Elucidation of the Correlation between Molecular Conformation and Shear Viscosity of Polymer Melts under Steady-State Shear Flow

TL;DR

This work addresses how molecular conformation under steady shear governs shear thinning in polymer melts, comparing linear and ring architectures across chain stiffness. Using non-equilibrium molecular dynamics with the Kremer–Grest bead-spring model, the authors compute the gyration tensor $G_{\alpha\beta}$ and relate its components to the steady-state viscosity $\eta$. They report universal scalings in the low-to-moderate viscosity regime: $\eta \propto \langle G_{yy}\rangle^{3/2}$ and $\eta \propto \langle G_{zz}\rangle^{5/2}$, largely independent of architecture and stiffness, with analogous relations for the diagonalized components $G_2$ and $G_3$. The results imply that molecular extension along the velocity-gradient direction and diffusion along the advection-free direction control friction under steady shear, and they discuss diffusion anisotropy and potential deviations from the Stokes–Einstein relation, connecting to prior findings on zero-shear viscosity and flow-induced conformation across architectures.

Abstract

The rheological behavior of polymer melts is strongly influenced by parameters such as chain length, chain stiffness, and architecture. In particular, shear thinning, characterized by a power-law decrease in shear viscosity with increasing shear rate, has been widely investigated through molecular dynamics simulations. A central question is the connection between molecular conformation under steady flow and the resulting shear-thinning response. In this study, we employ coarse-grained molecular dynamics simulations of linear and ring polymers with varying chain stiffness to examine this relationship, with chain conformations quantified by the gyration tensor. We identified a strong correlation between the velocity-gradient direction component of the gyration tensor and shear viscosity, which exhibits a clear scaling relationship. This indicates that chain extension along the velocity-gradient direction governs the effective frictional force. Notably, this behavior emerges as a general feature, independent of chain architecture and chain stiffness. In addition, shear viscosity was found to correlate with the component of the gyration tensor corresponding to the direction that is not directly influenced by advective effects of shear flow. Because advection is absent in the direction, polymer chains can be regarded as diffusing freely, and the extent of this diffusion appears to be controlled by the shear viscosity.

Figures (5)

• Figure 1: Shear rate $\dot{\gamma}$ dependence of shear viscosity $\eta$ for (a) linear (b) and ring polymers, with the chain stiffness $\varepsilon_\theta = 0$ (circle), 1.5 (triangle), and 3 (square). The straight lines indicate the slopes corresponding to $0.8$ for linear polymers (a) and $0.57$ for ring polymers (b), respectively.
• Figure 2: Shear rate $\dot{\gamma}$ dependence of $\langle G_{xx}\rangle$ [(a) and (d)], $\langle G_{yy}\rangle$ [(b) and (e)], and $\langle G_{zz}\rangle$ [(c) and (f)] for linear [(a)-(c)] and ring [(d)-(f)] polymers. Chain stiffness values are $\varepsilon_\theta = 0$ (circle), 1.5 (triangle), and 3 (square).
• Figure 3: Relationships between shear viscosity $\eta$ and $\langle G_{xx}\rangle$ [(a) and (d)], $\langle G_{yy}\rangle$ [(b) and (e)], and $\langle G_{zz}\rangle$ [(c) and (f)] for linear [(a)-(c)] and ring [(d)-(f)] polymers. The straight lines indicate the slopes corresponding to $3/2$ in (b) and (e), and $5/2$ in (c) and (f), respectively. Chain stiffness values are $\varepsilon_\theta = 0$ (circle), 1.5 (triangle), and 3 (square).
• Figure 4: Shear rate $\dot{\gamma}$ dependence of $\langle G_1\rangle$ [(a) and (d)], $\langle G_2\rangle$ [(b) and (e)], and $\langle G_3\rangle$ [(c) and (f)] for linear [(a)-(c)] and ring [(d)-(f)] polymers. Chain stiffness values are $\varepsilon_\theta = 0$ (circle), 1.5 (triangle), and 3 (square).
• Figure 5: Relationships between shear viscosity $\eta$ and $\langle G_1\rangle$ [(a) and (d)], $\langle G_2\rangle$ [(b) and (e)], and $\langle G_3\rangle$ [(c) and (f)] for linear [(a)-(c)] and ring [(d)-(f)] polymers. The straight lines indicate the slopes corresponding to $3/2$ in (b) and (e), and $5/2$ in (c) and (f), respectively. Chain stiffness values are $\varepsilon_\theta = 0$ (circle), 1.5 (triangle), and 3 (square).