  The formation of self assembled structures such as micelles has been
intensively studied and is well understood. The ability of a solution of
amphiphilic molecules to develop micelles is depending on the concentration and
characterized by the critical micelle concentration (cmc), above which micelle
formation does occur. Recent studies use a lattice approach in order to
determine cmc and show that the correct modelling and analysis of cluster
formations is highly non-trivial. We developed a minimalistic coarse grained
model for amphiphilic molecules in the continuum and simulated the time
evolution via dynamic Monte Carlo simulations in the canonical (NVT) ensemble.
Starting from a homogeneous system we observed and characterized how the
initial fluctuations, yielding small aggregates of amphiphilic molecules, end
up in the growth of complete micelles. Our model is sufficiently versatile to
account for different structures of surfactant systems such as membranes,
micelles of variable radius and tubes at high particle densities by adjusting
particle density and potential properties. Particle densities and micellization
rates are investigated and an order parameter is introduced, so that the
dependence of the micellization process on temperature and surfactant density
can be studied. The constant density of free particles for concentrations above
cmc, e. g. as expected from theoretical considerations, can be reproduced when
choosing a careful definition of free volumes. In the cmc regime at low
temperatures different non-equilibrium effects are reported, occurring even for
very long time-scales.
