Relaxation dynamics of shake-gels composed of silica nanoparticles and poly(ethylene oxide): Effects of polymer dose revealed by viscoelastic measurements

Shake-gels—mixed suspensions of silica nanoparticles and poly(ethylene oxide)—exhibit reversible sol-gel transitions, which are triggered by agitation and reversed by rest. Despite their unique reversibility, the mechanisms governing shake-gel formation and relaxation, as well as the parameters controlling their macroscopic mechanical properties, remain poorly understood. According to the findings of previous studies based on visual observations, the relaxation time of shake-gels exhibits a maximum at an intermediate polymer dose per particle surface area. However, a quantitative rheological characterization of these relaxation behaviors has been lacking. Here, we systematically investigated the time evolution of the storage modulus of shear-induced gels as a function of polymer dose per particle surface area ( C p ) using time-resolved viscoelastic measurements. The initial storage modulus increased with C p and reached a plateau at approximately C p = 0.03 mg/m 2 . Conversely, the relaxation time underwent a precipitous decline above this C p . These results suggest that both high elasticity and prolonged structural stability emerge around the intermediate C p . The observed nonmonotonic dependence on C p persists across different particle concentrations and polymer molecular weights, indicating that normalization by particle surface area provides a useful framework for comparing relaxation behavior across compositions. These results establish a quantitative rheological basis for interpreting previously reported visual observations and offer guidance for the design of tunable, reversible gel systems.