Schwinger-Dyson equations for composite electrolytes governed by mixed electrostatic couplings strengths

Abstract

The electrostatic Schwinger-Dyson equations are derived and solved for an electrolyte mixture composed of mono-and multivalent ions confined to a negatively charged nanoslit. The closure of these equations is based on an asymmetric treatment of the ionic species with respect to their electrostatic coupling strength; the weakly coupled monovalent ions are treated within a gaussian approximation while the multivalent counterions of high coupling strength are incorporated with a strong-coupling approach. The resulting self-consistent formalism includes explicitly the interactions of the multivalent counterions with the monovalent salt. In highly charged membranes characterized by a pronounced multivalent counterion adsorption, these interactions take over the salt-membrane charge coupling. As a result, the increment of the negative membrane charge brings further salt anions into the pore and excludes salt cations from the pore into the reservoir. The corresponding like-charge attraction and opposite-charge repulsion effect is amplified by the pore confinement but suppressed by salt addition into the reservoir. The effect is particularly pronounced in high dielectric membranes where the attractive polarization forces lead to a dense multivalent cation layer at the membrane walls. These cation layers act as an effective positive surface charge, resulting in a total monovalent cation exclusion and a strong anion excess even in the case of neutral membrane walls.

Nanofluidic charge transport under strong electrostatic coupling conditions

“…Based on the SD identity, a simplified version of the SCSD approach [35] will be derived. For the derivation of the SD Eq., one expresses first the variation of the partition function (4) by an infinitesimally small potential shift δφ(r) as δZ G = ´DφDψ e −βH[φ+δφ,ψ] − Z G .…”

“…with the bare partition function (27) taking the form k i (r) = e −Vi(r)−qi[Φ(r)−φc(r)]−q 2 i δG(r)/2 . The alternative form (35) of the SCPB Eq. ( 30) is used below for the computation of the beyond-MF ionic current.…”

“…Subsequently, this dressedion theory has been upgraded by us via the inclusion of an additional loop correction for the monovalent salt component [34]. Finally, through the gaussian-level variational treatment of the WC salt, and the inclusion of the SC multivalent ions via a virial expansion, we derived a fully self-consistent formalism of complex electrolytes called the SC-dressed Schwinger-Dyson (SCSD) theory [35].…”

“…Based on a restricted closure of the Schwinger-Dyson (SD) equation, this simplification enables us to account for the ionic hard-core (HC) interactions neglected in Ref. [35]. Within this formalism, we review the electrohydrodynamic mechanism behind the multivalent ion-driven streaming current inversion in anionic silica channels [9,20,21,36].…”

Electric double layer theory for room temperature ionic liquids on charged electrodes: milestones and prospects

“…First, as is well known [58], the mean-field theory describes the behavior of an RTIL and an electrolyte solution in the region of rather weak electrostatic interactions, completely neglecting the electrostatic correlations of the ions [59]. Significant advances have been lately made for the electrolyte solutions with polyvalent ions [51,60]. To the best of our knowledge, nowadays there is no such theory for RTILs.…”