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Silk is a semi-dilute solution of randomly coiled associating polypeptidechains that crystallise following the stretch-induced disruption, in the strongextensional flow of extrusion, of the solvation  shell around their amino acids. We propose that natural silk spinningexploits both the exponentially-broad stretch-distribution generated byassociating polymers in extensional flow and the criterion of a criticalconcentration of sufficiently-stretched chains to nucleate flow-inducedcrystallisation. To investigate the specific-energy input needed to reach thiscriterion in start-up flow, we have coupled a model for the coarse-grainedBrownian dynamics of the chain to the stochastic, strain-dependent binding andunbinding of their associations. Our simulations indicate that the associationshamper chain alignment in the initial slow flow, but, on the other hand,facilitate chain stretching at low specific work at later, high rates. Weidentify a minimum in the critical specific work at a strain rate just abovethe stretch transition (i.e, where the mean stretch diverges), which we explainin terms of analytical solutions of a two-state master equation. We furtherdiscuss how the silkworm appears to exploit the chemical tunability of theassociations to optimise chain alignment and stretching in different locationsalong the spinning duct: this delicate mechanism also highlights the potentialbiomimetic industrial benefits of chemically tunable processing of syntheticassociation polymers.

Theoretical rheo-physics of silk: Intermolecular associations reduce the critical specific work for flow-induced crystallisation