Biomedical Engineering Reference
In-Depth Information
Universal Quasi-Chemical Theory
The previous models are applicable to the case in which solute and solvent are of the same
size. For nonrandom solution containing nonelectrolyte molecules of different sizes, the
model universal quasi-chemical theory (UNIQUAC) was developed based on the same
local composition description [56]. In UNIQUAC equation, excess Gibbs free energy has
two parts, a combinatorial part that describes the dominant entropic contribution and a
residual part that is due primarily to short-range intermolecular forces that induce enthalpy
contribution. The combinatorial part is affected only by the composition, sizes, and shapes
of the molecules of pure component.
E
E
E
g
RT
g
RT
g
RT
=
+
(5.96)
combinatorial
residual
For binary:
*
*
E
g
RT
Φ
Φ
z
θ
θ
=
x
ln
1
1
+
x
ln
2
2
+
x
q
ln
1
+
x q
ln
2
1
2
1 1
2 2
x
x
2
*
*
Φ
Φ
combinatorial
1
2
g
RT
E
(
)
−
(
)
= −
x q
ln
+
x q
ln
+
θ
θ τ
θ
θτ
1 1
1
2 21
2 2
2
1 21
residu
al
coordination number z=10
segment fraction
(5.97)
x r
x
1 1
x r
*
=
Φ
*
Φ
1
1 1
=
2 2
2
r
+
x r
x r
+
x r
2 2
1 1
2 2
are
a fraction
x q
x q
x q
1 1
2 2
θ
=
θ
=
1
2
x q
+
x q
+
x q
1 1
2 2
1 1
2 2
x q
x q
x q
=
1 1
=
2 2
θ
θ
2
1
x q
+
x q
+
x q
1 1
2 2
1 1
2 2
R
,
q
, and
q
→
are pure-component molecular-structure constants.
q
→
is the surface of interac-
surface of interac-
tion, and
q
is the geometric external surface [58]. In the original derivation of Abrams and
Prausnitz [56],
q
→
and
q
were not distinguished, but for water and lower alcohols (for water,
r
= 0.92,
q
= 1.4,
q
→
= 1 [58]), they are different. Only for fluids other than water and lower
alcohols,
q
=
q
→
.
the surface of interac-
g
−
g
=
exp
−
12
22
τ
12
T
(5.98)
g
−
g
21
11
=
exp
−
τ
21
T
