Web Release Date: December 4,
Role of Condensed Counterions in the Thermodynamics of Surfactant Micelle Formation with and without Oppositely Charged Polyelectrolytes
Received June 29, 1998 In Final Form: September 28, 1998 Abstract: We present a simple model of micelle formation that includes any effects of condensed counterions. The
critical micelle concentration (cmc) of ionic surfactants has a much weaker dependence on surfactant tail
length than nonionic surfactants because condensed counterions on the ionic surfactant micelle lose their
translational entropy, as predicted by Murray and Hartley in 1935. The critical aggregation concentration
(cac) of ionic surfactants in the presence of oppositely charged polyelectrolytes is much smaller than the
cmc, and has a strong dependence on surfactant tail length, similar to the cmc of nonionic surfactants.
The oppositely charged polyelectrolyte has a strong electrostatic interaction with the micelle surface,
partially accounting for the low cac. The binding of micelle and polyelectrolyte also means that no condensed
counterions are necessary on the micelle surface, which also lowers the cac and changes the dependence
of the cac on surfactant tail length. For strongly charged polyelectrolytes, the cac is lowered further still
because counterions are released from the polyelectrolyte when the surfactant binds to it. Our model
correctly predicts that the cac increases as salt is added while the cmc decreases with added salt, owing
to the different roles of counterion condensation. The experimental increases in the cac as either the charge
density or concentration of the polyelectrolyte increases are also explained by the model. We experimentally
find that the number of counterions released from the polyelectrolyte per bound surfactant is roughly equal
to the fraction of neutralized monomers with bound counterions.
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