Biomedical Engineering Reference
In-Depth Information
where
z
(
)
−
(
)
l
=
r
−
q
r
−
1
j
j
j
j
2
The first three terms are derived from the combinatorial contribution, and the rest of the
three terms are from the residual part of the excess free energy.
Although
r
does not correspond to the exact size of molecules, it measures the relative
size of the solute over solvent. The relative size of the solute dramatically affects the solute
activity coefficient. The solute with a bigger size is more sensitive to composition, whereas
the solvent activity coefficient is independent of the solute size as long as protein solutes
are concerned.
UNIQUAC Functional-Group Activity Coeficients
The interaction between molecules is accounted by the residual part of UNIQUAC model.
By considering the interaction between functional groups of the molecules in the mixture,
the residual part of UNIQUAC model could be calculated from each functional group of
the molecule by
∑
γ
i
R
( )
i
( )
i
ln
=
n
ln
Γ
−
ln
Γ
(5.102)
k
k
k
k
where
n
k
( )
is the number of groups of type
k
in molecule
I
,
Γ
k
is the group residual activ-
ity coefficient, and Γ
k
( )
is the residual activity coefficient of group
k
in a reference solution
containing only molecules of type
i
.
Θ
∑
∑
τ
m km
ln
Γ
=
Q
1
−
ln
Θ
−
τ
∑
k
k
m mk
Θ
τ
m
m
n nm
n
Q x
Q x
Θ
=
m m
∑
m
(5.103)
n n
n
a
T
=
exp
−
mn
τ
mn
A
Q
wk
=
k
2 5 10
9
.
×
A
wk
is the group surface area.
a
mn
is the group interaction parameter and can be found
in the literature [59]. From this model, the activity coeffi cient can be estimated by struc-
activity coeficient can be estimated by struc-
ture analysis of the components in the system from available experimental data. This
model is widely known as UNIQUAC Functional-group activity coefficients, or UNIFAC
model.
the activity coeffi cient can be estimated by struc-
