Biomedical Engineering Reference
In-Depth Information
Flory-Huggin's Model
The partial molar excess Gibbs free energy is
E
g
RT
1
(
)
*
*
=
x
ln
1
−
Φ
1
−
−
x
ln
r
−
Φ
r
−
1
(5.107)
1
2
2
2
r
and
1
1
*
*
ln
=
ln
1
−
1
−
Φ
+
1
−
Φ
(5.108)
γ
1
2
2
r
r
For large value of
r
, the activity coefficient of the solvent is independent of
r
.
Since a real polymer solution is not athermal, the interaction between molecules plays
important roles. To account for the enthalpy contribution, an intermolecular interaction
parameter,
χ
, which is also known as Flory-Huggins interaction parameter, is introduced.
The activity coefficient then becomes
1
1
*
*
*
Φ
2
ln
=
ln
1
−
1
−
Φ
+
1
−
Φ
+
(5.109)
γ
χ
1
2
2
2
r
r
where
χ
=
w
kT
If
r
is the ratio of molar volume
v
RT
(
)
2
(5.110)
=
1
−
χ
δ
δ
1
2
UNIQUAC-Based Description for Polymer Solution
In polymer solution, where charged species are present, that is, protein solution and geomet-
ric distribution of molecules, intermolecular forces are very different from the uncharged
solution (nonelectrolyte). For the geometric distribution, because of electrostatic repulsion,
ions with the same charge are far apart, so in consideration of the local composition, only
neutral and counterions are present in the neighborhood. Therefore, the combinatorial
excess free energy becomes [60]
m
m
n
n
*
a
aiii
g
E
combinatorial
Φ
z
θ
∑
ln
∑
∑
∑
ji
ii
ii
=
x
+
q x
ln
+
q x
ln
a
+
θ
ln
ii
ii
ii
ii
ii
ii
j
RT
x
2
*
Φ
ii
ii
=
1
ii
=
1
ii
=
1
j
j
=
≠
1
ii
ii
1
θτ
(5.111)
a
=
∑
ii
j
ji
a
=
a
τ
ji
ji
ii
