Ion-pair correlation function in electric double layer theory. Part 2.—Relevance to the discreteness-of-charge effect

Abstract

The expression derived in Part 1 for the ion-pair correlation function in the electric double layer is applied to two ions adsorbed on a plane (the i.h.p.) in the Stern inner region. For ions i and j, charges e_i and e_j at separation ρ on the i.h.p., the correlation function is g^(ij)(ρ)=g^(ij)(ρ, ξ= 0) exp [–1//_kT∫¹₀ dξ{e_jϕ⁽ⁱ⁾(ρ, ξ)+e_iϕ^(j)(ρ, ξ)}], where ϕ⁽ⁱ⁾(ρ, ξ) is the potential due to ion i at distance ρ on the i.h.p. in the absence of ion j and ϕ^(j)(ρ, ξ) is defined similarly. Both ions are being charged to the same degree ξ. The potential ϕ⁽ⁱ⁾(ρ, ξ) may be written as ϕ⁽ⁱ⁾(ρ, ξ)=ξe_iϕ₀(ρ)+ϕ⁽ⁱ⁾_a(ρ)+ϕ⁽ⁱ⁾_d(ρ, ξ), where ϕ₀(ρ) is the potential due to a unit point charge, ϕ⁽ⁱ⁾_a(ρ) arises from the removal of the mean surface charge density from the exclusion disc on the i.h.p. around i and ϕ⁽ⁱ⁾_d(ρ, ξ) is due to the fluctuation in surface charge density on the i.h.p. beyond the exclusion disc. ϕ^(j)(ρ, ξ) can be expressed similarly. In the case of two oppositely charged ion species on the i.h.p., the contribution ϕ⁽ⁱ⁾_a(0, 1) to the discreteness-of-charge potential at ion i is determined by adapting to two-dimensions the ion-pairing theory of Bjerrum and Fuoss, as extended by Poirier and DeLap. The results are applied to a study of ionized monolayers.