Charged Micelles in Salt-Free Dilute Solutions

We study micelles in salt-free dilute aqueous solutions of diblock copolymers made of long charged A chains and short hydrophobic B chains. The number density of aggregates with p chains ( n p ) and the number of condensed counterions in a p -aggregated chain ( N c ( p )) are obtained equating the chemical potentials of the p -aggregated chains ( p = 2, 3, ...) with those of the free chains ( p = 1) and equating the chemical potentials of the condensed counterions in the aggregates ( p = 1, 2, ...) with those of the free counterions. The critical micelle concentration (cmc) and the degree of polydispersity are large in charged diblock copolymer solutions. Since N c ( p ) increases as p increases, micelles with p ≫ 1 are nearly neutral. The most populated micelles in experimetally accessible systems, however, have a small number of chains and their effective charge is not strongly reduced. As the concentration of copolymer increases above the cmc, the concentration of free chains decreases.