Here, we present a detailed theoretical model describing the growth of disclike surfactant micelles. The model is tested against light-scattering data for micellar solutions from mixed conventional surfactants and from fluorinated surfactants. Theoretical expressions are derived for the concentration dependencies of the number and mass average aggregation numbers. Central role in the theory is played by the difference between the chemical potentials of a surfactant molecule in cylindrical and discoidal micelles. This difference, scaled with the thermal energy kT, is denoted p. For p<0, the formation of cylindrical (rather than disclike) micelles is energetically favored. For p>0 disclike micelles are formed, but their growth is limited due to the rise of their positive peripheral energy. Because of that, disclike micelles can be observed in a relatively narrow interval, 0<p<0.1, and in a limited concentration range. Three sets of light-scattering data for different surfactants were processed. It is remarkable that in all cases the best fit gives small positive values of p, in agreement with the theoretical predictions. The model predicts that a strong increase in the viscosity of a surfactant solution should happen upon the transformation of disclike micelles into cylindrical ones at small variations in p. The model can be used for analyzing the shape and size of micelles in various surfactant solutions. The fact that typical disclike micelles form only in the special case 0<p<0.1 shows why such micelles represent a relatively rare form of stable surfactant self-assembly.
Keywords: Bicelles; Cylindrical micelles; Disclike micelles; Hydrodynamic radius; Nanodiscs; Radius of gyration; Self-assembly.
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