Universal properties of branched copolymers in dilute solutions

Abstract: We analyze the universal conformational properties of complex copolymer macromolecules, based on two topologies: the rosette structure containing $f_c$ linear branches and $f_r$ closed loops grafted to the central core, and the symmetric pom-pom structure, consisting of a backbone linear chain terminated by two branching points with functionalities $f$. We assume that the constituent strands (branches) of these structures can be of two different chemical species $a$ and $b$. Depending on the solvent conditions, the inter- or intrachain interactions of some links may vanish, which corresponds to $\Theta$-state of the corresponding polymer species. Applying both the analytical approach within the frames of direct polymer renormalization and numerical simulations based on the lattice model of polymer, we evaluated the set of parameters characterizing the size properties of constituent parts of two complex topologies and estimated quantitatively the impact of interactions between constituent parts on these size characteristics.