Ground state structure of a bilayer Wigner crystal with repulsive dielectric images

Abstract

We study the ground-state structures of identical classical point charges with Coulomb interactions, confined between two symmetric parallel charged walls. For the well understood homogeneous dielectric case with no electrostatic images, the charges evenly condense on the opposite walls, thereby forming a bilayer Wigner crystal; five structures compete upon changing the inter-wall separation. Here, we consider a dielectric jump between the walls and a solvent in which charges are immersed, implying repulsive images. Using recently developed series representations of lattice sums for Coulomb law, we derive the complete phase diagram. In contrast to the homogeneous dielectric case, the particles remain in a hexagonal Wigner monolayer up to a certain distance between the walls. Beyond this distance, a bifurcation occurs to a sequence of Wigner bilayers, each layer having a nonzero spacing from the nearest wall. Another new phenomenon is that the ground-state energy as a function of the wall separation exhibits a global minimum.

References in corpus (5)

• Reentrant transitions in colloidal or dusty plasma bilayers
• Critical phenomena and phase sequence in classical bilayer Wigner crystal at zero temperature
• Ground state of classical bilayer Wigner crystals
• Ground state structure and interactions between dimeric 2D Wigner crystals
• Long-range correlations of the surface charge density between electrical media with flat and spherical interfaces

Cited by in corpus (3)

• Electrolytes between dielectric charged surfaces: Simulations and theory
• Electric Fields Near Undulating Dielectric Membranes
• Counter-ion density profile around a charged disk: from the weak to the strong association regime