Feasibility of a single-parameter description of equilibrium viscous liquid dynamics

Molecular dynamics results for the dynamic Prigogine-Defay ratio are presented for two glass-forming liquids, thus evaluating the experimentally relevant quantity for testing whether metastable-equilibrium liquid dynamics is described by a single parameter to a good approximation. For the Kob-Andersen binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid, a single-parameter description works quite well. This is confirmed by time-domain results where it is found that energy and pressure fluctuations are strongly correlated on the $\alpha$ time scale in the constant-volume, constant-temperature ensemble; similarly, energy and volume fluctuations correlate strongly in the constant-pressure, constant-temperature ensemble.

Figure 1

(Color online) (a) shows the imaginary parts (scaled to maximum value) of $-c_v\left(\omega \right)$, $-{\beta }_v\left(\omega \right)$, and $1/{\kappa }_T\left(\omega \right)$ for the Kob-Andersen binary Lennard-Jones (BLJ) 80-20 mixture [27]; (c) shows the same for a system of asymmetric dumbbells [28]. The dashed lines indicate Debye relaxation with relaxation times ${\tau }_{\alpha }=2000$ ${\sigma }_{aa}\sqrt{m/{ϵ}_{aa}}$ and ${\tau }_{\alpha }=1600\text{ps}$, respectively. (b) and (d) show the corresponding dynamic Prigogine-Defay ratios, Eq. (2). For both systems the total simulation time covers more than ${10}^4{\tau }_{\alpha }$.

Figure 2

(Color online) (a) and (b) Fluctuations of energy and pressure in the $NVT$ ensemble for the Kob-Andersen binary Lennard-Jones mixture [27] and the asymmetric dumbbell system [28]. Each point represents an average over a time interval of $0.1{\tau }_{\alpha }$ where ${\tau }_{\alpha }$ is defined as the inverse loss-peak frequency [Figs. 1a, 1c]. Energy and pressure fluctuations are highly correlated, showing that a single-order-parameter description is a good approximation. (c) and (d) Fluctuations of energy and volume in the $NpT$ ensemble at the same state points as (a) and (b), respectively.