Chemistry Reference
In-Depth Information
like that used by Shah and Maginn
77
suffer from convergence problems, espe-
cially for systems that are dense and have specific interactions such as ionic
liquids. More sophisticated simulation methods are required to overcome
these limitations, and Shah and Maginn subsequently implemented an
expanded ensemble Monte Carlo method
79
that improves the test particle
insertion approach significantly. This method involves a series of Monte Carlo
moves that change the strength with which the solute molecule couples with
the solvent, ranging from no coupling (an ideal gas) to full coupling (a dis-
solved solute molecule). By collecting the frequency with which the system
visits the ideal-gas state and fully coupled state, the excess chemical potential
of the solute (and hence, Henry's law constant) can be computed. Additional
self-adapting bias factors were used to further improve sampling. The authors
used the method to compute the Henry's law constants of water, carbon diox-
ide, ethane, ethene, methane, oxygen, and nitrogen in [C
4
mim][PF
6
]. Their
results were in good qualitative agreement with experiment, and in many
cases, quantitative agreement was achieved. For example, the computed
Henry's law constant for water at 298 K is 0
:
07
0
:
02 bar, while the experi-
mental result is 0
16 bar,
while the experimental value is 53.4 bar. These results suggest that earlier
inaccuracies are due more to sampling problems than to inherent inaccuracies
in the force field used.
Complete isotherms for CO
2
, CO, and H
2
in [C
4
mim][PF
6
] were com-
puted by Urukova, Vorholz, and Maurer
80
using the isothermal-isobaric Gibbs
ensemble Monte Carlo method. In Gibbs ensemble Monte Carlo studies, sepa-
rate gas-phase and liquid-phase systems are coupled virtually so that
exchanges of molecules take place between the two phases to satisfy the phase
equilibrium condition. Temperatures ranging from 293 to 393 K and pressures
up to 9MPa were simulated, using a rigid model for the ionic liquid and para-
meters taken from Shah and Maginn.
39
They found that the simulations agree
remarkably well with available experimental data. The original study
80
contained a small conversion factor error, however, which, when corrected,
81
gives results that are not as close to experiment as indicated in the original
study.
Shi and Maginn
82
proposed a new type of Monte Carlo method they call
continuous fractional component Monte Carlo, or CFC MC. This is a simula-
tion procedure that enables isotherms to be computed accurately for gases and
vapors in ionic liquids by inserting and deleting molecules gradually, instead of
performing the moves all in one step. They used CFC MC to compute iso-
therms of water and carbon dioxide in 1-
n
-hexyl-3-methylimidazolium bis(tri-
fluoromethylsulfonyl)imide ([C
6
mim][Tf
2
N]).
83
Figure 9 shows an example of
the accuracy that can be obtained with the method; the computed isotherm is
in quantitative agreement with three independent sets of experimental data up
to about 70 bar.
84-86
At the very highest pressure of 200 bar, it appears that
the simulations underpredict slightly the CO
2
concentration, which may reflect
:
17
0
:
02 bar. For CO
2
the computed value is 46
