Evolution of Curvatures Between Lamellar and Bicontinuous Phases: Formation of Saddle‐Shaped Hierarchical Lamellar Structures in Binary Self‐Assembly System

Why It Matters

The saddle‑SML phase bridges a long‑standing gap in soft‑matter physics by confirming an intermediate curvature state, enabling precise control of nanostructures for advanced materials and offering a model for biological membrane transformations.

Key Takeaways

• First stable saddle-shaped lamellar phase with negative Gaussian curvature
• Formed by PS-b-PAA block copolymer and STAB surfactant
• Electrostatic screening vs volume expansion drives curvature balance
• Demonstrates smooth lamellar‑bicontinuous transition pathway
• Offers insights for membrane design and soft‑matter engineering

Pulse Analysis

In soft‑matter science, interfacial curvature dictates the morphology of block copolymers, surfactants, and lipid assemblies. Lamellar phases, characterized by flat layers, and bicontinuous phases, defined by negative Gaussian curvature, represent two extremes of curvature space. For decades, researchers have debated whether a stable intermediate—where lamellar sheets acquire saddle‑shaped geometry—can exist, because conventional block‑copolymer systems quickly jump from flat to highly curved structures. The lack of experimental evidence has limited theoretical models of the lamellar‑to‑bicontinuous transition, leaving a critical gap in nanostructure design.

The new study resolves this gap by combining a polystyrene‑b‑poly(acrylic acid) (PS‑b‑PAA) block copolymer with the cationic surfactant stearyltrimethylammonium bromide (STAB). STAB micelles insert into the PAA domains, simultaneously screening electrostatic repulsion—shrinking the effective volume—and swelling the polymer matrix through micelle incorporation. This dual action forces the lamellae to adopt saddle‑shaped configurations that possess negative Gaussian curvature while preserving the layered topology. Remarkably, the resulting saddle‑SML phase remains thermostable, confirming that curvature can evolve smoothly rather than through abrupt phase jumps.

The ability to stabilize a curvature intermediate opens new avenues for designing nanostructured materials with tunable pore networks, essential for filtration, energy storage, and drug delivery. Moreover, the saddle‑SML architecture mirrors transitional states observed in biological membranes during processes such as endocytosis, suggesting that synthetic analogues could be engineered to emulate cellular dynamics. Future work will likely explore other polymer‑surfactant pairs, quantify the energetic landscape of curvature modulation, and integrate the saddle‑SML phase into functional devices, advancing both soft‑matter physics and applied materials engineering.