Bicontinuous periodic patterns of block copolymers - Structural analysis based on curvature distributions

Bicontinuous microdomain structures appearing in diblock copolymers with copolymer composition of ca. 34∼ 38% are studied from the viewpoint of interface curvatures. Since interface minimization is a major driving force of the structure formation in such systems, infinite periodic minimal surfaces (IPMS) with a variety of symmetries (or space groups) are often used as models. However, characterization of a bicontinuous structure often involves a controversial decision about which type of IPMS to employ. This decision is difficult because only two-dimensional images of the structures can be usually obtained by conventional transmission electron microscopy (TEM) and many IPMS reproduce a similar image in projection. However, recent developement of three-dimensional imaging of nm scale structures by TEM enabled us to measure the local interface curvatures. In the present study, we demonstrate that the local curvature distribution is a sensitive measure to distinguish the type of IPMS and hence the space group of the bicontinuous structures.