Chemistry Reference
In-Depth Information
Fig. 9 Theory of Lifson and Katchalsky: Integration constant
b
as a function of the charge density
parameter
l
for several parameters
g
LK
c
p
VRTf
el
D
F
LK
¼
(39)
with:
h
i
n
l
g
LK
ð
Þ
ð
Þ
2
2
2
ð
exp
g
LK
Þ
1
ð
1
l
Þ
b
2
2
f
el
2
ln
1
ð
l
Þ
b
¼
;
(40)
l
ln
l
1
þ b
2
l
2
1
b
where
c
p
is the molarity of the polyelectrolyte in the solution, and
V
is the volume of
the solution (i.e.,
c
p
V
is the number of moles of polyelectrolyte in the solution) and
n
is the number of repeating units of the polyelectrolyte.
The osmotic pressure
p
is split into two contributions:
el
p ¼ p
id
:
mix
:
þ Dp
;
(41)
where the osmotic pressure of the ideal mixture
p
id.mix.
is calculated assuming that
the polyelectrolyte is completely dissociated. When the repeating unit is a 1:1
electrolyte that contribution is:
p
id
:
mix
:
¼ð
1
þ nÞ
c
p
RT
:
(42)
el
is caused by the electrostatic potential. It is
calculated from the contribution of the electrostatic forces to the Helmholtz energy:
The second contribution
Dp
T;
composition
:
F
el
@
¼
@
el
Dp
(43)
V
