Hidden Length, Microphase Separation and Deformation of Copolymer Brush Networks

Using molecular dynamics simulations and analytical theory, we study how side chain grafting density governs self-assembly and deformation in networks of brush-like strands with immiscible backbones and side chains. At low grafting densities, backbones and side chains microphase separate into hairy filaments (gyroid-like networks) and randomly oriented lamellae. This is manifested as shift of the main peak position in structure factors to smaller q, indicating assembly of thicker domains with decreasing grafting density. Crosslinks impose topological constraints that hinder redistribution of backbones and side chains, producing nonequilibrium morphologies distinct from those observed in graft-copolymer melts. Aggregates of entangled and confined backbones serve as reservoirs of hidden length enhancing extensibility and modulus of microphase separated networks. At high grafting densities, steric repulsion between side chains suppresses backbone aggregation, yielding network structures and mechanics similar to systems with miscible components. Guided by simulations, we develop models for equilibrium and nonequilibrium microphase separation that quantitatively capture the observed trends in nonlinear network elasticity.