Surface tension model for surfactant solutions at the critical micelle concentration

• Published in: Journal of colloid and interface science 2013-03, Vol.393, p.151-160
• Main Authors: Burlatsky, Sergei F., Atrazhev, Vadim V., Dmitriev, Dmitry V., Sultanov, Vadim I., Timokhina, Elena N., Ugolkova, Elena A., Tulyani, Sonia, Vincitore, Antonio
• Format: Article
• Language: English
• Subjects: Accuracy; Approximation; Constraining; equations; Mathematical analysis; Mathematical models; Micelles; Models, Molecular; Molecular modeling; Solutions; surface area; Surface Tension; Surface-Active Agents - chemistry; Surfactant effectiveness; Surfactants; Thermodynamic model
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/j.jcis.2012.10.020

[Display omitted] ► We developed a thermodynamic model for minimal surface tension of surfactant solutions. ► We obtained an approximate analytical equation for minimal surface tension. ► We proposed a simplified atomistic approach for calculating equation parameters. ► We obtained an agreement with experimental data with accuracy ∼30%. A model for the limiting surface tension of surfactant solutions (surface tension at and above the critical micelle concentration, cmc) was developed. This model takes advantage of the equilibrium between the surfactant molecules on the liquid/vacuum surface and in micelles in the bulk at the cmc. An approximate analytical equation for the surface tension at the cmc was obtained. The derived equation contains two parameters, which characterize the intermolecular interactions in the micelles, and the third parameter, which is the surface area per surfactant molecule at the interface. These parameters were calculated using a new atomistic modeling approach. The performed calculations of the limiting surface tension for four simple surfactants show good agreement with experimental data (∼30% accuracy). The developed model provides the guidance for design of surfactants with low surface tension values.