Strongly-coupled-counterions mediated interaction regimes for two oppositely charged plates

Complete text of publication follows. A system of two oppositely charged plates constitutes a model of choice to get physical insights about ion mediated interactions between two bodies in electrolyte solutions. This is of interest for various fields ranging from colloidal science to cellular and sub-cellular biology. In absence of salt reservoir the mean field treatment of the ions - when relevant - provides a very simple physical picture of what is happening in the system. In particular, a long range attraction is expected while a short range repulsion arises when the condensed counterions layers completely overlaps. This mean field understanding however breaks down in principle if one has to deal with multivalent counterions or highly charged surfaces. In this work, we propose simple physical ideas applicable for two plates with strongly coupled condensed counterions to capture the physics at play for different short distances regimes. We then rely on the exact contact value theorem to determine analytically the equation of state for each regime. To complete the picture we consider the large distance limit, from which one can retrieve a mean field picture for the interaction. A schematic phase diagram displaying a reentrant behaviour finally summarizes plausible interaction paths when the plate to plate distance is decreased from infinity.