Fig. 1.

Arrested associative gels exhibit broad nonexponential stress relaxations in response to linear perturbations. (A) Schematic illustration of the model polymer–particle system, consisting of four-arm PEGs (10 kDa) with nitrocatechol groups, and Fe₃O₄ NPs (7-nm diameter) stabilized by one-arm PEGs (2 kDa) with catechol groups. Upon mixing, the stronger-binding nitrocatechol ligand replaces the catechol ligand on the NP surface and gelation thus occurs via a dynamic ligand exchange from equilibrium. Details on the synthesis and compositions are available in Materials and Methods, and additional characterizations of the quiescent viscoelasticity of the gels are available in ref. 30. (B) Representative $G(t)$ of the arrested gel in response to a linear step strain (${\gamma }_0=0.5 \text{\%}$) at $25 °\text{C}\le T\le 65 °\text{C}$. Solid lines indicate fits to the stretched exponential function (Eq. 1) with a constant stretching exponent of $\beta =0.3$. The stretching exponent is consistent at all temperatures, as evidenced by the stretched exponential fit to the time and temperature–superposed data (SI Appendix, Fig. S1). Inset: Representative picture of the model gel material. Scale bar, 1 cm. (C) Step strain measurements of the relaxation modulus $G\left(t\right)$ of the gelled system measured at varying strain amplitudes ${\gamma }_0$ ($T=25 °\text{C}$). All $G\left(t\right)$ values are normalized by the initial storage modulus $G_i^{\prime }$ of the gel measured immediately after gelation (SI Appendix, Fig. S2A). Linear behavior is demonstrated up to a strain of ${\gamma }_0=1.0 \text{\%}$; this result is also in agreement with amplitude sweep characterizations on the system (SI Appendix, Fig. S2B).