Self-assembly of interacting polyelectrolytes and ionic surfactants

In this study, we employ Langevin dynamics simulations to investigate the self-assembly of anionic surfactants, multichain cationic polyelectrolytes, and counterions. By applying an aggregate indexing scheme (counting the number of surfactants and polyelectrolytes in each assembly), we construct a histogram that reveals a diverse spectrum of supramolecular structures: free surfactant micelles, isolated polyelectrolyte chains, and mixed clusters containing both species. As surfactant hydrophobicity increases, the histogram shifts from a dense distribution-where small aggregates dominate and multipolyelectrolyte mixed clusters are infrequent-to a sparse one, characterized by distinct aggregation zones separated by depletion regions. The emergence of populated zones at high aggregation indices indicates a sharp increase in large, mixed clusters containing multiple polyelectrolytes. Structurally, weakly hydrophobic surfactants result in solutions dominated by free polyelectrolytes, low-aggregation-number micelles, and small mixed clusters. Under strong hydrophobic conditions, surfactants engage in cooperative binding to form elongated micelles that associate with multiple polyelectrolyte chains. Meanwhile, most counterions remain uncondensed and freely diffuse, increasing their translational entropy. Together, our results support a model in which strong Coulomb interactions and counterion release jointly drive the mutual condensation of polyelectrolyte chains and surfactant micelles into large, anisotropic mixed clusters.