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.

假设：为了从离子表面活性剂正确预测蠕虫状胶束的聚集数量和大小，分子热力学理论必须计算出胶束中每个分子的自由能，其准确度要高于0.01 kT，这是一个严峻的挑战。如果能准确地描述胶束抗衡离子气氛相互限制的影响，以及双电层（EDL）中抗衡离子结合，表面曲率和离子相互作用的影响，则可以解决该问题。

理论：电场是使用适当的细胞模型计算的，其中考虑了上述影响。已经使用了活度系数的表达式，该表达式在整个EDL中有所不同，并描述了静电，硬球以及离子之间的特定相互作用。开发了一种用于静电自由能快速数值计算的新方法。

发现：数值结果表明，随着电解质浓度的升高，表征圆柱和球形胶束的EDL的数量变化。与被忽略的离子相互作用的情况相比，活度系数的影响导致胶束中每个表面活性剂分子的自由能值更高。这些结果对于从离子表面活性剂正确预测蠕虫状胶束的大小至关重要。这项研究可以扩展到离子和非离子表面活性剂的混合胶束，以解释观察到的协同作用。