Role of Chain Length in the Formation of Frank-Kasper Phases in Diblock Copolymers

The phase behavior of poly(styrene)-b-poly(1,4-butadiene) diblock copolymers with a polymer block invariant degree of polymerization N[over ¯]b≈800 shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers (N[over ¯]b<100) with the same conformational asymmetry. A universal self-concentration crossover parameter N[over ¯]ₓ≈400 is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when N[over ¯]b>N[over ¯]ₓ, while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when N[over ¯]b