Extension of the ladder model of self-assembly from cylindrical to disclike surfactant micelles

• The energy for molecule transfer from disclike to cylindrical micelle plays a central role.
• If it is positive, it favors the formation of disclike micelles.
• However, then the peripheral energy is also positive and limits the micelle growth.
• Therefore, disclike micelles are formed in a limited range of surfactant concentrations.
• Their mean aggregation number cannot exceed a certain maximal value.

The ladder model of growth of cylindrical micelles gives expressions for the micellar size distribution and for the mean aggregation number, which are in good agreement with the experiment. Here, we consider this model and its extension to the case of disclike micelles. In analogy with the modeling of elongated micelles as sphero-cylinders, the disclike micelles can be modeled as toro-discs. Upon micelle growth, the hemispherical caps of a cylindrical aggregate remain unchanged, whereas the semitoroidal periphery of a disclike micelle expands. This effect can be taken into account in the expression for the size distribution of the disclike micelles, which predicts the dependence of the micelle mean aggregation number on the surfactant concentration. It turns out that disclike micelles could form in a limited range of surfactant concentrations, and that their mean aggregation number cannot exceed a certain maximal value. Large disclike micelles can exist only near the border with the domain of cylindrical micelles. Then, small variations in the experimental conditions could induce a transformation of the disclike micelles into cylindrical ones.

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