Dynamics of self-assembly and structural transitions in amphiphilic systems play an important role in various technological and biological processes. In this talk we present a detailed model for two of the elementary steps involved in the self-assembly processes, namely addition/removal of a single surfactant molecule to/from a spherical micelle. Despite their apparent simplicity, these processes involve a complex interplay between micellar and monomer degrees of freedom. We develop a quantitative model for collective dynamics of these degrees of freedom. To achieve this goal, we perform a series of molecular dynamics simulations and use the simulation results to reconstruct a multi-dimensional free energy landscape of the monomer-micelle system. This landscape is parametrized by (1) the distance between the centers of mass of the micelle and the monomer, (2) the monomer orientation, (3) micellar shape, and (4) microstructure of the micellar surface.
The monomer addition/removal to/from a micelle can then be modeled as a stochastic process on the multi-dimensional energy landscape. We observe that timescales of the micellar shape and microstructure are often comparable with timescales of the monomer translational and rotational motions. This implies that the motion on the free energy landscape is truly multi-dimensional and cannot be reduced to motion along a one-dimensional path on this surface. In order to elucidate the collective dynamics of the multiple degrees of freedom, we apply the path integration formalism to solve the Langevin equation describing the motion on the multi-dimensional energy landscape.
It is anticipated that the approach discussed in this talk can be extended to investigation of other, more complex, self-assembly processes.