Chemistry Reference
In-Depth Information
2.4
2.0
1.6
1.2
0.8
0.4
0.0
-0.2
0
0.2
0.4
0.6
0.8
1.0
Mole Fraction Ethanol,
x
1
FIGURE 6.5
Activity coefficients (based on simulations) of (1) ethanol (◻,◼)/(2) HFC-
227ea (Δ,
▲
) at 283.17K (⎯) and 343.13 K (- - -). (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. Reprinted with per-
mission from Elsevier.)
the antiderivative of Equation 6.23 used is
(
)
+
(
)
−−
br c
(
)
Gr
smooth
()
=−
4π
apr
()cos(
d rc
−
)
qr
( )sin
dr c
(
−
)
e
+
f
d
bd
r
bd
bd
4
dbd
bd
3
−
+
3
2
2
pr
()
=
+
r
−
2
(6.24)
2
2
2
2
2
2
2
3
+
(
+
)
(
)
b
bd
r
2
(
bd
2
−
2
)
2
3
db b
bd
2
−
3
2
qr
()
=
+
r
−
2
2
2
2
2
2
2
3
+
(
b
+
d
)
(
+
)
The parameters for
G
smooth
(
r
) were fitted to the sampled
G
(
r
) for
r
ranging from
r
u
3
to
r
max
, as defined above. The method was used to obtain isothermal compressibili-
ties of five pure alkanes at three different state points and these were compared to the
values derived from simulated overall density fluctuations. Results showed that the
two approaches were fully consistent in values and uncertainties. Further, the com-
putations converged in approximately the same simulation times. This suggests that
computation of TCFIs is a route to isothermal compressibility, as accurate and fast
as well-established benchmark techniques, with the advantage that it can be used in
any ensemble (Puliti, Paolucci, and Sen 2011). Note that this approach has only been
successfully tested on pure fluids. The main limitation of both methods (Christensen
et al. 2007a, 2007b, 2007c; Wedberg, Peters, and Abildskov 2008) is that they apply
only to systems where the TCF tails can be approximated by the model equations,
which may not be true in general.
