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Dynamics of viscous liquids and the Random Barrier Model

Thomas B. Schrøder, Jeppe C. Dyre, Camille Scalliet

Abstract

This paper combines the particle-swap Monte Carlo algorithm with long GPU molecular dynamics simulations to analyze the dynamics of a ternary Lennard-Jones glass-forming liquid in the extremely viscous regime. The focus is on the inherent dynamics, obtained by quenching configurations along the configuration-space trajectory into their inherent state. We compare how two functional forms, the von Schweidler law and the random barrier model (RBM) prediction in the extreme disorder limit, fit data for the inherent mean-squared displacement as a function of time. We find that the RBM, which has no dimensionless free parameters, generally fits the data better than the von Schweidler law, despite the latters one dimensionless free parameter. In particular, this implies that the RBM predicts the value of the diffusion coefficient from short-time simulation data more accurately than does the von Schweidler expression. It remains an open question why the RBM reproduces well the inherent data despite this models (unrealistic) assumption of identical energy minima.

Dynamics of viscous liquids and the Random Barrier Model

Abstract

This paper combines the particle-swap Monte Carlo algorithm with long GPU molecular dynamics simulations to analyze the dynamics of a ternary Lennard-Jones glass-forming liquid in the extremely viscous regime. The focus is on the inherent dynamics, obtained by quenching configurations along the configuration-space trajectory into their inherent state. We compare how two functional forms, the von Schweidler law and the random barrier model (RBM) prediction in the extreme disorder limit, fit data for the inherent mean-squared displacement as a function of time. We find that the RBM, which has no dimensionless free parameters, generally fits the data better than the von Schweidler law, despite the latters one dimensionless free parameter. In particular, this implies that the RBM predicts the value of the diffusion coefficient from short-time simulation data more accurately than does the von Schweidler expression. It remains an open question why the RBM reproduces well the inherent data despite this models (unrealistic) assumption of identical energy minima.
Paper Structure (14 sections, 8 equations, 11 figures)

This paper contains 14 sections, 8 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Model
  4. Simulation methods
  5. Observables
  6. Results
  7. Validation of the numerical strategy
  8. Thermal and inherent MSD results
  9. Fitting the inherent MSD
  10. von Schweidler fit
  11. Random Barrier Model fit
  12. Predictive power of the two fits
  13. Discussion
  14. Appendix

Figures (11)

  • Figure 1: All-particle mean-square displacement (MSD) as a function of time in log-log plots at the three highest temperatures studied. Full lines: Results of MD simulations preceded by a MD equilibration run of same length. Data points: Results averaged over 20 independent MD simulations, each initiated by an equilibrium configuration generated by particle-swap. Error bars indicate one-standard-deviation error estimates. As expected, the dynamics is the same within the error bars.
  • Figure 2: Mean-square displacement as a function of time in log-log plots for (a) A, (b) B, (c) C, and (d) all particles at all temperatures studied. All initial configurations were equilibrated by swap. For each temperature, two curves are shown: The thermal MSD (for the three highest temperature these are the same data as in Fig. \ref{['fig:msd']}), and the inherent dynamics.
  • Figure 3: Fits (a,c) and residuals (b, d) for the inherent all-particle MSD data (crosses). (a, b)) Fitting to the inherent von Schweidler (IvS, Eq. (\ref{['eq:vonschweidler']})). (c, d) Fitting to the Random Barrier Model (RBM, Eq. (\ref{['eq:FitRBMs']})). The residuals are computed as $\log_{10}(\langle \Delta r^2(t) \rangle / \textrm{MSD}_{fit})$. Between the black dashed lines in (b, d), the fits are less than 10% off from the data. Despite having one less parameter, the RBM model fits the low temperature data better than the inherent von Schweidler law. In particular, the RBM fits the simulation data significantly better at long times.
  • Figure 4: Same as Fig. \ref{['fig:imsd_fits_All']}, except that fits are here restricted to $t<3\cdot 10^{5}$, highlighted by the shaded region.
  • Figure 5: Diffusion constant obtained by fitting the von Schweidler and RBM predictions to the IS MSD over a time window starting at 10 LJ time units, terminating at the time indicated on the horizontal axis. The horizontal dashed lines highlight the value obtained for fitting the whole trajectory, with the bullet/error bar (left) indicating an error of 10% around it. Temperature decreases from top to bottom.
  • ...and 6 more figures