Geometric-Thermodynamic Modelling of the Isotropic-to-Smectic A Phase— Collagen-Based Material as an Inspiration for Fibre Manufacturing

Functionalities in biological materials and Nature’s manufacturing processes are heavily influenced by order, structure, and organization such as position, alignment, and chirality. Liquid Crystals (LCs) are materials presenting these structural details, like orientational and positional order while being found in synthetic and biological settings. The order and alignment in LCs are maintained until a phase transition is induced by a gradient in a driving force (e.g. temperature, concentration, pH). One example in Nature, and the motivation of this work, is the collagen-based tethering system used by marine mussels: the mussel byssus or byssal thread. This smart material, fabricated in seawater environments, features high-toughness, self-assembly and self-healing properties. As building blocks, mussels use collagenous molecules packed in a liquid crystalline layered fashion inside tactoid-shaped vesicles. These tactoids offer rich storage principles and mechanisms to be extruded into the green tough functional and composite material used by the mussel. The organization of the byssal thread precursor is a smectic semisolid with oriented molecules perpendicular to the layers, which has been hypothesized to play a major role in the pre-organization and formation of the fibre.<br/>For the characterization of the liquid crystalline precursor structure, and the description of the roles of the LC in the formation of this collagen-based material from its pre-transitional state, it is essential to understand the assembly and phase transition mechanisms that govern the highly organized hierarchical molecular organization. The self-organization, self-assembly, and phase kinetics processes can be studied through the Landau-de Gennes (LdG) model. This model uses two non-conserved order parameters to describe the positional and orientational order and correlates them to the free energy of the system with phenomenological parameters. First, the energy landscape is developed to give an insight into the self-organization scheme. It provides information about the possible phases, or critical points, that exist at different conditions, which in this work are different temperatures or quenching regimes. In addition, the stability of the critical points has a predominant influence on the phase kinetics. It has been seen that is involved in drop formation systems where there is a presence of stable phases within a matrix of an unstable phase, ultimately showing a thin layered-like film structure. Finally, the decomposition of the contributions from all the critical points enables the study of the self-assembly process. The manifestation of these processes by nucleation and growth and spinodal transformation are studied by decomposing the index of the free energy landscape into the contributions of the different critical points and their respective phase under different quenching regimes.<br/>We present a new method to study the isotropic-to-smectic A liquid crystal phase transition by integrating thermodynamic stability modelling, polynomial index, non-linear differential equations and differential geometry to provide an insight into the multiple stable and unstable states and their dynamics as the quench regime changes, thus unravelling fundamental principles and roles of the LC in the formation of the multi-hierarchical structure. It was found that the emergence of different states which stability was then characterized as stable, unstable, and metastable using the energy landscape and their evolution through it. Consequently, it was observed that smectic ordering promotes nematic alignment. Ultimately, the understanding of the evolution and behaviour of the phases will pave the way for the development of green engineering principles, storage and delivery technologies, and advances in the processing of materials offering a greater comprehension of the tuning capabilities according to the material hierarchical organization.