Shape and structural relaxation of colloidal tactoids.

Facile geometric-structural response of liquid crystalline colloids to external fields enables many technological advances. However, the relaxation mechanisms for liquid crystalline colloids under mobile boundaries remain still unexplored. Here, by combining experiments, numerical simulations and theory, we describe the shape and structural relaxation of colloidal liquid crystalline micro-droplets, called tactoids, where amyloid fibrils and cellulose nanocrystals are used as model systems. We show that tactoids shape relaxation bears a universal single exponential decay signature and derive an analytic expression to predict this out of equilibrium process, which is governed by liquid crystalline anisotropic and isotropic contributions. The tactoids structural relaxation shows fundamentally different paths, with first- and second-order exponential decays, depending on the existence of splay/bend/twist orientation structures in the ground state. Our findings offer a comprehensive understanding on dynamic confinement effects in liquid crystalline colloidal systems and may set unexplored directions in the development of novel responsive materials.

Nucleation and growth of cholesteric collagen tactoids: A time-series statistical analysis based on integration of direct numerical simulation (DNS) and long short-term memory recurrent neural network (LSTM-RNN).

HYPOTHESIS: Liquid-crystalline phase separation by nucleation and growth (NG) is a crucial step in the formation of collagen-based biomaterials. However, the fundamental mechanisms are not completely understood for chiral lyotropic colloidal mesogens such as collagen. METHODOLOGY: To capture the dynamics of NG under a quenching process into the biphasic equilibrium zone, we use direct numerical simulation based on the time-dependent Ginzburg-Landau model allowing minimization of the total free energy comprised of five key contributions: phase separation (Flory-Huggins), ordering (Landau-de Gennes), chiral orientational elasticity (Frank-Oseen-Mermin), interfacial and coupling effects. LSTM-RNN is applied as a surrogate model to greatly enrich the results. Significant correlations are established using Symbolic Regression. FINDINGS: We quantify the NG boundaries existing in the collagen phase diagram that has recently been developed and validated by our thermodynamic model (Khadem and Rey, 2019 [1]). We characterize the three NG stages (induction, nucleation, and coarsening) in terms of tactoids' shape, morphology, growth laws, and population across the NG zone. Wide-range generic correlations are developed, revealing the quench depth dependence of NG characteristics and connecting the sequential NG stages. We confirm experimental observations on time-dependent growth law exponent changes from an initial n≈0.5 for the mass transfer limited regime to n≈1 for the volume-driven phase ordering regime upon increasing quench depth during the nucleation period and having exclusively a value of n≈0.5 for the coarsening period regardless of quench depth. We lastly uncover the underlying physics behind the NG phenomena.

Relaxation dynamics in bio-colloidal cholesteric liquid crystals confined to cylindrical geometry.

Para-nematic phases, induced by unwinding chiral helices, spontaneously relax to a chiral ground state through phase ordering dynamics that are of great interest and crucial for applications such as stimuli-responsive and biomimetic engineering. In this work, we characterize the cholesteric phase relaxation behaviors of ß-lactoglobulin amyloid fibrils and cellulose nanocrystals confined into cylindrical capillaries, uncovering two different equilibration pathways. The integration of experimental measurements and theoretical predictions reveals the starkly distinct underlying mechanism behind the relaxation dynamics of ß-lactoglobulin amyloid fibrils, characterized by slow equilibration achieved through consecutive sigmoidal-like steps, and of cellulose nanocrystals, characterized by fast equilibration obtained through smooth relaxation dynamics. Particularly, the specific relaxation behaviors are shown to emerge from the order parameter of the unwound cholesteric medium, which depends on chirality and elasticity. The experimental findings are supported by direct numerical simulations, allowing to establish hard-to-measure viscoelastic properties without applying magnetic or electric fields.

Thermodynamic modelling of acidic collagenous solutions: from free energy contributions to phase diagrams.

Tropocollagen is considered one of the main precursors in the fabrication of collagen-based biomaterials. Triple helix acidic solutions of collagen I have been shown experimentally to lead to chiral plywood architectures found in bone and "cornea" like tissues. As these plywoods are solid analogues of liquid crystal architectures, bio-inspired processing and fabrication platforms based on liquid crystal physics and thermodynamics will continue to play an essential role. For tissue engineering applications, it has been shown that dilute isotropic collagen solutions need to be flow processed first and then dehydrated. Thus, a complete fundamental understanding of the thermodynamics and free energy contributions in acidic collagen aqueous solutions is necessary to avoid expensive trial-and-error fabrication. To achieve this goal, we analyze the microscopic mechanisms of ordering and interactions in solutions of triple helix collagen, namely mixing, attraction, excluded-volume and chirality. To capture the mentioned physics, we then incorporate and integrate the Flory-Huggins, Maier-Saupe, Onsager and Frank theories. Nonetheless, they together are incapable of providing an acceptable mesophasic description in acidic collagenous solutions because tropocollagen biomacromolecules are positively charged. We then explore a simple and accurate electrostatic mean-field potential. Our results on collagen are in good agreement with experiments and include phase diagrams, phase transition thresholds, and critical isotropic/cholesteric order parameters. The present extended theory is shown to properly converge to classical liquid crystal models and is used to express the phenomenological Landau-de Gennes parameters with more fundamental quantities. This study provides a platform to derive accurate process models for the fabrication of collagen-based materials, considering and benefitting from the full range of underlying interactions.