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-Huckel-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. Copyright (c) 2024 EPLA All rights, including for text and data mining, AI training, and similar technologies, are reserved.
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