectified Electric Fields (AREFs) via numerical solution to the full nonlinear PNP equations [Hashemi Amrei et al. Phys. Rev. Lett. 2018, 121, 185504]. Importantly, the first-order solution is analytic, while the second-order AREF is semi-analytic and obtained by numerically solving a single linear ordinary differential equation, obviating the need for full numerical solutions to the PNP equations. We demonstrate that at sufficiently high frequencies and electrode spacings the semi-analytical AREF accurately captures both the complicated shape and the magnitude of the AREF, even at large applied potentials

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Supplementary files

Article information


Submitted
09 Mar 2020
Accepted
04 May 2020
First published
11 May 2020

Soft Matter, 2020, Accepted Manuscript
Article type
Paper

A Perturbation Solution to the Full Poisson-Nernst-Planck Equations Yields an Asymmetric Rectified Electric Field

S. M. H. Hashemi Amrei, G. R. Miller, K. J.M. Bishop and W. Ristenpart, Soft Matter, 2020, Accepted Manuscript , DOI: 10.1039/D0SM00417K

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