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  • Open Access

Charging Dynamics of Overlapping Double Layers in a Cylindrical Nanopore

Ankur Gupta1,†, Pawel J. Zuk1,2,‡, and Howard A. Stone1,*

  • 1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 2Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106 Warsaw, Poland

  • *hastone@princeton.edu
  • †ankur@princeton.edu
  • ‡pjzuk@ippt.pan.pl
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Phys. Rev. Lett. 125, 076001 – Published 11 August, 2020

DOI: https://doi.org/10.1103/PhysRevLett.125.076001

Abstract

The charging of electrical double layers inside a cylindrical pore has applications to supercapacitors, batteries, desalination and biosensors. The charging dynamics in the limit of thin double layers, i.e., when the double layer thickness is much smaller than the pore radius, is commonly described using an effective RC transmission line circuit. Here, we perform direct numerical simulations (DNS) of the Poisson-Nernst-Planck equations to study the double layer charging for the scenario of overlapping double layers, i.e., when the double layer thickness is comparable to the pore radius. We develop an analytical model that accurately predicts the results of DNS. Also, we construct a modified effective circuit for the overlapping double layer limit, and find that the modified circuit is identical to the RC transmission line but with different values and physical interpretation of the capacitive and resistive elements. In particular, the effective surface potential is reduced, the capacitor represents a volumetric current source, and the charging timescale is weakly dependent on the ratio of the pore radius and the double layer thickness.

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Outline

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Phys. Rev. Lett. 125, 076001– Published 11 August, 2020
  • Received 26 March 2020
  • Revised 3 May 2020
  • Accepted 10 July 2020
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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