Steady-shear rheology of block copolymer melts and concentrated solutions: Disordering stress in body-centered-cubic systems

We use steady-shear rheology to study the shear-disordering phenomenon in block copolymers in the body-centered-cubic (bcc) mesophase. Polystyrene-polyisoprene and polystyrene-poly-(ethylene-alt-propylene) diblock, triblock, and starblock systems of varying molecular weight and composition were studied in the melt and as concentrated solutions in a selective solvent. The bcc lattice exhibits a low-frequency modulus G_bcc⁰ which scales with the cube of the lattice spacing and additionally depends only on the proximity to the order disorder transition (ODT). Steady shear destroys the bcc lattice at a critical shear stress, which is found to be directly proportional to the lattice modulus: τ_c = 0.038G_bcc⁰ for all block copolymer melts and highly concentrated solutions investigated. The critical stress is thus uniquely determined by the lattice spacing and the proximity to the ODT. The rheological behavior conforms in a remarkably quantitative manner to the shear-melting processes observed in other soft crystalline systems, such as colloidal crystals.