Chemistry Reference
In-Depth Information
from a more globular structure in state 2 (where the polymer is neutral) to a more
stretched structure in state 6 (where the polymer backbone is charged):
fv
þ
comb
p
þ D
56
m
D
conf
D
56
m
p
¼D
23
m
:
(151)
p
It is assumed that the fraction of polyions in a stretched configuration equals the
total degree of dissociation
a
of the repeating units. Furthermore, the difference
between the chemical potentials of a polyion in its stretched and its globular
structures is approximated using the combinatorial part of the UNIQUAC (univer-
sal quasichemical) model of Abrams and Prausnitz [
117
] for the excess Gibbs
energy of nonelectrolyte solutions. In the UNIQUAC model, the shape of a mole-
cule
i
is described by a volume parameter
r
i
and a surface parameter
q
i
. A change in
the polyelectrolyte's conformation changes only its surface parameter resulting in:
q
st
D
56
m
p
RT
¼
ln
ðY
st
Þ
ð
Þ
q
gl
q
st
5
a
q
gl
X
þ
ð
1
X
Þ
q
gl
q
st
:
(152)
ðY
gl
Þ
q
st
and
q
gl
are the polyelectrolyte's surface parameters in the stretched and the
globular configuration, respectively. Similarly,
Y
gl
are the polyelectro-
lyte's surface fractions in the stretched and the globular configuration, respectively,
and
Y
st
and
is the volume fraction of the polyelectrolyte in the aqueous solution. The
polyelectrolyte's surface fraction is:
X
m
p
m
o
q
ab
Y
ab
¼
for ''
ab''
either ''
st''
or ''
gl''
;
(153)
m
p
m
o
q
ab
þ
55
:
5
q
w
where
q
w
is the surface parameter of water. The surface parameter of the stretched
polyion is calculated using the surface parameter
q
rp
of a repeating unit and the
number
n
of repeating units which form that polyion:
q
st
¼ nq
rp
:
(154)
The surface parameter of the globular polyion is smaller than that of the
stretched polyion. It is approximated by introducing a configurational parameter
b
(that is close to, but smaller than 0.5):
2
b
q
rp
:
q
gl
¼ n
(155)
The polyelectrolyte's volume fraction is:
m
p
m
o
n
r
rp
X ¼
5
r
w
;
(156)
m
p
m
o
n
r
rp
þ
55
:
where
r
rp
and
r
w
are the volume parameters of a repeating unit of the polyion and of
water, respectively.
