Ion and site correlations of charge regulating surfaces: a simple and accurate theory

Charge regulation is a fundamental mechanism in most chemical, geochemical, and biochemical systems. Various minerals surfaces and proteins are well-known to change their charge state as a function of the activity of the hydronium ions, i.e., the pH. Besides being modulated by the pH, the charge state is sensitive to salt concentration and composition due to screening and ion correlations. Given the importance of electrostatic interactions, a reliable and straightforward theory of charge regulation would be of utmost importance. This paper presents such a theory that accounts for salt screening, site and ion correlations. Our approach shows an impeccable agreement compared to Monte Carlo simulations and experiments of 1:1 and 2:1 salts. We furthermore disentangle the relative importance of site-site, ion-ion and ion-site correlations. Contrary to previous claims, we find that ion-site correlations are subdominant to the two other correlation terms.