Dressed counterions: Strong electrostatic coupling in the presence of salt

Abstract

We reformulate the theory of strong electrostatic coupling in order to describe an asymmetric electrolyte solution of monovalent salt ions and polyvalent counterions using field-theoretical techniques and Monte Carlo simulations. The theory is based on an asymmetric treatment of the different components of the electrolyte solution. The weak coupling Debye-Hückel approach is used in order to describe the monovalent salt ions while a strong coupling approach is used to tackle the polyvalent counterions. This combined weak-strong coupling approach effectively leads to dressed interactions between polyvalent counterions and thus directly affects the correlation attraction mediated by polyvalent counterions between like-charged objects. The general theory is specifically applied to a system composed of two uniformly charged plane-parallel surfaces in the presence of salt and polyvalent counterions. In the strong coupling limit for polyvalent counterions, the comparison with Monte Carlo simulations shows good agreement for large enough values of the electrostatic coupling parameter. We delineate two limiting laws that in fact encompass all the Monte Carlo data.

Dressed counterions: Polyvalent and monovalent ions at charged dielectric interfaces

“…It is also amended compared to the definition in our previous work in Ref. [13], where the regime of relatively high monovalent salt concentration was of main interest. Note however that the above PB equation cannot properly treat polyvalent ions due to high correlation effects.…”

“…In what follows we will apply the "dressed counterion" approach to our model system, which was introduced recently [13] in a different context and was not thoroughly examined by explicit simulations. This approach is based on the fact that for highly asymmetric solutions with q ≫ 1, the monovalent ions can be integrated out from the partition function and their effect is replaced by an effective ("dressed") DH interaction that acts between the remaining polyions and the surface charges.…”

“…The idea stems from a realization that monovalent ions, because of their small valency, are only weakly coupled to all other charges, i.e., polyvalent counterions as well as surface charges. As a result, they can be integrated out, a procedure that can be justified systematically in a full field-theoretical framework [13].…”

“…Such screened interactions are then used to perform implicit MC simulations that treat all charges explicitly except the monovalent ions, and show an extremely good agreement with explicit MC, confirming the validity of the approach based on dressed counterions in highly asymmetric systems q ≫ 1. Finally, we implement the dressed counterions strong coupling theory [13], which allows us to obtain an analytical description of ionic distributions and overcharging in the limit of strong coupling with the local surface field. The validity of the SC dressed counterion theory is thus examined by making a comparison with both explicit and implicit simulations.…”

“…In the second, dressed counterion approach, we integrate out the monovalent ion degrees of freedom by replacing the Coulomb interaction between remaining charges with an effective screened Debye-Hückel (DH) interaction (as first described in Ref. [13] for a dielectrically homogeneous system with uniform screening). Such screened interactions are then used to perform implicit MC simulations that treat all charges explicitly except the monovalent ions, and show an extremely good agreement with explicit MC, confirming the validity of the approach based on dressed counterions in highly asymmetric systems q ≫ 1.…”