Hidden Length, Microphase Separation, and Deformation of Copolymer Brush Networks

Using a combination of molecular dynamics simulations and analytical calculations, we study the effect of the side chain grafting density on the self-assembly and deformation of networks made of brush-like strands with immiscible backbones and side chains (networks of graft copolymers). At low grafting densities, brush backbones and side chains microphase separate, leading to the formation of hairy filaments arranged into a gyroid-like network and lamellae domains of aggregated backbones covered by a brush of stretched side chains spanning the entire system volume. In these systems, the peak positions of the structure factors shift toward smaller q values as grafting density of side chains decreases, indicating formation of the thicker domains. The emerging aggregates of entangled and confined brush backbones act as reservoirs of hidden length, which are accessed upon large network deformations, thereby improving the network extensibility. The microphase morphologies formed at lower side chain grafting densities differ from those observed in simulations of the corresponding precursor copolymers in the melt. This is due to cross-links which impose topological constraints, preventing the redistribution of immiscible blocks and eliminating the pathways toward equilibrium structure formation. In networks of brush strands with high grafting density, the steric repulsion between side chains precludes backbone aggregation, resulting in structural and mechanical properties such as those of networks with miscible backbones and side chains. Building on the results of the molecular dynamics simulations, we developed models to describe both equilibrium and nonequilibrium microphase separation of brush backbones and side chains, which successfully capture the observed nonlinear network elasticity.