Geometric and Dynamic Properties of Entangled Polymer Chains in Athermal Solvents: A Coarse-Grained Molecular Dynamics Study

Abstract: We used a coarse-grained model to study the geometric and dynamic properties of flexible entangled polymer chains dissolved in explicit athermal solvents. Our simulations successfully reproduced the geometrical properties including the scaling relationships between mean-square end-to-end distance $<R_{ee}^2>$, chain entanglement lengths $N_{e}$ and concentration $\Phi$. Specifically, we find that $<R_{ee}^2>\sim N*\Phi^{-1/4}$,$N_{e} = 30.01\Phi^{-5/4}+31.23$. Dynamically, our model confirmed the ratio of the dynamic critical entanglement $N_{c}$ and the geometric entanglement length $N_{e}$ is constant, with $N_{c}/N_{e} = 5\sim 6$. To account for the local swelling effect for chains confined in athermal solvents, we treated the chains using the concept of blobs where each blob occupies a volume $\Omega_{b}$, with length $g$. Direct MD simulations and scaling analysis showed that $g \sim \Phi^{-25/36}$, $\Omega_{b}\sim\Phi^{-5/4}$. Using these together with the concentration dependent packing length $p \sim \Phi^{-5/12}$, we obtained a modified the Lin-Noolandi ansatz for concentrated flexible polymer chains in athermal solvents: $G \sim \frac{\Phi}{\left(N_{e} / g\right) \Omega_{b}} \sim \Phi^{-2.28}$. We demonstrate this modified ansatz agrees well with our coarse-grained numerical simulations.