A molecular dynamics study of free energy of micelle formation for sodium dodecyl sulfate in water and its size distribution

Free energy of micelle formation has been evaluated for spherical sodium dodecyl sulfate (SDS) in water by a thermodynamic integration method combined with a series of large-scale molecular dynamics calculations following the chemical species model. In particular, free energy change delta mu(n+1)0 with respect to the addition of one surfactant molecule to the spherical micelle of size n was obtained as a function of n. The free energy profile showed a minimum followed by a maximum, which corresponds to a peak in the size distribution. The calculated peak size n = 57 near its critical micelle concentration is in good agreement with the experimental averaged aggregation number n = 55-75 of the SDS micelle. The distribution showed a rather sharp peak, indicating that the size is almost a monodisperse one. The size is likely to be insensitive to the total concentration of the surfactant.