Interaction regimes for oppositely charged plates with multivalent counterions

Abstract

Within a mean-field treatment of the interaction between two oppositely charged plates in a salt-free solution, the distance at which a transition from an attractive to a repulsive regime appears can be computed analytically. The mean-field description, however, breaks down under strong Coulombic couplings, which can be achieved at room temperature with multivalent counterions and highly charged surfaces. Making use of the contact theorem and simple physical arguments, we propose explicit expressions for the equation of state in several situations at short distances. The possibility of Bjerrum pair formation is addressed and is shown to have profound consequences on the interactions. To complete the picture, we consider the large-distance limit, from which schematic phase diagram discriminating attractive from repulsive regions can be proposed.

Counter-Ions Between or at Asymmetrically Charged Walls: 2D Free-Fermion Point

“…(49). The same scenario was discussed in [21], and occurs in the mean-field treatment [14]. The dependence of βP/σ 2 on σd for η = −1/2 is represented in Fig.…”

Charge neutrality breakdown in confined aqueous electrolytes: Theory and simulation

“…Care, however, is required when extrapolating this simple picture to the case of strongly correlated electrolytes -such as aqueous electrolytes made of multivalent ions, organic electrolytes, or ionic liquids. In these cases, the structure of the EDL is dominated by ionic correlations 13 , giving rise to complex phenomena such as charge reversal in multivalent ionic electrolytes and layering in ionic liquids 14 . Even in situations of low electrostatic couplings, the packing effects in strongly confined electrolytes can alone be responsible for oscillatory profiles which cannot be captured at a mean-field level of GCS theory 15 .…”

Short-Range Disorder and Electrostatic Interactions in Macromolecules

“…5 Roughly speacking, the effective charge density σ e f f scales as ∼ e − √ Ξ and goes rapidly to zero as the coupling parameter goes to infinity [33,25]. 6 The physics becomes very similar to the DLVO theory [37] where ionic contributions are accounted for by the PB theory and separated from the medium-related van der Waals interactions.…”

“…The WSC approach starts from the fact that we know what is the exact ground state of a system of charges next to a plate (a Wigner crystal with a triangular lattice) and therefore we can expand thermodynamic quantities around this ground state [10,23,24,12,13,21,25,22,26,27]. If we focus on the one-particle densityρ 1 , it is in fact exactly related to the fugacity λ and the excess chemical potential µ ex via the relation [15]:…”

“…Let us say here that for small enough distances L, a ⊥ is defined as 2πa 2 ⊥ |σ| = q while for infinite distances we have πa 2 ⊥ |σ| = q. density 5 . The counterion density far away from them is then described by a PB regime [34,33,25].…”