Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

Role of Dynamical Heterogeneities on the Mechanical Response of Confined Polymer.

Confinement induces various modifications in the dynamics of polymers as compared to bulk. We focus here on the role of dynamical heterogeneities on the mechanics of confined polymers. Using a simple model that allows computation of the mechanical response over 10 decades in frequency, we show that the local mechanical coupling controlling the macroscopic response in the bulk disappears in a confined geometry. The slowest domains significantly contribute to the mechanical response for increasing confinement. As a consequence, the apparent glass transition is broadened and shifted towards lower frequencies as confinement increases. We compare our numerical predictions with experiments performed on poly(ethylacrylate) chains in model filled elastomers. We suggest that the change of elastic coupling between domains induced by confinement should contribute significantly to the polymer mobility shift observed on filled systems.