Segmental distribution functions for a micelle comprised of small symmetric diblock copolymers (short chain amphiphiles)

The micelle formed by short chain amphiphiles (small diblock copolymers) in a selective solvent has been simulated on a cubic lattice. The system contains twenty chains, each with ten beads of A and ten beads of B, at a volume fraction of 0.0376. These chains form a single micelle when the pairwise interaction of nonbonded beads in the insoluble block contribute an energy of −0.5 kT, all other interaction energies being zero. The micelle consists of an internal core that is a close packed region occupied almost exclusively by the insoluble blocks, and a corona, the outer portion of which consists primarily of solvent and the soluble blocks. However, the interface between these two regions is not sharp, as judged by distribution functions for the two types of beads, and for the junctions between the blocks. Letting 〈r 2j〉 denote the mean square radius of gyration of the junctions, the close packed core of insoluble beads extends from the center of mass no farther than ∼0.5 〈r 2j〉. The free ends of the insoluble block have a mean square radius of gyration of 0.88 〈r 2j〉, which places them, on average, farther from the center of mass than a randomly chosen bead in the insoluble block. The results are not compatible with models for a diblock copolymer micelle that assume a sharp interface, nor with models that assume the free ends of the insoluble block seek out the center of mass, or are randomly distributed throughout the core.