Simulation of Free Surface of Block Copolymers

Due to their self-assembling properties, block copolymers are used in a variety of engineering applications, from patterning of microchips to targeted drug delivery. The study of these materials has been significantly accelerated by the powerful self-consistent field theory (SCFT), which has been particularly effective at studying polymer self-assembly in bulk or in confinements with a-priori known geometry. However, in many situations the surface of polymer material is free to deform (e.g, polymer/air interface) and its shape must be determined simultaneously while solving the SCFT equations. In this talk, we present a computational framework for simulating free surfaces block copolymers based on an analytical shape sensitivity analysis. Specifically, we consider an incompressible polymer melt described by the SCFT equations and derive an analogue of the Young-Laplace equation for block copolymers. Selective interactions of surrounding materials with distinct polymer chain blocks are taken into account by a new approach for imposing boundary conditions, consistent with the incompressibility property. To demonstrate the capabilities of this methodology, we present examples of suspended and substrate-supported diblock copolymer droplets.