Models for randomly hyperbranched polymers: Theory and simulation.

We derive theoretical models for the structures of randomly hyperbranched polymers in solution, and test them against computer simulations. The models are based on the same basic approach: Building a structure by the random assembly of "simple units," which may be monomers, linear chains, or larger branched species. Comparisons to simulation reported here show that the conformations of hyperbranched species, i.e., their radii of gyration and full density profiles, are accurately described by this approach. These stringent tests complement previous tests against experiment. We include the effects of solvent quality at the mean-field level. Our model works best for hyperbranched structures, but also reproduces very well the simulated density profiles of dendrimers. The models reported here provide a simple, but realistic, picture of the physical influences that affect the conformations of hyperbranched species.