Polyelectrolytic Amphiphilic Model Networks in Water:  A Molecular Thermodynamic Theory for Their Microphase Separation

The aqueous aggregation behavior of networks comprising hydrophilic ionic blocks and hydrophobic nonionic blocks was studied by formulating a molecular thermodynamic theory, which considers the Gibbs free energies of the two possible states of the networks: the micelle-like state and the unimer-like state. The appropriate expressions for the elastic, mixing, and electrostatic components of the Gibbs free energy were developed for each of the two cases. For the micelle-like state, the interfacial free energy for the contact of the micellar core with the aqueous solvent was also included. For each of the two states, the total Gibbs free energy was minimized with respect to the polymer volume fraction. The lower from the two minimum Gibbs free energies corresponds to that of the more stable state. The effects of the length and degree of ionization of the hydrophilic block, the effect of the length of the hydrophobic block, the effect of the value of the Flory−Huggins interaction parameter between the hydrophobic block and water, the effect of the initial polymer volume fraction, and the effect of the number of arms per cross link were investigated. Under certain conditions, a unimer-to-micelle transition was observed, accompanied by a discontinuous change in the degree of swelling of the networks.