Microphase separation in block copolymer systems forms well-defined, periodic structure on the sub-micron length scale. This structure arises from the system striving to satisfy the delicate balance of minimizing the area of contact between incompatible chain segments and maximizing the conformational entropy of the macromolecules. Candidate geometries satisfying these constraints possess intermaterial dividing surfaces (IMDS) of constant mean curvature. These include triply periodic, bicontinuous structures related to minimal surfaces. These structures, recently observed in microphase-separated block copolymer systems, also arise in phase-separated surfactant-water systems, indicating the two phenomena may be driven by similar physical mechanisms. A complete description of block copolymer phase morphology requires characterization of the long-range ordered single grain microdomain structure, the defect structures within grains, and the microstructure of the boundary region between grains. The type of structure observed is sensitive to the architecture, chemical composition, and molecular mass of the copolymers. Thermodynamic treatments using a geometrical description of the IMDS provide a means for probing the physics of phase morphology in block copolymers.
Anatomy of triply-periodic network assemblies: characterizing skeletal and inter-domain surface geometry of block copolymer gyroids
