Spider silk has outstanding mechanical properties despite being spun at close to ambient temperatures and pressures using water as the solvent. The spider achieves this feat of benign fibre processing by judiciously controlling the folding and crystallization of the main protein constituents, and by adding auxiliary compounds, to create a composite material of defined hierarchical structure. Because the 'spinning dope' (the material from which silk is spun) is liquid crystalline, spiders can draw it during extrusion into a hardened fibre using minimal forces. This process involves an unusual internal drawdown within the spider's spinneret that is not seen in industrial fibre processing, followed by a conventional external drawdown after the dope has left the spinneret. Successful copying of the spider's internal processing and precise control over protein folding, combined with knowledge of the gene sequences of its spinning dopes, could permit industrial production of silk-based fibres with unique properties under benign conditions.

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Liquid crystalline spinning of spider silk.

Silk features exceptional mechanical properties such as high tensile strength and great extensibility, making it one of the toughest materials known. The exceptional strength of silkworm and spider silks, exceeding that of steel, arises from beta-sheet nanocrystals that universally consist of highly conserved poly-(Gly-Ala) and poly-Ala domains. This is counterintuitive because the key molecular interactions in beta-sheet nanocrystals are hydrogen bonds, one of the weakest chemical bonds known. Here we report a series of large-scale molecular dynamics simulations, revealing that beta-sheet nanocrystals confined to a few nanometres achieve higher stiffness, strength and mechanical toughness than larger nanocrystals. We illustrate that through nanoconfinement, a combination of uniform shear deformation that makes most efficient use of hydrogen bonds and the emergence of dissipative molecular stick-slip deformation leads to significantly enhanced mechanical properties. Our findings explain how size effects can be exploited to create bioinspired materials with superior mechanical properties in spite of relying on mechanically inferior, weak hydrogen bonds.

Nanoconfinement controls stiffness, strength and mechanical toughness of β-sheet crystals in silk

Fractals arise from a variety of sources and have been observed in nature and on computer screens. One of the exceptional characteristics of fractals is that they can be described by a noninteger dimension. The geometry of fractals and the mathematics of fractal dimension have provided useful tools for a variety of scientific disciplines, among which is chaos. Chaotic dynamical systems exhibit trajectories in their phase space that converge to a strange attractor. The fractal dimension of this attractor counts the effective number of degrees of freedom in the dynamical system and thus quantifies its complexity. In recent years, numerical methods have been developed for estimating the dimension directly from the observed behavior of the physical system. The purpose of this paper is to survey briefly the kinds of fractals that appear in scientific research, to discuss the application of fractals to nonlinear dynamical systems, and finally to review more comprehensively the state of the art in numerical methods for estimating the fractal dimension of a strange attractor.

/pdf/estimating-fractal-dimension-4bfbt20bh2.pdf

Estimating fractal dimension

Diffusion in regular and disordered lattices

The molecular origin of the exceptional mechanical properties of spider silk is unclear. This paper presents solid-state 2H nuclear magnetic resonance data from unoriented, oriented, and supercontracted fibers, indicating that the crystalline fraction of dragline silk consists of two types of alanine-rich regions, one that is highly oriented and one that is poorly oriented and less densely packed. A new model for the molecular-level structure of individual silk molecules and their arrangement in the fibers is proposed. These data suggest that it will be necessary to control the secondary structure of individual polymer molecules in order to obtain optimum properties in bio-inspired polymers.

https://science.sciencemag.org/content/sci/271/5245/84.full.pdf

Molecular Orientation and Two-Component Nature of the Crystalline Fraction of Spider Dragline Silk

We introduce the first comprehensive molecular model of spider dragline elasticity which clearly integrates most of the information known to date about the structure of the fiber. In accordance with X-ray evidence, the dragline is represented by a large number of small crystallites separated by amorphous regions made of rubber-like chains. Our model results clearly indicate the important role of the crystallites which act as multifunctional cross-links and create inside the amorphous regions a thin layer with modulus higher than in the bulk. The role of the crystallites in spider silk is found to be amazingly similar to that speculated for carbon black in synthesized elastomers

Molecular modeling of spider silk elasticity

Theoretical study of the influence of the molecular weight on the maximum tensile strength of polymer fibers

Deformation de polymeres flexibles solides. Modele base sur la theorie de vitesse d'activation chimique d'Eyring. Application au polyethylene cristallise a l'etat fondu

Kinetic model for tensile deformation of polymers

On donne une estimation de la dimension fractale D F ' des attracteurs etranges. Des amas de n points plus proches voisins sont echantillonnes a partir d'une serie temporelle; on trouve D F ' a partir de R DF' ∼n ou R est le rayon d'amas moyen

Yves Termonia

Papers

Molecular modeling of spider silk elasticity

Theoretical study of the influence of the molecular weight on the maximum tensile strength of polymer fibers

Kinetic model for tensile deformation of polymers

Fractal Dimension of Strange Attractors from Radius versus Size of Arbitrary Clusters

Kinetic model for tensile deformation of polymers. 2. Effect of entanglement spacing