Title of the talk: "Theoretical study of micellization kinetics with spherical
and cylindrical micelles based on the Becker-D.ring difference equations"

Speaker: Ilya A. Babintsev

Scientific supervisor: Prof. L. Ts. Adzhemyan

Micelles are relatively stable molecular aggregates in a solution of surfactant
matter in a polar or nonpolar solvent consisting of 50-10000 molecules. They are
observed at surfactant concentrations above the critical micelle concentration
(cmc). Micelles may have different shape: sphere, cylinder and disc. Further we
will talk about the direct micelles which consist of surfactant molecules formed
by dissolving the surfactant in the polar solvents. With the passage of time,
an aggregative equilibrium is achieved in micellar systems. Aggregative equilibrium
is described by the equilibrium distribution function of aggregates in aggregation
number (the number of molecules in the aggregate). This function has the form of
the Boltzmann exponential function with the exponent determined by the work of
aggregation (the minimal work of aggregate formation). This work includes, in
addition to contributions associated with the formation surface and volume of
the aggregate, the contributions associated with the hydrophobic effect and the
electrostatic interaction of the head groups of surfactant molecules. As at
condensation of liquid droplets of supersaturated vapor, there is a critical size
of the aggregate in the micellization process. The aggregate with the aggregation
number less than the critical one is unstable and shrinks, and the aggregate with
the aggregation number larger than  the critical one continues to grow. However,
this growth, unlike condensation, does not lead to irreversible phase change since
it is limited due to electrostatic repulsion of the polar heads of the surfactant
molecules on the surface of the micelles.

Kinetics of micellization and transition to aggregative equilibrium is described
by the kinetic balance equations. The set of equations with stepwise mechanism
of resizing aggregate by attachment and emission of individual surfactant molecules
is the set of the Becker-D.ring difference equations. In the analytic theory
considering the number of aggregation as a continuous variable, this set of equations
is approximated by partial differential equation. The analytical approach has several
limitations and has not been checked yet, and this explains why numerical integration
of the equations of Becker-D.ring has been carried out in this study. The complexity
of such task is associated as well as with a large number of equations and with the
need to describe processes on a very different time scales, to take into account the
existence of aggregates of different shapes and sizes.

The study revealed the range of applicability of the linear and nonlinear analytical
theory for polydisperse systems with spherical micelles, cylindrical micelles,
coexisting spherical and cylindrical micelles. New features of micellization and
relaxation in various micellar systems have been found.