  Hypotheses: To correctly predict the aggregation number and size of wormlike
micelles from ionic surfactants, the molecular-thermodynamic theory has to
calculate the free energy per molecule in the micelle with accuracy better than
0.01 kT, which is a serious challenge. The problem could be solved if the
effects of mutual confinement of micelle counterion atmospheres, as well as the
effects of counterion binding, surface curvature and ionic interactions in the
electric double layer (EDL), are accurately described. Theory: The electric
field is calculated using an appropriate cell model, which takes into account
the aforementioned effects. Expressions for the activity coefficients have been
used, which vary across the EDL and describe the electrostatic, hard sphere,
and specific interactions between the ions. New approach for fast numerical
calculation of the electrostatic free energy is developed. Findings: The
numerical results demonstrate the variation of quantities characterizing the
EDL of cylindrical and spherical micelles with the rise of electrolyte
concentration. The effect of activity coefficients leads to higher values of
the free energy per surfactant molecule in the micelle as compared with the
case of neglected ionic interactions. The results are essential for the correct
prediction of the size of wormlike micelles from ionic surfactants. This study
can be extended to mixed micelles of ionic and nonionic surfactants for
interpretation of the observed synergistic effects.
