The Davies equation of state of ionic surfactant adsorbed monolayer and related problems

Abstract

The Davies equation and relative expressions belong to the most popular tools for describing the equilibrium state of ionic surfactants on the water–air or water–hydrocarbon interface. During over half a century, this equation was repeatedly discussed and modified and various attempts of its derivation/reconsideration were proposed for both insoluble and soluble monolayers. In this paper, the corresponding publications are regarded. Basing on the previously derived modification of the fundamental Gibbs equation [Surface Eng. 50 (2014) 173–182; https://doi.org/10.3103/S1068375514020100.], another expression for the monolayer of the adsorbed ionic surfactant (2D layer) is proposed, which implies dividing the total effect into the electrostatic and non-electrostatic contributions. The dependence of the surface pressure, П, on the area per adsorbed amphiphilic ion in the interface, A, excluded area, A0, and the electrical potential Ψ of the compact monolayer against the bulk aqueous phase is obtained taking into account the degree of counter ion binding, β, and cohesion. In the following equation, the second term of the right-hand side is caused by the electrostatic energy of transfer of the charged amphiphile from the bulk to the monolayer, whereas the third one represents the electrostatic contribution to the surface pressure:Π + Πc= − kT∫∞A(1 + β)(A − A0)−2dA + ∫0Ψ(1 + β) z2eA−1dΨ + ∫0Ψ(1 − β)z2eA−1dΨ, where k, T, and e have their usual meaning. In particular, in its limited form, for β=0 and neglecting the cohesion term, Πc, the equation of state is as follows:Π=kT(A−A0)−1+2∫0ΨeA−1dΨ.This relation differs from the common Davis equation by the coefficient "2" in the last rhs term. Some limiting cases are considered, and an attempt to adapt the equation to experimental data is made.