Effect of polydispersity on the tensile modulus of diblock copolymers in a lamellar phase

We have calculated the tensile moduli of nanomaterials having lamellar microstructures prepared through the self-assembly of a polydisperse diblock copolymer. We observed that the extensional moduli K33 provided the major contribution to the tensile modulus and that the value of K33 depended mainly on the contribution of K33U (the internal energy contribution to K33). We found that a larger polydispersity index (PDI) weakens the material for our polydisperse model; we attribute this phenomenon to the larger lamellar domain size at equilibrium when the polydispersity of the block increases and to the competition between short and long chains. We found that longer chains in this system strengthen the material, but shorter chains weaken it as a result of the influence of the PDI. The shear modulus contributed negligibly to the extensional moduli.