Surface tension model for surfactant solutions at the critical micelle concentration

TL;DR

This paper presents a new analytical model for the limiting surface tension of surfactant solutions at the critical micelle concentration, incorporating atomistic parameters and validated against experimental data.

Contribution

It introduces a novel analytical equation and atomistic modeling approach to predict surface tension at the cmc for surfactants.

Findings

Model agrees with experimental data within ~30% accuracy

Parameters derived from atomistic modeling characterize micelle interactions

Guides surfactant design for low surface tension

Abstract

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.