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3.4. THE DONNAN EQUILIBRIUM
3.4.1. Definition
The Donnan equilibrium can de defined as the description – including
mathematical expressions for chemical potential or osmotic pressure – for a
system involving a dissolved polyelectrolyte in equilibrium with a solution
containing added salt.
The Donnan equilibrium becomes effective when polymer is separated from
pure solvent by a semipermeable membrane (as described for osmometry
above). Consider a polyelectrolyte, for example chitosan chloride, or sodium
alginate, dissolved in water at the
α
-side:
The counter-ions will dissociate from the polymer, but will remain on the
α
-
side due to the electroneutrality criterium. The large increase in entropy
because of their dissociation is in fact the thermodynamic driving force for
solubility (
Δ
H may not be very large). Consequently, the osmotic pressure and
hence – A
2
– will be large (remember the laboratory exercise on alginate in
the absence of salt). If the molecular weight is determined from osmotic
pressure measurements in such a system, the error will be enormous (factor
z+1 underestimated of M
n
).
Consider a salt, for example NaCl, being added to the system. What will
happen to the distribution of ions, osmotic pressure, and A
2
? For simplicity we
add the salt to the
β
-side (but addition to the
α
-side or both sides give the
same equilibrium situation).
This is obviously an unstable situation. The membrane is permeable to the
salt, and it will (slowly) start diffusing over to the
α
-side until a new equilibrium
has been established, as schematically illustrated below:
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-side
β
-side
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+ - + - + - +-
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