Nonlinearity In A Crosslinked Polyelectric Polypeptide

Abstract: Youngs modulus of soft solids composed of crosslinked synthetic polypeptides has been determined under different conditions. Co-poly-(L-glutamic acid$_4$, L-tyrosine$_1$) [PLEY (4:1)] was crosslinked with poly-L-lysine (PLK) and 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC). Elasticity was assessed by subjecting samples to a compressive strain. Cross-linked material at high relative humidity, RH 75-85%, exhibited non-linear elasticity. Stress-strain response was approximately linear at low strain but nonlinear above a threshold strain. Analysis of the secant modulus revealed apparent softening of samples at low strain and hardening at high strain, as in biological soft tissues. Fitting stress-strain data with a neo-Hookean model yielded approximately 40 $\le E \le$ 300 kPa at high RH. Viscoelasticity was nonlinear at low RH. The average viscosity-driven relaxation time was 13 min at high strain and 6 min at low strain. Analysis of the derivative of the secant modulus for non-linear elastic materials revealed a transient response up to a strain of $\varepsilon \approx$ 0.18-0.20. Above this range, oscillations tended to zero. Non-linear viscoelastic materials showed lower-amplitude oscillations than samples at high RH up to $\varepsilon \approx$ 0.06 and strong damping thereafter. The data suggest that it will be possible to engineer mechanical properties of polypeptide materials.