Electrostatic correlations at the Stern layer: physics or chemistry?

We introduce a minimal free energy describing the interaction of charged groups and counterions including both classical electrostatic and specific interactions. The predictions of the model are compared against the standard model for describing ions next to charged interfaces, consisting of Poisson-Boltzmann theory with additional constants describing ion binding, which are specific to the counterion and the interfacial charge ("chemical binding"). It is shown that the "chemical" model can be appropriately described by an underlying "physical" model over several decades in concentration, but the extracted binding constants are not uniquely defined, as they differ depending on the particular observable quantity being studied. It is also shown that electrostatic correlations for divalent (or higher valence) ions enhance the surface charge by increasing deprotonation, an effect not properly accounted within chemical models. The charged phospholipid phosphatidylserine is analyzed as a concrete example with good agreement with experimental results. We conclude with a detailed discussion on the limitations of chemical or physical models for describing the rich phenomenology of charged interfaces in aqueous media and its relevance to different systems with a particular emphasis on phospholipids.