  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.
