Anisotropic Cooperative Structural Rearrangements in Sheared Supercooled Liquids

A supercooled liquid generally exhibits marked shear-thinning behavior, but its detailed mechanism remains elusive. Here we study the dynamics of structural rearrangements in supercooled liquids under shear, using two-dimensional (2D) molecular dynamics simulation. To elucidate the relationship between heterogeneous dynamics and the rheological behavior, we extend the four-point correlation function, which has been used for analyzing “dynamic heterogenity” in a quiescent condition, to a system under steady shear. In the Newtonian regime, the rearrangement dynamics is strongly heterogeneous in space, but remains isotropic. Contrary to this, in the non-Newtonian regime, where marked shear-thinning behavior appears, we find a novel dynamic effect: The mobile region tends to form anisotropic “fluidized bands.” This finding suggests a link between nonlinear rheology and inhomogeneization of flow.

Figure 1

(a) $F_s({\mathit{k}}_0,t)$, (b) $⟨{\sigma }_{xy}(t)⟩$, (c) $⟨Q(t)/N⟩$, and (d) ${\chi }_4(t)$ for several shear rates at $k_{B}T/ϵ=0.526$.

Figure 2

Snapshots of $\delta \mathit{U}({\mathit{r}}_J,\Delta t)$ for various $\dot{\gamma }$ at $k_{B}T/ϵ=0.526$. Note that another definition, $\delta \tilde{\mathit{U}}({\mathit{r}}_J,\Delta t)\equiv 1/N_j\sum _{i\in V_J}[{\mathit{r}}_i(\Delta t)-{\mathit{r}}_i(0)-{\int }_0^{\Delta t}d{t}^{\prime }\dot{\gamma }{y}_i(t^{\prime })\widehat{\mathit{x}}]$, gives almost the same spatial structure as $\delta \mathit{U}({\mathit{r}}_J,\Delta t)$ for the present $\Delta t$.

Figure 3

(a) Temporal change in $S_4(\mathit{k},\Delta t)$. (b) A snapshot of $\delta \mathit{U}({\mathit{r}}_J,\Delta t)$ at $\dot{\gamma }=0.001$. Particle trajectories are also shown in both the less mobile region (left) and the mobile region (right), where a point-to-point interval is about $0.25{\tau }_{\chi }$.

Figure 4

(a) $\eta (\dot{\gamma })$ vs $\dot{\gamma }$ for various $k_{B}T/ϵ$’s. (b) $S_u(\mathit{k},\Delta t=10{\tau }_{\chi })$ for ($T$, $\dot{\gamma }$) numbered (i) to (vi) in (a).

Figure 5

(a) ${\Sigma }_i^{xy}(\Delta t)$ scaled by its maximum value ${\Sigma }_{i\max }^{xy}(\Delta t)$ for three values of $\dot{\gamma }$ for $\Delta t\cong {\tau }_{\chi }$. The inset shows the normalized distribution function of $\sqrt{\delta {\mathit{u}}_i^2(\Delta t)}$, which satisfies ${\int }_0^{\infty }dxf(x)=1$. (b) ${\Sigma }_i^{xy}(\Delta t)$ is plotted against $\lambda =\sqrt{\delta {\mathit{u}}_i^2(\Delta t)}/{\sqrt{\delta {\mathit{u}}_i^2(\Delta t)}}_{\mathrm{peak}}$ for three values of $\Delta t$ at $\dot{\gamma }=0.001$. Here ${\sqrt{\delta {\mathit{u}}_i^2(\Delta t)}}_{\mathrm{peak}}$ is the peak position of the distribution function, which grows as $\sim \Delta t^{1/2}$. The inset shows the scaled distribution function ${\sqrt{\delta {\mathit{u}}_i^2(\Delta t)}}_{\mathrm{peak}}f$, which approaches the Gaussian indicated by the purple dotted curve with increasing $\Delta t$, as a function of $\lambda$.