We investigated the bilayer-folded lamellar (Lf) mesophase appearing in the aqueous solution of amphiphilic random copolymers. A series of copolymers were synthesized by reversible addition–fragmentation chain transfer copolymerization of oligo(ethylene glycol) acrylate with alkyl acrylate with different alkyl chain lengths from octyl (C8) to octadecyl (C18). The alkyl acrylate composition was adjusted between 50–60 mol %. In the concentrated solution with the carbon number of the alkyl side chain higher than 10, the copolymers associated in water via hydrophobic interaction between the alkyl chains to produce micellar bilayers, which were periodically folded into bilayer-folded lamellae. The appearance of a small-angle X-ray scattering (SAXS) peak at a low scattering vector corresponding to >10 nm length scale clearly distinguished the bilayer-folded lamellae from the micellar lamellae with the domain spacing of 5–7 nm. Two-dimensional (2D) SAXS corroborated the presence of bilayer-folded lamellae developing perpendicularly to the micellar lamellae, which is consistent with our previous report. While the Lf phase was observed at room temperature for dodecyl (C12) and tetradecyl (C14) side chains that formed amorphous packing, crystalline hexadecyl (C16) and octadecyl (C18) chains seem to disturb bilayer folding. Heating the solution above the melting temperature of the alkyl chains produced the Lf phase with the largest folding height in the case of C16. The scaling relationship of the folding height to the carbon number supports the idea that the bending rigidity of the bilayer influences the length scale of folding.

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 > 1015 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.