Emergence of Disordered Hyperuniformity in Melts of Linear Diblock Copolymers*

The self-assembly of block copolymers near the order-disorder transition often suffers from slow dynamics, making it difficult to achieve true equilibrium behaviors in experiments. In particular, a mysterious state of liquid-like packings has been reported to emerge upon rapid cooling from the disordered homogeneous state. In this work, using point patterns that correspond to the local energy minimum of the Quantizer energy where similarly-sized sphere-like polyhedra that tile space are preferred, we initialize large-cell self-consistent field theory simulations and obtain a new type of disordered micelle mesophases with a hidden long-range order known as disordered hyperuniformity, i.e., the infinite-wavelength (normalized) density fluctuations is completely suppressed. We demonstrate that this new type of metastable mesophase is considerably more energetically favorable than previously obtained disordered fluid-like packings, and captures the salient features of disordered packings in the neat, micelle-forming melts of block copolymers observed in experiments. Our findings shed light on the understanding of the mysterious state of liquid-like packings formed by block copolymers, and suggest new possibilities for technological applications, e.g., novel non-iridescent structural colors.