Shear thinning behavior of linear polymer melts under shear flow via nonequilibrium molecular dynamics

Abstract

The properties of both untangled and entangled linear polymer melts under shear flow are studied by nonequilibrium molecular dynamics simulations. The results reveal that the dependence of shear viscosity η on shear rate \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }$\end{document}γ̇, expressed by \documentclass[12pt]{minimal}\begin{document}$\eta \sim \dot{\gamma }^{-n}$\end{document}η∼γ̇−n, exhibits three distinct regimes. The first is the well-known Newtonian regime, namely, η independent of shear rate at small shear rates \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }<\tau _{0}^{-1}$\end{document}γ̇<τ0−1 (where τ0 is the longest polymer relaxation time at equilibrium). In the non-Newtonian regime (\documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }>\tau _{0}^{-1}$\end{document}γ̇>τ0−1), the shear dependence of viscosity exhibits a crossover at a critical shear rate \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }_{\mathrm{c}}$\end{document}γ̇c dividing this regime into two different regimes, shear thinning regime I (ST-I) and II (ST-II), respectively. In the ST-I regime (\documentclass[12pt]{minimal}\begin{document}$\tau ^{-1}_0<\dot{\gamma }<\dot{\gamma }_{\mathrm{c}}$\end{document}τ0−1<γ̇<γ̇c), the exponent n increases with increasing chain length N, while in the ST-II regime (\documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }>\dot{\gamma }_{\mathrm{c}}$\end{document}γ̇>γ̇c) a universal power law \documentclass[12pt]{minimal}\begin{document}$\eta \sim \dot{\gamma }^{-0.37}$\end{document}η∼γ̇−0.37 is found for considered chain lengths. Furthermore, the longer the polymer chain is, the smaller the shear viscosity for a given shear rate in the ST-II regime. The simulation also shows that a characteristic chain length, below which \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }_{\mathrm{c}}$\end{document}γ̇c will be equal to \documentclass[12pt]{minimal}\begin{document}$\tau _{0}^{-1}$\end{document}τ0−1, lies in the interval 30 < N < 50. For all considered chain lengths in the ST-II regime, we also find that the first and second normal stress differences N1 and N2 follow power laws of \documentclass[12pt]{minimal}\begin{document}$N_{1} \sim \dot{\gamma }^{2/3}$\end{document}N1∼γ̇2/3 and \documentclass[12pt]{minimal}\begin{document}$N_{2} \sim \dot{\gamma }^{0.82}$\end{document}N2∼γ̇0.82, respectively; the orientation resistance parameter mG follows the relation \documentclass[12pt]{minimal}\begin{document}$m_{\mathrm{G}} \sim \dot{\gamma }^{0.75}$\end{document}mG∼γ̇0.75 and the tumbling frequency ftb follows \documentclass[12pt]{minimal}\begin{document}$f_{\mathrm{tb}} \sim \dot{\gamma }^{0.75}$\end{document}f tb ∼γ̇0.75. These results imply that the effects of entanglement on the shear dependences of these properties may be negligible in the ST-II regime. These findings may shed some light on the nature of shear thinning in flexible linear polymer melts.