Molecular Origins of Higher Harmonics in Large-Amplitude Oscillatory Shear Flow: Shear Stress Response

Recent work has focused on understanding the molecular origins of higher harmonics that arise in the shear stress response of polymeric liquids in large-amplitude oscillatory shear flow. These higher harmonics have been explained using only the orientation distribution of a dilute suspension of rigid dumbbells in a Newtonian fluid, which neglects molecular interactions and is the simplest relevant molecular model of polymer viscoelasticity [R.B. Bird et al., \textit{J Chem Phys}, \textbf{140}, 074904 (2014)]. We explore these molecular interactions by examining the Curtiss-Bird model, a kinetic molecular theory that accounts for restricted polymer motions arising when chains are concentrated [Fan and Bird, \textit{JNNFM}, \textbf{15}, 341 (1984)]. For concentrated systems, the chain motion transverse to the chain axis is more restricted than along the axis. This anisotropy is described by the link tension coefficient, $\epsilon $, for which several special cases arise: $\epsilon =0_{\mathrm{\thinspace }}$corresponds to reptation, $\epsilon >1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-\nulldelimiterspace} 8_{\mathrm{\thinspace }}$to rod-climbing, $1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2\ge \epsilon \ge 3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-\nulldelimiterspace} 4$ to reasonable shear-thinning predictions in steady simple shear flow, and $\epsilon =1_{\mathrm{\thinspace }}$to a dilute solution of chains. We examine the shapes of the shear stress versus shear rate loops for the special cases, $\epsilon =\left( {{0,1} \mathord{\left/ {\vphantom {{0,1} {8,3 \mathord{\left/ {\vphantom {3 8}} \right. \kern-\nulldelimiterspace} 8}}} \right. \kern-\nulldelimiterspace} {8,3 \mathord{\left/ {\vphantom {3 8}} \right. \kern-\nulldelimiterspace} 8},1} \right)$, of the Curtiss-Bird model, and we compare these with those of rigid dumbbell and reptation model predictions.