The transition to linear-nonlinear dichotomy in rheological responses

The term "linear-nonlinear dichotomy" specifies that the viscoelastic behavior is nonlinear in the sense that the storage modulus G' and loss modulus G" depend strongly on the strain amplitude while, in contrast, linearity is implied at each of the strain amplitudes based on the sinusoidal stress response which is simply offset from the oscillatory strain input. This kind of nonlinearity contains two mutually exclusive and contradictory parts that coexist together at the same time. Recently, we analyzed the rheological behavior of a series of particle-filled polymer solutions using the ratio of the third and first harmonics, I3/I1, as a function of the concentration of the polymer in the solutions for a given particle concentration and the analysis of the structural characteristics of the polymer solutions. We found there is a transition to linear-nonlinear dichotomy in the theological responses of these materials at a critical polymer concentration, which is insensitive to strain amplitude, G'/G'0, and filler loading, but very sensitive to the particle size. This transition happens when the mesh size of the entangled polymer network in the matrix becomes smaller than the filler particle size. Here, I will report the milestone results of this research in Tongji, and intend to explain the nature of this unusual nonlinear behavior associated with nanoparticle-filled rubber materials.