Bilayer-folded lamellar mesophase induced by random polymer sequence.

Randomness is perceived in two different extremes, in macroscopic homogeneity and local heterogeneity, but apparently far away from order. Here we show that a periodic order spontaneously arises from a binary random copolymer when self-assembly occurs in an ensemble containing > 10 15 possible chain sequences. A Bernoullian distribution of hydrophilic and hydrophobic side chains grafted onto a linear backbone was constructed by random copolymerization. When the polymer chains associate in water, a sequence matching problem occurs because of the drastic heterogeneity in sequence: this is believed to generate local curvature mismatches which deviate from the ensemble-averaged interfacial curvature. Periodic folding of the self-assembled bilayer stabilizes the curvature instability as recurring hinges. Reminiscent of chain-folded lamellae found in polymer crystallization, this new liquid crystalline mesophase, characterized as bilayer-folded lamellae, manifests itself as an anisotropically alignable birefringent hydrogel with structural hierarchy across multiple length scales.