Progress on Frank-Kasper phases in soft matter

Man's exploration of the microstructure of matter has never stopped,and understanding how particles stack up in space is still remaining a great challenge for scientists and technicians. The soft matter often shows abundant self-assembly morphologies and phase topological structures due to the drive of weak intermolecular interactions and the competition of entropic enthalpies. Among them,Frank-Kasper phases are the most fascinating,which have complex topologically dense stacking structures. As a transition state between crystal and quasicrystal,the Frank-Kasper phase has a kind of complex spherical phase structure with a dense icosahedral shell and a high coordination number (CN=14,15,16). The soft matter offers novel molecular and self-assembled structures for study of Frank-Kasper phase. This paper presents a brief review of the research process on soft matters such as small molecule surfactants,block copolymers, dendritic macromolecules and giant amphiphilic molecules that can form Frank-Kasper phases. These soft matters can be used as a material for studying the spatial accumulation of non-homogeneous and deformable soft spheres. The Frank-Kasper phase plays a crucial role in the mechanism of soft matter self-assembling into complex topological close-packing structures,which should contribute to understanding the growth mechanism of quasicrystals.