Gradient-Based Explicit Theoretical Framework for Simulation of Block Copolymer-Nanoparticle Co-assembly

The co-assembly of dispersed nanoparticles in block copolymers is a promising avenue for creating ordered structures at the nanoscale and materials with unique properties. Consequently, the theoretical understanding of this phenomenon is of great interest. In this talk, we present a novel theoretical framework for the simulation of the block copolymer-nanoparticle co-assembly. In this approach, we explicitly keep track of each particle in a sharp fashion while describing the polymer material using the Self-Consistent Field Theory. We consider particles of arbitrary shapes and allow the particle's surface affinity for different polymer components to be variable in space. The relaxation of block copolymer-nanoparticle mixtures to (meta) stable configurations is performed using a gradient-type approach based on the analytically derived expression for the virtual work of nanoparticles or, in other words, the full derivative of the system's energy with respect to the particles's orientations and positions. We provide several benchmark examples to demonstrate the capabilities of the proposed framework.