Handbook of Solvents - George Wypych - ChemTech - Ventech!

730 Ranieri Urbani and Attilio Cesàro
Figure 12.2.14. The rigid chain (a), the corresponding polyelectrolyte model (b) and the realistic flexible model of
a polysaccharidic chain (c).
structural values of ξ> 1, a defined amount of counterions will “condense” from the solution
into the domain of the polymer chain so as to reduce the “effective” value of ξto unity. For
water, ξ = 0.714/b (with b expressed in nm), and is practically independent of T, being the
electrostatic-excess Gibbs free energy of the solution given by:
[ ( ) ]
1
G =−ξln −exp −Kb
el
where K is the Debye-Hückel screening parameter. Application of this theory has been
made to many experimental cases, and in particular an extensive correlation has been made
between the theoretical predictions and the thermodynamic data on the processes of
protonation, dilution and mixing with ions. 76
Besides these nice applications of the theory to problems with a strong “academic”
character, there is another very striking example of prediction of solvent-induced
conformational changes for the effects of salts on the conformational stability of ordered
polyelectrolytes. In fact, in addition to the condensation phenomena predicted by the
polyelectrolitic theory, other physical responses may also occur (also simultaneously),
which may mask this central statement of the Manning theory “that the onset of the critical
value ξ (for univalent ions ξ > 1) constitutes a thermodynamic instability which must be
compensated by counterion condensation”. In fact, chain extension and/or disaggregation
of aggregated chains may occur or change upon the variation of charge density, and the energetic
instability effectively becomes a function of the thermodynamic state of the
polyelectrolytic chain.
The range of theoretical and experimental approaches has been, in particular, addressed
to the problem of conformational transitions between two different states, provided
they have different charge densities. For thermally induced, conformational transitions be-