Density fluctuations and random walks in an overdamped and supercooled simple liquid

In this work, the short-time dynamics of simple liquid is explored both analytically and numerically with the focus on the interplay between the density fluctuations in a volume surrounding a chosen particle and its random walk motion. The particles interact via the Lennard-Jones potential with parameters corresponding to liquid argon. For large times, analytical calculations based on the fluctuation theory provides an explicit expression reproducing isothermal change of the self-diffusion coefficient in liquid argon corresponding to the experimental data. These results lead to the conclusion that such behavior is based on the reduced mobility of particles reflected in their density fluctuations that can be equivalently achieved in the cases of either low temperatures and pressures (supercooling) or moderate temperatures and high pressures (overdamping).

Figure 1

The logarithm of inverse reduced density fluctuations (1) density calculated using actual thermodynamic data of liquid argon at the saturation conditions from $T=90\mathrm{K}$ to the triple point and along the isotherm $T=90\mathrm{K}$. Thin solid line is a linear fit of the saturated data.

Figure 2

Mean square displacements for the coordinates, i.e., Eq. (5) with $f_{x,y,z}=(x,y,z)$ (MSD) (a) and the velocity, i.e., Eq. (5) with $f_{x,y,z}=(v_x,v_y,v_z)$ (MSV) with two kinds of scaling (b), (c) in L-J liquids mimicking liquid argon at $T=90\mathrm{K}$ under saturation conditions (black solid curve), $P=20M\mathrm{MPa}$ (blue dashed curve), and the density corresponding to the latter at at $T=81.27\mathrm{K}$ (red dash-dotted curve). The green dotted line fits a ballistic motion at very short times.

Figure 3

The normalized power spectral density of the random force $\xi \left(i\right)$ included into Eq. (7) for three cases considered—their coloring is the same as in Fig. 2. The green dotted line is an exponential function shown for guidance.

Figure 4

Experimental (red circles) and calculated via FT-EoS values of the density (a) and the reduced self-diffusion coefficient (b) of liquid argon along the isotherm $T=90\mathrm{K}$. For the density, the experimental data uncertainty range does not exceed markers size; for the coefficient of self-diffusion, it is denoted explicitly.