Counter-ions between or at asymmetrically charged walls: 2D free-fermion point

Abstract

This work contributes to the problem of determining effective interaction between asymmetrically (likely or oppositely) charged objects whose total charge is neutralized by mobile pointlike counter-ions of the same charge, the whole system being in thermal equilibrium. The problem is formulated in two spatial dimensions with logarithmic Coulomb interactions. The charged objects correspond to two parallel lines at distance d, with fixed line charge densities. Two versions of the model are considered: the standard "unconstrained" one with particles moving freely between the lines and the "constrained" one with particles confined to the lines. We solve exactly both systems at the free-fermion coupling and compare the results for the pressure (i.e. the force between the lines per unit length of one of the lines) with the mean-field Poisson-Boltzmann solution. For the unconstrained model, the large-d asymptotic behaviour of the free-fermion pressure differs from that predicted by the mean-field theory. For the constrained model, the asymptotic pressure coincides with the attractive van der Waals-Casimir fluctuational force. For both models, there are fundamental differences between the cases of likely-charged and oppositely-charged lines, the latter case corresponding at large distances d to a capacitor.

References in corpus (13)

• New Developments in the Casimir Effect
• Screening of a macroion by multivalent ions: Correlation induced inversion of charge
• Beyond Poisson-Boltzmann: Fluctuations and Correlations
• Novel Electrostatic Attraction from Plasmon Fluctuations
• Weak and Strong-Coupling Electrostatic Interactions between Asymmetrically Charged Planar Surfaces
• Test-charge theory for the electric double layer
• Electrostatic Attraction of Coupled Wigner Crystals: Finite Temperature Effects
• Critical phenomena and phase sequence in classical bilayer Wigner crystal at zero temperature
• Screening of classical Casimir forces by electrolytes in semi-infinite geometries
• Counter-ion density profile around charged cylinders: the strong-coupling needle limit
• Microscopic origin of universality in Casimir forces
• Interaction regimes for oppositely charged plates with multivalent counterions
• Translation Symmetry Breaking in the One-Component Plasma on the Cylinder

Cited by in corpus (7)

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• Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry
• Counter-Ions Near a Charged Wall: Exact Results for Disc and Planar Geometries
• Finite-Size Effects in Non-Neutral Two-Dimensional Coulomb Fluids
• Electric double layers with modulated surface charge density: Exact 2D results
• Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids
• Contact value theorem for electric double layers with modulated surface charge density