Strong-coupling theory of counterions with hard cores between symmetrically charged walls
arXiv:2011.09720 · doi:10.1103/PhysRevE.102.042604
Abstract
By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis have focused on point-like counterions, we treat them as charged hard spheres. We thus work out the fate of like-charge attraction when steric effects are at work. The analytical approach partitions counterions in two sub-populations, one for each plate, and integrates out one sub-population to derive an effective Hamiltonian for the remaining one. The effective Hamiltonian features plaquette four-particle interactions, and it is worked out by computing a Gibbs-Bogoliubov inequality for the free energy. At the root of the treatment is the fact that under strong electrostatic coupling, the system of charges forms an ordered arrangement, that can be affected by steric interactions. Fluctuations around the reference positions are accounted for. To dominant order at high coupling, it is found that steric effects do not significantly affect the interplate effective pressure, apart at small distances where hard sphere overlap are unavoidable, and thus rule out configurations.
arXiv comment18 pages, 15 figures
References in corpus (27)
- Electrostatic correlations: from Plasma to Biology
- Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation
- The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration
- Effective interactions between electric double-layers
- Screening of a macroion by multivalent ions: Correlation induced inversion of charge
- Beyond Poisson-Boltzmann: Fluctuations and Correlations
- Wigner crystal model of counterion induced bundle formation of rod-like polyelectrolytes
- Strong-Coupling Theory for Counter-Ion Distributions
- Stability, dynamical properties and melting of a classical bi-layer Wigner Crystal
- Computing Counterion Densities at Intermediate Coupling
- Screening of a macroion by multivalent ions: A new boundary condition for Poisson-Boltzmann equation and charge inversion
- Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions
- Reentrant transitions in colloidal or dusty plasma bilayers
- Strong Coupling Electrostatics in the Presence of Dielectric Inhomogeneities
- Melting of the classical bilayer Wigner crystal: influence of the lattice symmetry
- Weak and Strong Coupling Theories for Polarizable Colloids and Nano-Particles
- Attraction Between Like-Charged Walls: Short-Ranged Simulations Using Local Molecular Field Theory
- Electrostatic image effects for counter-ions between charged planar walls
- Wigner-Crystal Formulation of Strong-Coupling Theory for Counter-ions Near Planar Charged Interfaces
- Enhanced stability of the square lattice of a classical bilayer Wigner crystal
- Critical phenomena and phase sequence in classical bilayer Wigner crystal at zero temperature
- Attractive Interaction between Fully Charged Lipid Bilayers in a Strongly-Confined Geometry
- Ground state of classical bilayer Wigner crystals
- Ground state structure and interactions between dimeric 2D Wigner crystals
- A correlation-hole approach to the electric double layer with counter-ions only
- Interaction regimes for oppositely charged plates with multivalent counterions
- Phase diagram and critical properties of Yukawa bilayers