Mechanical properties of glass forming systems

We address the interesting temperature range of a glass forming system where the mechanical properties are intermediate between those of a liquid and a solid. We employ an efficient Monte Carlo method to calculate the elastic moduli, and show that in this range of temperatures the moduli are finite for short times and vanish for long times, where short and long depend on the temperature. By invoking some exact results from statistical mechanics we offer an alternative method to compute shear moduli using molecular dynamics simulations, and compare those to the Monte Carlo method. The final conclusion is that these systems are not “viscous fluids” in the usual sense, as their actual time-dependence concatenates solidlike materials with varying local shear moduli.

Figure 1

(Color online) The shear modulus computed from Monte Carlo simulations as a function of the number of $h$ sweeps, for different values of the temperature.

Figure 2

(Color online) Trajectories of measured values of ${ϵ}_{xy}$ in the Monte Carlo simulations as a function of $n_{\mathit{h}}$. Upper panel, $T=0.1$. Middle panel, $T=0.3$. Lower panel, $T=0.5$.

Figure 3

(Color online) Results of molecular dynamics simulations. Black stars, exact calculation of ${\mu }_{\infty }^L$. Cyan diamonds and green circles, simulation results for ${\mu }_{\infty }$. Magenta squares and red triangles, the shear modulus according to Eq. (14).

Figure 4

(Color online) Trajectories from molecular dynamics simulations in the stress-energy plane, for three different temperatures. $U∕N$ is the potential energy of the system per particle. Each point represents an average over a duration of $50\tau$, connected with straight lines. The time of simulation is $1.5\times {10}^5\tau$. During this time with $T=0.2$ the system fluctuates around a single “solid state.” During the same simulation time when $T=0.3$ the system hops between three different and distinct “solid states.” When $T=0.4$ the fluctuations are so large that the shear modulus averages to zero during the simulation time.