  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.
