Chemistry Reference
In-Depth Information
425 K. They used a large system (864 ion pairs) and carried out impressively
long runs, equilibrating their system for 5 ns and performing a 16-ns produc-
tion run. To compute the shear viscosity, they took the average of 10 separate
Green-Kubo integrations, each of which was over a 1-ns time period. Like-
wise, the electrical conductivity was evaluated from 11 independent 90-ps
Green-Kubo integrations. The self-diffusivity was not evaluated from a
Green-Kubo integral, but rather from the integrated Einstein formula
(Eq. [15]). Figure 16 depicts the short- and long-time behavior of the cation
and anion mean-square displacement, obtained from a single 6-ns trajectory.
Both ions appear (by the heuristics defined earlier) to be in the diffusive
regime;
the computed self-diffusivities
for
the anion and cation are
10
10
and 1
10
10
m
2
1
s, respectively. It is interesting to see that
the larger cation actually has a greater self-diffusivity than the smaller chloride
anion. This curious behavior has been observed repeatedly for imidazolium-
based ionic liquids in simulations
49,60,104
as well as in experiments.
105,106
It
is not a universal phenomenon for ionic liquids, however, as Cadena and
co-workers showed with simulation and NMR experiments of alkylpyridi-
nium [Tf
2
N] ionic liquids.
64
Urahata and Ribeiro
100
were the first to explain
why imidazolium cations have larger self-diffusivities than the anions to which
:
33
:
88
=
12
2
1
8
0
0
10
20
4
Cl
[mmim]
(a)
0
0
100
200
300
400
500
60
40
20
(b)
0
0
1000
2000
3000
Time (ps)
Figure 16
(a) Mean-squared displacement data of [C
1
mim] and [Cl] at 425 K. The inset
shows the same data at short times. Note the larger inertial motion of chloride ions, as
expected. (b) Mean-squared displacement data from a single long trajectory of 6 ns.
(Taken from Ref. 103 and used with permission.)
