Chemistry Reference
In-Depth Information
Summing up the contributions from the five steps gives the chemical potential of
the polyion in an aqueous solution. The chemical potential of the polyion on the
molality scale is also given by:
RT
ln
m
p
ref
p
m
g
ðmÞ
m
p
¼ m
þ
(157)
p
and the activity coefficient is:
ln
g
ðmÞ
p
¼ n
ln
k
k
1
Þ
ð
1
kÞ
G
A;
5
ð
k
a
q
st
ln
ðY
st
Þ
ð
Þ
q
gl
q
st
þ
5
a
q
gl
X
þ
ð
1
X
Þ
q
gl
q
st
:
(158)
ðY
gl
Þ
The model requires pure-component surface (
q
rp
and
q
w
) and size (
r
rp
and
r
w
)
parameters for the monomer unit and for water, the degree of counterion dissocia-
tion in infinite dilution (
k
), the total degree of dissociation of the repeating units (
a
),
the configurational parameter (
b
), and interaction parameters (in the expressions
for the activity coefficients in state 5 where the solution is a mixture of water,
undissociated as well as dissociated repeating units and counterions).
Surface and size parameters are either available in the literature or are calculated
following the proposals by Bondi [
118
]. The degree of counterion dissociation in
infinite dilution is estimated from experimental data for the limiting osmotic
coefficient of an aqueous solution of the polyion. Following the ideas outlined in
the description of the Pessoa and Maurer model above, one finds when the repeating
unit is a 1:1 electrolyte:
1
þ
kn
0
;ð
m
Þ
F
¼
þ n
k
:
(159)
p
1
G
i;
5
, where
i
is any solute that is present in
state 4, i.e., the neutral repeating unit
A
, the dissociated repeating unit
F
and the
counterion CI) are calculated using the VERS model of Großmann et al. [
112 114
].
The activity coefficient
The activity coefficients in state 5 (
G
i
is assumed to consist of contributions from van der
vdW
i
el
Waals-like interactions
G
and electrostatic interactions
G
i
:
vdW
i
el
i
G
i
¼ G
G
:
(160)
The electrostatic contribution is expressed in a similar way as the long-range
contribution in the model of Pessoa and Maurer [cf. (
125
)] from the Debye H¨ckel
parameter
A
'
, the charge number
z
i
of groups/species
i
and the ionic strength
I
m
(on
molality scale):
p
p
þ
1
2
1
k
2
1
I
m
el
A
'
z
i
ln
G
i
¼
2
ln 1
þ
1
:
2
I
m
p
:
(161)
an
:
1
þ
1
:
2
I
m
