Hybrid particle-field simulations of polymer-grafted nanoparticles in block copolymer melts

Modelling of the co-assembly of block copolymers and polymer-grafted nanoparticles within Self-Consistent Field Theory (SCFT) is challenging due to several aspects: the complex geometry of interparticle space, singularities in the pressure field on grafting surfaces, and the difficulty of finding the system's minimum energy. In this talk we present a hybrid particle-field approach for simulating grafted particles of arbitrary shapes in which the particles' boundaries are treated sharply without invoking any simplifying diffuse-interface approximations. We, first, show that the standard system of SCFT equations for grafted polymer chains is formally inconsistent and derive an equivalent one that does not lead to singularities in the pressure field. Second, we analytically derive the full derivatives of the system's energy with respect to positions and orientations of particles. Finally, the necessary PDEs are accurately and efficiently solved using a combination of an implicit geometry description, adaptive mesh refinement, and a specialized finite volume approach for imposing boundary conditions in complex geometries. To demonstrate the capabilities of the proposed approach we present simulations of the co-assembly of grafted Janus nanorods and diblock copolymers.