Linear Viscoelasticity of Polymers and Polymer Nanocomposites: Molecular-Dynamics Large Amplitude Oscillatory Shear and Probe Rheology Simulations

In this chapter, we discuss coarse-grained and atomistic molecular-dynamics simulation studies of the rheological properties of bulk polymer systems and polymer nanocomposites. Both systems contain monodispersed and non-crosslinked chain molecules. A multiscale strategy is applied to characterize the rheological behavior on different length scales of the systems structural organization. Fully atomistic simulations provide insights in rheological properties on smaller length scales than those accessible through coarse-grained simulations. Different approaches are utilized to obtain rheological moduli at these different length scales. At both levels of description, cyclic shear deformation is performed to characterize macroscopic properties of the systems before and after filler insertion. In the fully atomistic simulations of polyimide R-BAPB, passive microrheology approach is employed in addition to active rheology. To this end, a probe particle is immersed into the atomistic polymer matrix. Then, local rheological properties on the length scales at and beyond the Kuhn length are estimated. Results are compared with macroscopic rheological properties obtained by shear deformation. Additionally, the influence of the strain amplitude on the resulting rheological properties is examined. The reported coarse-grained simulations show a strong decrease of the nanocomposites storage modulus with increasing strain amplitude, which is accompanied by a maximum in the loss modulus (the so-called Payne effect); the onset of the softening is observed in the linear regime of deformation at strain amplitude of about 0.01. Moreover, the dependence of the storage modulus on the instantaneous strain exhibits both softening and hardening regimes, in agreement with recently reported [22] Large Amplitude Oscillatory Shear (LAOS) experiments. The simulations suggest that the observed hardening is caused by the shear-induced decrease of the non-affine diffusion of the polymer segments due to filler particles acting as effective crosslinks between polymeric chains and, hence, hindering diffusion. Moreover, the formation of “glassy” immobile layers at the nanoparticle interface strongly increases the storage modulus at low strain amplitudes. The strain softening with increasing strain amplitude is connected to the mobilization of these glassy layers and an increase in the dynamic heterogeneity of the polymer matrix. A breakup of the network structure plays a role as well.