Shear Modulus of an Irreversible Diblock Copolymer Network from Self-Consistent Field Theory

Using self-consistent field theory, we investigate the. stretching-induced microphase separation in an irreversibly cross-linked polymer network composed of diblock copolymer chains and estimate its . shear modulus. The topology of the network is fixed to a planar square lattice. The monomer density, the distribution of cross-links, and the free energy of the system are calculated. We find that the system develops circular domains at equilibrium, which may merge to lamellae upon compression or stretching. The lamellae are oriented perpendicular to the stretching direction. Crosslinks are localized, but their distribution may be anisotropic. For asymmetric strands, the distributions of different type of cross-links differ from each other, indicating that the cross-link fluctuations are inhomogeneous. The stress is evaluated from the derivative of the free energy of stretched systems with respect to the deformation in the stretching direction. Using the elasticity theory of isotropic solids allows us to estimate the shear modulus. We find that the shear modulus increases if the network fluctuations are inhomogeneous. Our findings may provide guidance for the design of stiffer soft matter materials.