Impacts of filler loading and particle size on the transition to linear-nonlinear dichotomy in the rheological responses of particle-filled polymer solutions

Abstract

In this study, the nonlinear behavior of carbon black-filled polybutadiene solutions under large-amplitude oscillatory shear is investigated. The results show that in the nonlinear regime, the third harmonic intensity, as measured by the ratio of the third to the first harmonics I3/I1, decreases significantly above a critical concentration ϕc of the polymer in the matrix, which results in the amplitude stress deviating strongly from the linear dependence of strain, while the time dependence of stress remains sinusoidal. Increasing the filler particle size significantly decreases the critical ϕc. However, increasing the filler loading basically has no effect on the transition to linear-nonlinear dichotomy. This transition happens when the mesh size ξ of the entangled polymer network in the matrix becomes smaller than the primary filler particle size. Above ϕc, the topological hindrance of the entangled polymer chains apparently considerably slows down the recovery speed of the broken filler network in the material. Hence, the quasisinusoidal response in the system that has a strain-dependent modulus is probably due to the restoration of the broken filler network requiring longer than the time scale of a typical dynamic perturbation.