Effects of chain stiffness on the breakdown of the Cox-Merz rule in linear and ring polymer melts
The Cox-Merz rule is an empirical relation between the magnitude of the complex viscosity, $\lvertη^*(ω)\rvert$, obtained from linear viscoelasticity, and the steady-shear viscosity, $η(\dotγ)$. In this study, we performed molecular dynamics simulations of coarse-grained polymer melts using the Kremer-Grest model and systematically examined the validity of the Cox-Merz rule as a function of chain length and chain stiffness for linear and ring polymers. For short chains and, more generally, for flexible chains, $\lvertη^*(ω)\rvert$ and $η(\dotγ)$ show good agreement at corresponding values of angular frequency $ω$ and shear rate $\dotγ$. For linear polymers, however, the discrepancy between the two viscosities becomes increasingly pronounced with increasing chain length and chain stiffness, with $\lvertη^*(ω)\rvert$ exceeding $η(\dotγ)$ at high corresponding values of $ω$ and $\dotγ$. This deviation is associated with the pronounced nonlinear response under strong steady shear, where flow-induced chain extension and alignment can modify the entanglement constraints that govern relaxation near equilibrium. In contrast, ring polymers retain substantially better agreement between $\lvertη^*(ω)\rvert$ and $η(\dotγ)$ with increasing chain length and stiffness within the range examined here, indicating a weaker breakdown of the Cox-Merz rule. These results demonstrate that the applicability of the Cox-Merz rule depends strongly on chain length, chain stiffness, and molecular architecture. When the molecular response under steady shear deviates substantially from the relaxation behavior characterized by linear viscoelasticity near equilibrium, the complex viscosity can no longer accurately predict the steady-shear viscosity, resulting in a pronounced breakdown of the Cox-Merz rule.