Adsorption and structure of the adsorbed layer of ionic surfactants

Our goal in this study was to investigate theoretically and experimentally the adsorption of ionic surfactants and the role of different factors in the mechanism of adsorption, the adsorption parameters and the structure of the adsorbed layer. We used available literature data for the interfacial tension, σ, vs. concentration, Cs, for sodium dodecyl sulfate (SDS) in three representative systems with Air/Water (A/W), Oil/Water (O/W) and Oil/Water + 0.1 M NaCl (O/WE) interfaces. We derived 6 new adsorption isotherms and 6 new equations of state (EOS) based on the adsorption isotherms for non-ionic surfactants of Langmuir, Volmer and Helfand–Frisch–Lebowitz (HFL) with interaction term βθ2 / 2 in the EOS, θ = αΓ being the degree of coverage, with Γ — adsorption and α — minimum area per molecule. We applied Gouy equation for high surface potentials and modified it to account for partial penetration of the counterions in the adsorbed layer. The equations were written in terms of the effective concentration C = [Cs(Cs + Cel)]1 / 2, where Cs and Cel are, respectively concentrations of the surfactant and the electrolyte. We showed that the adsorption constant K was model independent and derived an equation for the effective thickness of the adsorbed layer, δs. We found also that the minimum area per molecule, α, is larger than the true area, α0, which depends on the adsorption model and is a function of the adsorption Γ. The interaction term βθ2 / 2 in the Langmuir EOS was found to be exact for small β ≪ 1, but for the Volmer EOS it turned out to be only a crude approximation. Semi-quantitative considerations about the interaction between adsorbed discrete charges revealed that at A/W interface part of the adsorbed surfactant molecules are partially immersed in water, which leads to decreased repulsion and increased adsorption Γ. At O/W the larger adsorption energy keeps the surfactant molecules on the surface, so that the electrostatic repulsion is stronger, which translates into negative β's, larger α's and smaller adsorption. The addition of electrolyte partly screens the repulsion at O/W, leading to decreased α and increased adsorption. We determined K, α and β by a three-parameter fit. The constant K was found to be model independent and smaller for A/W than for O/W, because of the smaller adsorption energy. The values of α were larger for O/W than for A/W and decreased for O/W upon addition of electrolyte in agreement with the theory. For the Volmer model α was smaller than for Langmuir's model and both were found to increase with decreasing Γ — again in agreement with the theoretical predictions. It turned out that θ never exceeds 0.5 i.e. the adsorbed layer is never saturated. We tried to determine which adsorption model gave better results by calculating theoretically the Gibbs elasticity, but it turned out that when the results were plotted vs. an experimental variable, say C, all curves collapsed in a single one, which coincided with the respective experimental curve. This means that it is impossible to determine the adsorption model by using only interfacial tension data.