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Note: At very low concentrations where A
2
c << 1/M the equation reduces to
the van’t Hoff equation for ideal solutions:
∏
c
=
RT
1
M
⎛
⎝⎜
⎞
⎠⎟
∏ =
RT c
M
⎛
⎝⎜
⎞
⎠⎟ =
RTC
where C is the molar concentration of polymer.
b) Polyelectrolytes at high ionic strength (typically 0.1 M NaCl)
The equation used for uncharged polymers is also valid for polyelectrolytes
provided the ionic strength is sufficiently high. The additional Donnan effect is
incorporated in A
2
(which is much higher than for neutral polymers)
c) Polyelectrolytes in pure water or at very low salt.
In this case no exact equation is given here, but the magnitude of high
osmotic pressure can be approximated assuming:
i) All counterions dissociate from the polymer
ii) All counterions behave as ‘osmotically active’ particles and add to the
osmotic pressure
iii) van’t Hoff’s equation still applies
Example: Na-alginate in pure water.
c
alg
= 1 g/l
M
n
= 100.000 g/mol
M
0
= 198 g/mol (monomer equivalent weight
for C
6
H
8
O
7
Na)
C
alg
= 1/100.000 M = 1.0E-5 M
Molar concentration of alginate monomers C
mono
= c
alg
/M
0
= 1/198 mol/l (M) =
5.05 mM
Since each alginate monomer releases one Na
+
ion, we obtain: