Three-dimensional periodic complex structures in soft matter: investigation using scattering methods

Three-dimensional periodic complex structures are encountered in various soft matter systems such as liquid crystals, block-copolymer phases and the related nano-structured materials. Here, we review several well-defined topologies: two-dimensional hexagonal phase, three-dimensional packing of spheres, tetrahedral close packing (tcp) bi-continuous and tri-continuous cubic phases. We illustrate how small-angle X-ray scattering experiments help us to investigate these different structures and introduce the main available structural models based on both direct and inverse methods.