Athermal jamming versus thermalized glassiness in sheared frictionless particles

Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study the behavior of a simple liquid as a function of temperature $T$, packing fraction $\varphi$, and uniform applied shear strain rate $\dot{\gamma }$. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters $\varphi$ and $T/\dot{\gamma }$. Here $T/\dot{\gamma }\to 0$ defines the athermal limit in which a shear-driven jamming transition occurs at a well defined ${\varphi }_J$ and $T/\dot{\gamma }\to \infty$ defines the thermalized limit where an equilibrium glass transition may take place at ${\varphi }_G$. This conclusion argues that athermal jamming and equilibrium glassy behavior are not controlled by the same critical point. Preliminary results suggest ${\varphi }_G<{\varphi }_J$.

Figure 1

Shear viscosity $\eta$ vs (a) $T$ and (b) $T/\dot{\gamma }$, at fixed packing fraction $\varphi =0.72$ below jamming, for several different shear strain rates $\dot{\gamma }$. In (a) solid dots are the linear response ${\eta }_{\mathrm{GK}}$ computed from the Green-Kubo formula in equilibrium. In (b) the horizontal dashed line is the hard-core equilibrium limit ${\eta }_{\mathrm{HCeq}}$; the horizontal dotted line is the athermal value ${\eta }_0$ at $T=0$.

Figure 2

(a) Inverse reduced pressure $nT/p$ and (b) stress anisotropy $\sigma /p$ vs $T/\dot{\gamma }$, at packing fraction $\varphi =0.72$ for several different shear strain rates $\dot{\gamma }$. The dashed horizontal line in (a) is the hard-core equilibrium value of $nT/p$.

Figure 3

Shear viscosity $\eta$ vs (a) $T$ and (b) $T/\dot{\gamma }$, at fixed packing fraction $\varphi =0.80$, closer to the jamming ${\varphi }_J=0.843$, and several different shear strain rates $\dot{\gamma }$.

Figure 4

(a) Peak value of viscosity ${\eta }_{\mathrm{peak}}$ and (b) location of the peak viscosity $T_{\mathrm{peak}}$, vs strain rate $\dot{\gamma }$ for different packing fractions $\varphi$.

Figure 5

(a) Scaling collapse of ${\eta }_{\mathrm{peak}}$ according to the scaling relation of Eq. (6). (b) Mean square displacement $\langle \Delta r^2\rangle$ vs MC passes for different $\varphi$. The inset shows the diffusion constant $D$ vs $\varphi$.