Abstract
The process of liquid-liquid crystalline phase separation (LLCPS) in filamentous colloids is at the very core of multiple biological, physical and technological processes of broad significance. However, the complete theoretical understanding of the process is still missing. LLCPS involves the nucleation, growth and up-concentration of anisotropic droplets from a continuous isotropic phase, until a state of equilibrium is reached. Herein, by combining the thermodynamic extremum principle with the Onsager theory, we describe the nucleation and growth of liquid crystalline droplets, and the evolution of their size and concentration during phase separation, eventually leading to a multitude of order-order phase transitions. Furthermore, a decreasing pitch behaviour can be predicted using this combined theory during tactoid growth, already observed experimentally but not yet explained by present theories. The results of this study are compared with the experimental data of cholesteric pitch, observed in three different systems of biological chiral liquid crystals. These findings give an important framework for predicting the formation, growth and phase behaviour of biological filamentous colloids undergoing LLCPS, advancing our understanding of liquid-liquid phase separation and self-assembly mechanisms in biological systems, and provide a valuable rationale for developing nanomaterials and applications in nanotechnology.