3-Dimensional Topology in Materials Science

Abstract

In this article, we discuss applications of topology to materials science. We explain how topology is used to express the structure and shape of materials. The structure of a multicyclic polymer is described by applying graph theory and the 3-dimensional shape is described by applying knot theory. Polycontinuous patterns of microphase separation of a block copolymer melt can be analyzed by applying the 3-dimensional topology. We also discuss the topological structures of interlocking molecules composed of metal-peptide rings using the concept of polyhedral links.