Microscopic and mesoscopic simulation of entropic micelles

We present simulations of a purely athermal model for surfactant solutions. Using semi-grand-ensemble simulations, we determine the (excess) free energy of micelles as a function of the cluster size. From this information,we compute the critical micelle concentration. Subsequently, we use the information of the dilute micellar system as input for a coarse-grained polydisperse hard-sphere simulation. The aim of this simulation is to study the effect of inter-micellar interactions on the size distribution. We find that, to a first approximation, the effect of these interactions can be accounted for by a mean-field theory — the size distribution of interacting micelles is equal to that of non-interacting micelles at a lower chemical potential. The techniques used in this paper can be used to simplify the numerical study of realistic models of surfactant solutions.