The emergence of quasi-sinusoidal nonlinearity in particle-filled polymer solutions

Systematic rheometric measurements are carried out to explore the nonlinear responses of carbon black-filled polyisoprene/squalene solutions with the polymer concentrations f in the matrix ranging from the coil overlapping state (Φ =Φ^*) to the melt state (Φ =1). At the coil overlapping state when Φ <<1, the system shows the classic nonlinearity, where the storage modulus G’ decreases as strain amplitude increases and the resulting stress responses are deviated from sinusoidal waves. At the melting state when Φ = 1, the system displays a new nonlinearity, where the stress responses are surprisingly sinusoidal regardless the reduction of G’. Between the two states when Φ^*< Φ <1, the system exhibits a complex nonlinear behavior throughout a wide range of Φ. The ratio of the third to the first harmonics I₃/I₁ in the stress responses first decreases rapidly reaching a minimum when Φ ≈ 0.1, then increases to a maximum when Φ ≈ 0.3, after which it decreases again as Φ approaches 1. Remarkably, the filler flocculation in the system also displays the corresponding minimum and maximum values. The quasi-sinusoidal response in a system is apparently due to the restoration of broken filler network requiring longer than the time scale of a typical dynamic perturbation.