Molecular dynamics (MD) simulations are used to measure dynamical properties of a simple bead-spring model of A-B diblock copolymer molecules, and to characterize rates and mechanisms of several dynamical processes. Dynamical properties are analyzed within the context of a kinetic population model that allows for both stepwise insertion and expulsion of individual free molecules and occasional fission and fusion of micelles. Kinetic coefficients for stepwise processes and micelle fission have been extracted from MD simulations of individual micelles. Insertion of a free surfactant molecule into a preexisting micelle is shown to be a completely diffusion-controlled process for the model studied here. Estimates are given for rates of rare events that create and destroy entire micelles by competing mechanisms involving stepwise association and dissociation or fission and fusion. Both mechanisms are shown to be relevant over the range of parameters studied here, with association and dissociation dominating in systems with more soluble surfactants and fission and fusion dominating in systems with less soluble surfactants.
Bibliographical noteFunding Information:
This work was supported primarily by NSF Grant No. DMR-1310436, with partial support from the NMP and MP programs of the University of Minnesota Industrial Partnership for Interfacial and Materials Engineering (IPRIME) center. We acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing computational resources for the work reported here. We are also grateful to G. Geyer of the University of Minnesota School of Statistics for his help with statistical analysis of the fission lifetimes. Professor Geyer suggested the use of a maximum likelihood estimator and provided us with the analysis outlined in Appendix D .