Self-Organized Systems: Spherical Micelles
Self-organized systems constitute a rich field of investigations
playing an important role not only in physics and chemistry, but
also in social sciences. Individual properties of monomers and
their interactions define structure and form of the composed object:
micelle, vesicle or bilayer.
Among different structures the simplest one is a spherical micelle.
Applying the methods of classical nucleation theory, one can study
- equilibrium distribution of aggregates
- thermodynamical properties of micelles
- kinetics of micellization
- relaxation processes
We studied the kinetics of micellization, in particular,
re-distribution of aggregates forced by certain external
action [3,4]. Solving numerically the Becker-Doring kinetic equation,
we found three stages of the transitional process:
- re-arrangement of small aggregates
- re-distribution in the micellar well
- re-distribution of monomers through the activation barrier
The first and second processes are called the fast relaxation while
the third process is the slow relaxation .
We calculated relaxation times whose values were predicted
theoretically. It confirms the analytical treatment of the problem.
In 2000-2001, we developped the method of parametric equations [2]. Using the notion of aggregation work, we construct a system of differential equations for the aggregation number of micelles which is a function of the parameters of micellization. We found explicit solutions for two important models of spherical micelles: the drop model and Grinin's model . Based on these solutions, we obtain an analytical expression for the equilibrium concentration of surfactant monomers and consequently for the whole spectrum of equilibrium concentrations of molecular aggregates in this framework.