Decoupled length scales for diffusivity and viscosity in glass-forming liquids

The growth of the characteristic length scales both for diffusion and viscosity is investigated by molecular dynamics utilizing the finite-size effect in a binary Lennard-Jones mixture. For those quantities relevant to the diffusion process (e.g., the hydrodynamic value and the spatial correlation function), a strong system-size dependence is found. In contrast, it is weak or absent for the shear relaxation process. Correlation lengths are estimated from the decay of the spatial correlation functions. We find the length scale for viscosity decouples from the one of diffusivity, featured by a saturated length even in high supercooling. This temperature-independent behavior of the length scale is reminiscent of the unapparent structure change upon supercooling, implying the manifestation of configuration entropy. Whereas for the diffusion process, it is manifested by relaxation dynamics and dynamic heterogeneity. The Stokes-Einstein relation is found to break down at the temperature where the decoupling of these lengths happens.

Figure 1

System-size-dependent diffusion coefficient for particle $A$. The data are normalized by the factor $D_0^A$, which is the diffusivity for infinite system size, obtained via the fitting of formula (2) (solid green lines). Numbers of particles used for the points from right to left are $N=200$, 400, 800, 1600, 3000, 6000, 12 000, 24 000, 50 000, 100 000.

Figure 2

System-size-dependent shear viscosity. The vertical dashed line is an estimation of the constant critical box length ( = 9 $\sigma$) above which the finite-size effect disappears for all low-temperature liquids.

Figure 3

Modulus of the spatial correlation function of the displacement field for different systems. In the lower two panels, (c) and (d), clear dip points emerge as the correlation function turns from positive to negative. The decay of the correlation and the dip points show a clear system size dependence.

Figure 4

Spatial correlation function of atomic-level shear-stress field for (a) $N=6000$ particles system and (b) $N=100000$ particles system. The decay of the correlation function does not show a clear system-size dependence.

Figure 5

Spatial correlation function of the atomic shear stress field at different times. The left panels (a)–(d) are for high-temperature liquid ($T=1$), while the right panels (e)–(h) are for low-temperature liquid ($T=0.47$). Two different system sizes are shown, i.e., $N=1600$ and $N=100000$, for a comparison.

Figure 6

(a) The critical box length required to reach the hydrodynamic value for the diffusivity (from Fig. 1) and the viscosity (from Fig. 2). The inset picture (b) is the Stokes-Einstein relation for a small and large box-length systems. (c) The correlation lengths calculated by exponential fitting of the spatial correlation function for displacement (Fig. 3) and atomic shear-stress (Fig. 4) fields. The green arrows mark the temperature point where the SER significantly brakes down.