An examination of the one-parameter adsorption equation without using the Gibbs adsorption equation

The study of surfactant adsorption kinetics at a gas-liquid interface has essentially been built with the Gibbs adsorption equation. A simple one-parameter adsorption equation without using the Gibbs adsorption equation was proposed and tested on surfactants C₁₄TAB and C₁₆TAB [Phan et al., Colloids Surfaces A 406 (2012) 24 and Langmuir 29 (2013) 4743] to describe equilibrium surface tension. The applicability of this one-parameter adsorption equation was examined in this study. Theoretical equilibrium surface tension (ST) of nonionic and ionic surfactants generated from the Langmuir and Frumkin isotherms and several sets of experimental ST data were compared with the one-parameter adsorption equation. This study demonstrates that this one-model adsorption equation predicts the equilibrium ST of the aqueous surfactant solutions well following: (i) the nonionic Langmuir isotherm with Γ_∞ ∼ 20 × 10⁻¹⁰ mol/cm² or (ii) the nonionic Frumkin isotherm with a specific correlation between maximum surface concentration and intermolecular interaction, K = 0.12 (Γ_∞ × 10¹⁰) − 2.6. It is concluded from this study that the one-parameter adsorption equation is not a general predictive model and cannot describe general equilibrium ST data except under the above conditions.