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Titratable Macroions in Multivalent Electrolyte Solutions: Strong Coupling Dressed Ion Approach

We present a theoretical description of the effect of polyvalent ions on the interaction between titratable macro-ions. The model system consists of two point-like macro-ions with dissociable sites, immersed in an asymmetric ionic mixture of monovalent and polyvalent salts. We formulate a {\em dressed ion strong coupling theory}, based on the decomposition of the asymmetric ionic mixture into a weakly electrostatically coupled monovalent salt, and into polyvalent ions that are strongly electrostatically coupled to the titratable macro-ions. The charge of the macroions is not considered as fixed, but is allowed to respond to local bathing solution parameters (electrostatic potential, $pH$ of the solution, salt concentration) through a simple {\em charge regulation} model. The approach presented, yielding an effective polyvalent-ion mediated interaction between charge-regulated macro-ions at various solution conditions, describes the strong coupling equivalent of the Kirkwood-Schumaker interaction.