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 bar (b) approximate to 800 shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers ((N) over bar (b) < 100) with the same conformational asymmetry. A universal self-concentration crossover parameter <(N)over bar>(x) approximate to 400 is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when (N) over bar (b) > (N) over bar (x), while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when (N) over bar (b) < <(N)over bar>(x).