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 ${\overline{N}}_{b}\ensuremath{\approx}800$ shows no evidence of Frank-Kasper phases, in contrast to low molar mass diblock copolymers (${\overline{N}}_{b}l100$) with the same conformational asymmetry. A universal self-concentration crossover parameter ${\overline{N}}_{x}\ensuremath{\approx}400$ is identified, directly related to the crossover to entanglement dynamics in polymer melts. Mean-field behavior is recovered when ${\overline{N}}_{b}g{\overline{N}}_{x}$, while complex low symmetry phase formation is attributed to fluctuations and space-filling constraints, which dominate when ${\overline{N}}_{b}l{\overline{N}}_{x}$.