Stiffness by design in biological fibers: The influence of microstructure and temperature.

Silk fibers exhibit unique mechanical properties such as high stiffness, toughness, and elasticity. The stiffness of silk fibers is governed by a hierarchical microstructure that is highly sensitive to the extraction method, post-processing, and environmental factors such as temperature. Commonly, the microstructure features an amorphous matrix comprising polypeptide chains that interact through weak intermolecular bonds and interconnect via crystalline domains. In this work, we develop a microscopically motivated energy-based model that provides fundamental insights into the underlying mechanisms governing the stiffness of silk fibers. The initial deformation is driven by (1) the entropic extension of polypeptide chains, (2) the elastic stretching and rotation of rigid crystalline domains, and (3) the distortion of weak intermolecular interactions, which lead to the relative sliding of polypeptide chains. The model quantitatively captures the influence of key physical microstructural quantities such as chain alignment, initial chain stretch, intermolecular bond strength, and crystallite size on the overall stiffness. The merit of the model is demonstrated through a comparison to spider silk and cocoon silk fibers. We also employ the model to better understand the influence of the reeling speed during the extraction of spider silk fibers on the microstructure and, consequently, on the stiffness. We follow with a parametric analysis that studies the influence of different microstructural quantities on the fiber stiffness. Lastly, the framework is extended to account for thermally-induced microstructural changes and the model predictions are compared to experimental data on the stiffness of cocoon silk fibers as a function of temperature. The findings from this work delineate the role of microstructure on the overall stiffness and offer a pathway for the efficient design of tunable and optimized biomimetic fibers for target applications. Statement of Significance: This work addresses a critical gap in the engineering of biological fibers by introducing a microscopically motivated, energy-based model that sheds light on the influence of key microstructural parameters on stiffness. By explicitly incorporating localized deformation kinematics and thermal effects, the model is used to capture the stiffness of diverse protein-based fibers, such as spider and cocoon silk, under different processing conditions and temperature regimes. This framework provides new insights into the role of key microstructural quantities on the overall stiffness, thereby paving the way to the design of tunable and optimized biomimetic fibers with targeted mechanical profiles that can be used in various applications.