Chemistry Reference
In-Depth Information
Figure 17 where the convergence of the Green-Kubo integral is plotted.
Despite the fact that the actual stress-stress correlation function has essentially
reached zero after about 3 ps, the integral itself is still increasing after 500 ps.
This behavior is entirely consistent with the results of Urahata and Ribeiro
(shown in Figure 15), and the other dynamical studies discussed earlier. There
is a large separation of time scales for different motions, so computing a trans-
port coefficient that depends on these different modes requires time scales
longer than the longest relevant relaxation time. A similar observation was
made by Rey-Castro and Vega for [C
2
mim][Cl],
107
who computed the self-
diffusivity, shear viscosity, and electrical conductivity using equilibrium MD
over a temperature range of 380-486 K. These authors improved their
estimates by fitting their time correlation function results to empirical analytic
expressions and then integrating those expressions.
Before leaving the topic of Green-Kubo integrals for transport proper-
ties, we mention briefly the characteristics of the electric current correlation
functions that are used to compute the electrical conductivity. Figure 18 shows
the electric current and velocity autocorrelation functions for [C
2
mim][Cl] at
486 K and 1 bar. The current fluctuations decay rapidly and appear to vanish
1
0.5
0.4
0.3
0.2
0.5
0.1
0
∆(
t
)
0 0 0 0
t
(ps)
80
100
0
Total v
acf
Current acf
0
0.2
0.4
0.6
0.8
t
(ps)
Figure 18
Normalized electric current autocorrelation function of [C
2
mim][Cl] at
486K and 1 bar (bold solid line); total velocity autocorrelation function (dashed line);
and difference between them (gray). The inset shows the running integral of the
electrical conductivity (gray line), together with the best-fit exponential decay function
(black line). (From Ref. 107 and used with permission.)
