Low-frequency dielectric response of a periodic array of charged spheres in an electrolyte solution: The simple cubic lattice

Chang-Yu Hou, Jiang Qian, and Denise E. Freed
Phys. Rev. E 99, 032604 – Published 11 March 2019

Abstract

We study the low-frequency dielectric response of highly charged spheres arranged in a cubic lattice and immersed in an electrolyte solution. We focus on the influence of the out-of-phase current in the regime where the ionic charge is neutral. We consider the case where the charged spheres have no surface conductance and no frequency-dependent surface capacitance. Hence, the frequency dispersion of the dielectric constant is dominated by the effect of neutral currents outside the electric double layer. In the thin double-layer limit, we use Fixman's boundary condition at the outer surface of the double layer to capture the interaction between the electric field and the flow of the ions. For periodic conditions, we combine the methods developed by Lord Rayleigh for understanding the electric conduction across rectangularly arranged obstacles and by Korringa, Kohn, and Rostoker for the electronic band structure computation. When the charged spheres occupy a very small volume fraction, smaller than 1%, our solution becomes consistent with the Maxwell Garnett mixing formula together with the single-particle polarization response, as expected, because interparticle interactions become less prominent in the dilute limit. By contrast, the interparticle interaction greatly alters the dielectric response even when charged spheres occupy only 2% of the volume. We found that the characteristic frequency shifts to a higher value compared to that derived from the single-particle polarization response. At the same time, the low-frequency dielectric enhancement, a signature of charged spheres immersed in an electrolyte, becomes less prominent for the periodic array of charged spheres. Our results imply that the signature of the dielectric response of a system consisting of densely packed charged spheres immersed in an electrolyte can differ drastically from a dilute suspension.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 30 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.032604

©2019 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsPolymers & Soft Matter

Authors & Affiliations

Chang-Yu Hou1,*, Jiang Qian2,†, and Denise E. Freed1,‡

  • 1Schlumberger-Doll Research, 1 Hampshire Street, Cambridge, Massachusetts 02139, USA
  • 24097 Silsby Road, University Heights, Ohio 44118, USA

  • *CHou2@slb.com
  • jiang.qian@post.harvard.edu
  • freed1@slb.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 99, Iss. 3 — March 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×