Dynamics of self-assembly and structural transitions in surfactant systems play a key role in various industrial and biological processes. Understanding of self-assembly process in surfactant system is of immense importance to develop new nanostructured materials, drug delivery methods and novel separation techniques. One of the challenges toward fundamental understanding of self-assembly processes is that theoretical and computational investigations are complicated by non-trivial interplay between different length- and timescales.

In this talk, we discuss development of a computational method that can probe the self-assembly dynamics at different length and time scales. We have applied this method to study the dynamics of formation and disintegration of spherical micelles in solution and have predicted the relative stabilities of spherical aggregates along with micelle size distribution and critical micelle concentration for model non-ionic surfactant. The modeling is performed on two levels: molecular and mesoscopic. On the molecular scale, we use the coarse-grained molecular dynamics model. On the mesoscopic scale, we use a stochastic model which is based on the population balance of amphiphilic molecules. This population balance assumes that micelle formation (disintegration) can take place through a mechanism that contains the following two types of the elementary steps: (i) stepwise addition (removal) of single monomers to (from) surfactant aggregate and (ii) coalescence of small clusters of surfactant molecules (respectively, break up of an aggregate into smaller aggregates). These elementary steps are modeled by the Langevin equation. The parameters for this equation (potential of mean force and diffusion coefficient) are obtained from a series of short-scale molecular dynamics simulations with a surfactant molecule (or a center of mass of a cluster of surfactant molecules) constrained within a prescribed distance from the center of mass of a micelle. The obtained Langevin equations are solved to obtain the kinetics of the elementary steps.

The developed model is validated by comparison of several thermodynamic properties, such as micelle size distribution and critical micelle concentration, predicted by this model with predictions of the existing thermodynamic theory. We then apply the developed model to predict the dominant mechanism of self-assembly of the spherical micelles (i.e. the step-wise addition of monomers or coalescence of small surfactant aggregates). The obtained timescales of the self-assembly and disintegration of micelles are compared with experimental findings. In the conclusion of the talk, we discuss possible extension to the developed method to investigate more complex structural transitions in self-assembled systems.