Ideal Mixing

Free Gibbs energy of association

The thermodynamic data obtained here show that mixing for a popular pair of polyelectrolytes is driven almost exclusively by entropy, that is, by the release of counterions and waters of hydration from the dissolved polyelectrolyte chains. Interestingly, the free energy of association is not large, as might be expected from electrostatic arguments. Polyelectrolyte association is fundamentally an ion exchange process, where polymer-counterion associations are replaced by polymer-polymer ion pairs. Because of the underlying requirement for polyelectrolyte charge neutralization, whether by counterions or by oppositely-charged polymer, the mechanism for polyelectrolyte complexation would be more appropriately termed “electroneutralization.”

Isothermal calorimetry titration

Heat flow per injection vs. time for the isothermal injection of PDADMA (11.36 mM) into a cell containing PSS (0.44 mM) to form a complex. Inset depicts the heat of injection vs. mole ratio of PDADMA to PSS with a fit for Ka=9. All solutions contain 0.3M NaCl and were maintained at 25 oC. A 1:1 stoichiometry was observed.

When separate component polyelectrolytes are mixed from the aqueous phase the first ion pairing removes the complex from bulk solution and it is therefore incorrect to refer to a “concentration” of the remainder of the polymer. The difference in association energy between Pols and Polc association is small – a polymer segment loses about 0.25 kT (~0.6 kJ) in configurational entropy on adsorption.

Obtaining crucial thermodynamic data for polyelectrolyte complexation by calorimetry is problematic due to the lack of heat evolved. While no data for PECs was provided in the earlier studies, modern ultrasensitive calorimetric techniques are capable of shedding some quantitative insight. For example, this figure shows the isothermal calorimetry titration (ITC, a technique commonly used to study the interaction of biological molecules) of poly(styrene sulfonate) (PSS) by poly(diallyldimethylammonium) (PDADMA).

Claudiu Bucur,
Feb 2, 2010, 1:05 PM