Torsional Linearity in Nonlinear Stress-Optical Regimes for Polymeric Materials

The birefringence on anisotropic materials under flow has been tremendously useful for understanding the physical states of nonequilibrium materials. It is, however, well-known that the linear relationship between the anisotropy of the stress and that of the birefringence breaks down above a certain flow strength, severely limiting its practical applicability. Here we present an encouraging result which helps overcome this limitation and extends our knowledge beyond the conventional the stress-optical rule regime. Through a detailed molecular-level analysis of the stress-optical behaviors of various polyethylene melts under shear via direct atomistic nonequilibrium molecular dynamics simulations, we found a universal feature in the stress-optical behaviors of polymeric materials that there exists a strictly linear relationship between the birefringence tensor and the stress tensor contributed solely by the bond-torsional interaction in the whole range of flow strength. While a limited range of chain length and architecture (unentangled and moderately entangled linear and H-shaped polymer melts) under shear flow was investigated in this study, the main features and conclusions as drawn are considered to be general and valid regardless of (i) the chain length and molecular architecture, (ii) flow types, and (iii) force fields of polymeric materials. They are further useful as guidance in developing an accurate coarse-grained polymer model.