Basic HTML Version
153
A
2
(Donnan)
=
z
2
4
M
2
2
C
BX
This equation shows two important features:
a) The A
2
for polyelectrolytes increases with the number of charges per
molecule. Example:
Alginate has a single charge per monomer (-COO
-
), i.e. one mole of charges
per 198 g: z/M
2
= 1/198. If we prepare an alginate where 50% of the carboxyls
are COOH (acid form) and 50% are on the COOHNa form, only the Na+ ions
dissociate (COOH is a weak acid, i.e. marginal dissociation), the z/M is
0.5/198, and A
2
reduces 4 times.
b) A
2
is inversely proportional to the salt concentration (or ionic strength I).
Hence increasing C
NaCl
from e.g. 1 mM to 1 M leads to a 1000-fold decrease
in A
2
. This is manifested in a drastic lowering of the osmotic pressure (as you
have seen in the laboratory).
Sufficiently high ionic strength effectively eliminates the polyelectrolyte effect,
and osmometry will give the correct molecular weight (M
n
!) using the standard
approach.
3.4.5. Osmotic pressure of polyelectrolytes: Calculations and
examples.
(Dilute polymer solutions only)
a) Uncharged polymers
Uncharged polymers behave as any other uncharged molecule. Hence, the
osmotic pressure is given by:
∏
c
=
RT
1
M
+
A
2
c
⎛
⎝⎜
⎞
⎠⎟
c: Polymer concentration in g/ml
M: Molecular weight (M
n
if polydisperse)
A
2
: Second virial coefficient
R = 8.315 J/mol K = 0.0820 L atm/mol K
T = absolute temperature (K)