On the Effective Charge of Hydrophobic Polyelectrolytes

In this paper, we analyze the behavior of hydrophobic polyelectrolytes. It has been proposed that this system adopts a pearl necklace structure reminiscent of the Rayleigh instability of a charged droplet. Using a Poisson-Boltzmann approach, we calculate the counterion distribution around a given pearl, assuming the latter to be penetrable for the counterions. This allows us to calculate the effective electric charge of the pearl as a function of the chemical charge. Our predictions are in good agreement with the recent experimental measurements of the effective charge by Essati et al. (Essafi, W.; Lafuma, F.; Baig], D.; Williams, C. E. Europhys. Lett. 2005, 71, 938.). Our results allow us to understand the large deviation from the Manning law observed in these experiments.