Biomedical Engineering Reference
In-Depth Information
The combinatorial part is given by [65]
z
q
φ
φ
ln
C
ln
i
ln
i
γ
= −
1
φ
+
φ
−
1
−
+
i
i
i
i
2
F
F
i
i
(5.104)
r
r x
q
r x
=
i
,
F
=
i
φ
∑
∑
i
i
j
j
j
j
j
j
r
and
q
can also be estimated by
∑
∑
( )
i
( )
i
r
=
v R
q
=
v Q
i
k
k
i
k
k
k
k
(5.105)
V
R
=
wk
k
15 17
.
R
k
and
Q
k
are the van der Waals group volume and surface area, respectively, and their
value can also be found in literature [59].
Polymer Solution
In the delivery of macromolecules, there are specific issues to be considered: first of all,
the solute and solvent molecules are of different sizes; second, they are chemically dis-
; second, they are chemically dis-
similar; and third, proteins are usually charged. Hence, the solution equations for nonelec-
s; second, they are chemically dis-
equations for nonelec-
trolytes are not completely applicable to polymer solution (protein solution). Recall from
the UNIQUAC model that excess Gibbs free energy is composed of a combinatorial term,
which accounts for the entropy of mixing, and a residual term, which accounts for the
enthalpy of mixing. We start by considering the entropy contribution of a polymer solu-
ion equations for nonelec-
polymer solu-
tion; this is because of the huge difference in size and shape between solvent and solute. By
applying Lattice model again, assume athermal solution behavior and consider that poly-
mer is composed of
r
segments, each having the same size as that of a solvent molecule.
Change in Gibbs free energy is
a polymer solu-
c
G
RT
ln
*
ln
*
)
=
(
N
Φ
+
N
Φ
1
1
2
2
where
(5.106)
N
N rN
N
*
*
Φ
=
1
Φ
=
2
1
2
+
N
+
rN
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
+
rN
2
.
r
, according to the definition, is the ratio of the molecular volumes of the polymer and
the solvent. As in the UNIQUAC model, the ratio of surface area of the polymer and the
solvent gives
q
, and
q
/
r
is a measure of polymer shape.
