Surface electrostatic force in presence of dimer counter-ion

Abstract

Combining classical density functional theory with modified interfacial statistical associating fluid theory, we investigate the surface electrostatic force (SEF) between two negatively and similarly charged planar surfaces immersed in electrolyte solution consisting of monomer anion and dimer cation. The dimer cation is comprised of two hard spheres (HSs) tangentially bonded together and freely rotating on the top of each other; one of the two HS sites is positively charged and the other is neutral. New findings about novel properties of the SEF caused by the dimer counter-ion are summarized below. (i) In the presence of only univalent counter-ion, the SEF always becomes more and more repulsive with increasing of the dimer counter-ion neutral site size, whether the bulk electrolyte solution is dense or not, and the surface charge strength is small, moderate, or large; repulsion strength of the SEF always reduces with the bulk concentration, and at equal surface distance rapidly increases with the surface charge strength. (ii) In the presence of bivalent counter-ion of monomer or dimer, rather complex SEF behavior emerges. Specifically, (a) at low surface charge strength, the dimer counter-ion with small neutral site size induces one obvious like-charge attraction (LCA) at lower bulk concentrations; whereas at higher bulk concentrations, a repulsive SEF emerges instead, whose strength monotonously decreases with the neutral site size. (b) For high surface charge strengths, the SEF curves exhibit oscillatory structure with the LCA feature; moreover, the dimer counter-ion always induces larger LCA position and strength than the monomer counter-ion does; the LCA strength decreases with the counter-ion neutral site size, and the LCA position always reduces with increase of the surface charge strength. (c) Dependence of the LCA strength on the bulk concentration is conditional on the surface charge strengths considered; to speak specifically, for very high surface charge strength, the LCA strength reduces with the bulk concentration, whereas for not so high value, the opposite is true. The above observations can be analyzed from fluctuation and balance of the three factors: osmotic pressure difference between inside and outside the plates; hard sphere repulsion in congested space, and “hydrogen bond” formation.