The underlying mechanisms behind the hydration-induced and mechanical response of spider silk

Abstract

Spider silk is a unique protein material that exhibits counterintuitive behaviors such as a significant reduction in stiffness of up to three orders of magnitude and a decrease in length of up to ∼60%, commonly termed supercontraction, upon exposure to high relative humidity (RH). In this work a robust free energy-based model is derived for the humidity-induced and mechanical response of spider silk. As opposed to the classical treatment of gels, the penetration of water molecules into a silk network results in an anisotropic response. First, the kinematics that describe the hydration-induced behavior are discussed and the balance laws and equilibrium requirements are reviewed. Next, the balance of free energy is used to derive constitutive relations that relate the free energy-density to the stress, the chemical potential, and the supercontraction stretch that develop in a spider silk fiber. Following experimental observations, a free energy-density that comprises four contributions is proposed: the first two contributions account for the entropic gain and the loss of chain orientation due to water uptake and the consequent dissociation of intermolecular hydrogen bonds, respectively, the third contribution describes the mixing process between the water and the polymer molecules in the silk, and the fourth contribution arises from the supercontraction phenomenon. Explicit forms are proposed for the four free energy-density contributions. The model is validated through a comparison to five different sets of experimental data under different boundary conditions. With an eye to future applications, the response of a spider silk fiber that is radially constrained and subjected to increasing humidity is also explored. The findings from this work pave the way to the design of silk-based composites and biomimetic materials with fascinating non-trivial properties and behaviors.