Free Energy Profile for Chain Expulsion from a Diblock Copolymer Micelle

The process of single chain exchange is the dominant mechanism for micelle equilibration near equilibrium, and understanding it is important for applications such as drug delivery and oil-based lubrication technology. Previous methods of extracting an activation barrier to chain exchange in block copolymer micelles involve fitting a calculated intensity relaxation function to time-resolved small angle neutron scattering measurements; however, this method does not provide information about the shape of the barrier. We utilize umbrella sampling to probe the full free energy profile of expulsion of a single chain from a diblock copolymer micelle in solvent. Our simulations are carried out using dissipative particle dynamics, and the weighted histogram analysis method (WHAM) is utilized to extract the free energy profile as a chain is held at various distances from the micelle center-of-mass via a biasing potential. The free energy profile is characterized as a function of interaction energy between the core block and solvent. Further, the dependence of the free energy barrier on aggregation number is explored. Contrary to past approaches, this study allows for determination of the full free energy landscape of chain expulsion.