Biomedical Engineering Reference
In-Depth Information
In this model, coordination number
z
(nearest neighbors) is between 6 and 12 depending
on the type of packing. For typical liquids at ordinary condition,
z
is close to 10.
By ignoring the size difference of solute and solvent, if the distribution of molecules is
totally random, the total change in Gibbs free energy is given by
∆
G
RT
=
(
N
ln
Φ
+
N
ln
Φ
)
(5.86)
1
1
2
2
where
N
N
Φ
=
1
Φ
=
2
1
2
N
+
N
N
+
N
1
2
1
2
N
1
is number of solvent molecules, and
N
2
is the number of solute molecules; therefore,
total number of lattice site is
N
1
+
N
2
. The excess Gibbs free energy in this case is zero, cor-
responding to ideal solution.
Wilson Model
Wilson [54] considered interaction between molecules in a mixing (Figure 5.8) and pro-
posed a new expression for excess Gibb's free energy. In his derivation, the interaction
between molecules surrounding a central molecule is considered based on the random
distribution of molecules described by Flory and Huggins. The models derived based on
this assumption are called “local composition models.”
In a binary system, the mole fraction of molecule 2 around molecule 1 and the mole frac-
tion of molecule 1 around molecule 1 are assumed to be related by:
x
x
x
x
exp(
−
−
g
/
RT
)
21
11
=
2
1
21
11
(5.87)
g
RT
exp(
/
)
g
is are energies of interaction between molecules, and
x
i
is the overall mole fraction in the
mixture. For athermal mixtures, the excess Gibbs free energy is
1
2
1
2
1
2
2
1
1
FIGURE 5.8
Local composition lattice.
