Strain amplitude sweep testing of oscillatory shear of transient networks with controlled network structures

The origin of nonlinear stress behaviors in transient networks during oscillatory shear measurements is investigated in this study via two-dimensional rheo-optics observations of a systematically controlled model system comprising tetra-armed polyethylene glycols (Tetra-PEG slime). Transient networks are characterized by their temporary crosslinks. However, the strain scale at which nonlinear viscoelastic responses begin to emerge under strain amplitude sweep in oscillatory shear deformations remains poorly characterized. The uncertainty of nonlinear onset can be attributed, at least in part, to the heterogeneous structures inherent to conventional transient networks, as well as to the limited availability of detailed experimental evaluations. We overcome these limitations by employing Tetra-PEG slime, which possesses a well-defined network structures with uniform strand lengths and functionalities. Rheo-polarization imaging reveals homogeneous deformation in the linear regime and a scaling change of retardation - strain relation around the onset of nonlinearity. Meanwhile, Rheo-SAXS measurements confirmed the absence of nanoscale structural changes. The elastic contribution per network strand at the critical strain (W _c,0) approximately collapses onto a single master curve when plotted against the Weissenberg number (Wi_max), following the relation W _c,0 ∝ Wi_max ². This scaling suggests that the onset of nonlinearity is governed by the balance between molecular relaxation and applied deformation. These findings provide molecular-level insights into the nonlinear elasticity of transient networks and offer a framework to design soft materials with tunable nonlinear responses.