Soft matter with orientational order: Geometry and phenomenology

Soft condensed matter is an exciting and rich field to work in. Advances in optical microscopy, proliferation of new materials and systems, open new avenues and pose new questions which cannot be answered within existing theoretical approaches. It is quite clear that chemistry and genetics alone cannot explain the variety of shapes and forms present in nature, and that multidisciplinary and multiscale approaches should be adopted. In this talk, I will show how phenomenological models can give insight into the development of complex self-assembled structures with characteristic patterns and geometries. I will argue that topological defects can capture essential features of macroscopic shape and relate it to microscopic order, providing a natural way to connect different length scales and to account for large deformations in soft and biological systems. I will describe liquid crystalline materials with 2-fold (nematic), 3-fold (triatic) and 4-fold (tetratic) orientational order and construct new energetically favourable solutions for 1/3 and 1/4 disclinations, with the latter resulting into the formation of cube as a ground state. The proposed continuum description allows to compare our results with recent experiments on confined fd-viruses. On the larger scale, I will introduce a novel framework of defect guided folding, relevant to discuss the development of biological materials with layered microstructure, in particular cerebral cortex, fingerprints and lung surfactant.