Electrostatic-elastic coupling in colloidal crystals

¹ Wenzhou Institute, University of Chinese Academy of Sciences - Wenzhou, Zhejiang 325001, China
² Institute of Theoretical Physics, Chinese Academy of Sciences - Beijing 100190, China
³ School of Physical Sciences, University of Chinese Academy of Sciences - Beijing 100049, China
⁴ Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences - Beijing 100049, China
⁵ Institute of Physics, Chinese Academy of Sciences - Beijing 100190, China

Received: 9 July 2024
Accepted: 6 November 2024

Abstract

Electrostatic-elastic coupling in colloidal crystals, composed of a mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloids, is studied on the continuum level in order to analyze the lattice-mediated interactions between mobile charges. The linearized, Debye-Hückel–like mean-field equations incorporating a minimal coupling between electrostatic and displacement fields imply an additional effective attractive interaction between mobile charges. For small screening lengths, the interactions between like mobile charges exhibit colloid-lattice–mediated effective interaction, ranging from weak to strong attraction, while for large screening lengths the lattice-mediated interaction is purely repulsive. Continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges, augmented by the minimal electrostatic-elastic coupling terms, can serve as a baseline for more detailed microscopic models.