Size Effect on Transport Properties of Gaseous Argon: A Molecular Dynamics Simulation Study

Results and Discussion

The mean square displacement (MSD) of gaseous argon increases nonlinearly over 500 ps and shows a straight line between 1000 and 3000 ps.,1 but the MSD of liquid argon shows a linear behavior within 3 ps (see the inset of Figure 2 in Ref. 1). The velocity auto-correlation (VAC) function also shows a dramatic difference. The VAC of liquid argon decays to 0 within 0.5 ps and has a negative value due to the collision with the neighboring particle (see the inset of Fig.3 in Ref. 1), but the VAC of gaseous argon decays very slowly to 0 over 3000 ps.1

Table 1 lists diffusion coefficients of the gaseous argon for N = 432, 1728, and 6912 at 273.15 at 1 atm obtained from MSD’s using Eq. (1) and VAC’s using Eq. (2) which are in good agreement with the experimental measures4 and are superior to the predictions of the kinetic theory from mole-cular collision4 as discussed in Ref.1. As the number of argon molecules increases, D obtained from MSD appro-aches the exact experimental measure (0.153→0.156→ 0.157) but D obtained from VAC lacks the accuracy (0.165 →0.154→0.156). The results using other LJ parameters8 for N = 1728 are slightly better than those using the original LJ parameters.

Stress auto-correlation (SAC) and heat-flux auto-corre-lation (HFAC) functions of the gaseous argon at 273.15 K and 1 atm are plotted in Figures 1 and 2. Both correlation functions are monotonically decreased and decays very slowly to 0 over 3000 ps. In the inset of Figure 1, we plot the detailed SAC functions in the very narrow y-axis around the zero correlation. For N = 432, the fluctuation of the SAC function is very high, but it lowered with increasing number of argon molecules. The SAC function for N = 1728 is acceptable and that for N = 6912 is more perfect.

Figure 1.Stress auto-correlation functions (kJ/mol·K·Å·ps3) of gaseous argon at 273.15 K and 1.00 atm. The inset shows the detailed behavior of SAC functions.

Running integrals for η(t) of gaseous argon for N = 432, 1728, and 6912 at 273.15 K and 1 atm are plotted as a function of time in Figure 3. All the running integrals for viscosity clearly show plateaus which signify that the corre-sponding SAC functions have decayed to zero and are fluctuating along the horizontal time axis except for N = 432. As shown in the inset of Figure 1, all the SAC functions reach zero at about 1200 ps and we report the shear viscosities for N = 432, 1728, and 6912 at 273.15 K and 1 atm in Table 1 by averaging the running integrals for shear viscosity in Figure 3 for 1200-3000 ps.

The shear viscosities, η, obtained by MD simulations at 273.15 K and 1 atm underestimate the experimental measure for all the values of N. η for N = 432 is closer to the experi-mental measure than those for larger N’s in Figure 3, but the result for N = 432 is unreliable due to the high fluctuation of the SAC function as seen in the inset of Figure 1. η for N = 6912 is better than η for N = 1728 and increasing N makes the result slightly better. η obtained for N = 1728 using other LJ parameters8 is also comparable to that using the original LJ parameters.

Figure 2.Heat-flux auto-correlation functions (kJ/mol·Å3) of gaseous argon at 273.15 K and 1.00 atm. The inset shows the detailed behavior of SAC functions.

Figure 3.Running integrals for η(t) (μP) of gaseous argon at 273.15 K and 1 atm.

Figure 4.Running integrals for λ(t) (J/m·s·K) of gaseous argon at 273.15 K and 1 atm.

The situation for HFAC is very similar to that for SAC. In the inset of Figure 2, the detailed HFAC functions in the very narrow y-axis around the zero correlation show the high fluctuations of the HFAC function for N = 432 and 1728, but it lowered with increasing number of argon molecules. The HFAC function for N = 1728 is better than that for N = 432, and that for N = 6912 is more reliable.

Running integrals for λ(t) of gaseous argon for N = 432, 1728, and 6912 at 273.15 K and 1 atm are plotted as a function of time in Figure 4. All the running integrals for thermal conductivity clearly show plateaus which signify that the corresponding HFAC functions have decayed to zero and are fluctuating along the horizontal time axis. As shown in the inset of Figure 2, all the HFAC functions reach zero at about 1500 ps and we report the thermal conduc-tivities for N = 432, 1728, and 6912 at 273.15 K and 1 atm in Table 1 by averaging the running integrals for thermal conductivity in Figure 3 for 1500-3000 ps.

The thermal conductivities, λ, obtained by MD simula-tions at 273.15 K and 1 atm overestimate the experimental measure for N = 432 and underestimate for N = 1728 and 6912. λ for N = 432 is too high compared to the experi-mental measure and this result is unreliable due to the high fluctuation of the HFAC function as seen in the inset of Figure 2. λ for N = 6912 is better than λ for N = 1728 and increasing N makes the result closer to the experimental measure. λ obtained for N = 1728 using other LJ parameters8 is much better than that using the original LJ parameters.

In summary, we have carried out a series of equilibrium molecular dynamics (EMD) simulations of gaseous argon at 273.15 K and 1.00 atm for the calculation of transport properties as a function of the number of argon molecules (N). While the diffusion coefficients (D) of gaseous argon approach to the experimental measure with increasing N, the viscosities (η) and thermal conductivities (λ) obtained for N = 432 are unreliable due to the high fluctuation of the time correlation functions and those for N = 1728 are rather acceptable. Increasing further to N = 6912 has improved the MD results a little closer to the experimental measures for η and λ. Both the EMD results for η and λ for N = 6912 underestimate the experimental measures and it is not expected that the more increasing N makes the closer results to the experimental measures. One possible explanation for the large disagreement between MD results and the experi-mental measures for η and λ may be due to the use of LJ parameters which were used for liquid argon.