Polymer science

Engineering

Liquid crystal

Biomedical engineering

Lyotropic

Lyotropic liquid crystal

Biomimetics

Nanotechnology

Materials science

Geometry

Surface (topology)

Soft materials

Biological materials

Liquid crystalline

Minimal surface

Mathematics

Optoelectronics

Advanced Materials

Triply periodic minimal surface structures and related geometries are widely identified in many natural systems, such as biological membranes and biophotonic structures in butterfly-wing scales. Inspired by their marvelous and highly symmetrical structures and optimized physical properties, these structures have sparked immense interest for creating novel materials by extracting the design from nature. Significant progress has been made to understand these biological structures and fabricate artificial materials by top-down and bottom-up approaches for numerous applications in chemistry and materials science. Herein, research achievements, including theoretical and experimental discoveries, in both biological systems and the artificial synthesis of materials with triply periodic minimal surface structures and related materials are summarized. Recent developments in self-assembled lyotropic liquid crystal phases, block copolymer systems, and their inorganic replicas are discussed in detail.

An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self-Assembled Systems