Chemistry Reference
In-Depth Information
1600
1400
1200
1000
800
600
400
200
0
0
0.2
0.4
0.6
0.8
1.0
Mole Fraction Ethanol,
x
1
FIGURE 6.4
Ethanol/HFC-227ea pressure-composition diagram at 343 K. --◻--
Experiment. (Data from F. H. Case, J. Brennan, A. Chaka, K. D. Dobbs, D. G. Friend,
D. Frurip, P. A. Gordon, J. Moore, R. D. Mountain, J. Olson, R. B. Ross, M. Schiller,
and V. K. Shen, 2007, The Third Industrial Fluid Properties Simulation Challenge,
Fluid
Phase Equilibria,
260, 153. With permission.) ⎯
From simulation. ⎯
• •
⎯
Ideal solution.
(Data from S. Christensen, G. H. Peters, F. Y. Hansen, J. P. O'Connell, and J. Abildskov,
2007b, Generation of Thermodynamic Data for Organic Liquid Mixtures from Molecular
Simulations,
Molecular Simulation
, 33, 449; Modified from S. Christensen, G. H. Peters,
F. Y. Hansen, J. P. O'Connell, and J. Abildskov, 2007c, State Conditions Transferability of
Vapor-Liquid Equilibria via Fluctuation Solution Theory with Correlation Function Integrals
from Molecular Dynamics Simulation,
Fluid Phase Equilibria
, 260, 169.)
behavior, as shown in Figure 6.5. The total pressures show positive deviations from
Raoult's law, but the activity coefficients have a maximum for HFC-227ae and a
minimum for ethanol near
x
1
= 0.45.
The approach of Christensen was later modified by Wedberg, Peters, and
Abildskov (2008). First, the 5-parameter form of Equation 6.18 was changed to a
4-parameter form,
[
]
(
)
indirect
−−
br c
(
)
g
()
r
=+⋅
1
a
exp
sin
d rc
(
−
)
(6.22)
ij
Next, a tail model corresponding to the antiderivative of the trial expression for
g
(
r
)
was fitted to the truncated numerical integral of
g
(
r
) as a function of the upper inte-
gration limit. This tail model was then used to extrapolate
H
(
R
lim
) to
R
lim
= ∞, which
yielded the value of the TCFI. Defining the running integrals of the RDF,
G
(
r
),
r
∫
[
]
2
Gr
()
=
4
π
rgr
′
()
′ −
1
drH
′
,
=
lim
ρ
G
(6.23)
r
→∞
0
