Analytical modeling of micelle growth. 2. Molecular thermodynamics of mixed aggregates and scission energy in wormlike micelles

TL;DR

This paper develops a comprehensive molecular-thermodynamic model for the growth of giant wormlike micelles in mixed surfactant solutions, accurately predicting their size and composition without adjustable parameters.

Contribution

It introduces a generalized analytical model that accounts for multicomponent, polydisperse micelles, extending classical theories to include detailed free energy components and endcap composition effects.

Findings

Model predicts mean mass aggregation number accurately.

Endcaps enriched with smaller packing parameter surfactants.

Additional term in growth parameter accounts for composition differences.

Abstract

Hypotheses: Quantitative molecular-thermodynamic theory of the growth of giant wormlike micelles in mixed nonionic surfactant solutions can be developed on the basis of a generalized model, which includes the classical phase separation and mass action models as special cases. The generalized model describes spherocylindrical micelles, which are simultaneously multicomponent and polydisperse in size. Theory: The model is based on explicit analytical expressions for the four components of the free energy of mixed nonionic micelles: interfacial-tension, headgroup-steric, chain-conformation components and free energy of mixing. The radii of the cylindrical part and the spherical endcaps, as well as the chemical composition of the endcaps, are determined by minimization of the free energy. Findings: In the case of multicomponent micelles, an additional term appears in the expression for the micelle growth parameter (scission free energy), which takes into account the fact that the micelle endcaps and cylindrical part have different compositions. The model accurately predicts the mean mass aggregation number of wormlike micelles in mixed nonionic surfactant solutions without using any adjustable parameters. The endcaps are enriched in the surfactant with smaller packing parameter that is better accommodated in regions of higher mean surface curvature. The model can be further extended to mixed solutions of nonionic, ionic and zwitterionic surfactants used in personal-care and house-hold detergency.