Quantification of interaction and topological parameters of polyisoprene star polymers under good solvent conditions

Mass fractal scaling, reflected in the mass fractal dimension d_{f}, is independently impacted by topology, reflected in the connectivity dimension c, and by tortuosity, reflected in the minimum dimension d_{min}. The mass fractal dimension is related to these other dimensions by d_{f}=cd_{min}. Branched fractal structures have a higher mass fractal dimension compared to linear structures due to a higher c, and extended structures have a lower dimension compared to convoluted self-avoiding and Gaussian walks due to a lower d_{min}. It is found, in this work, that macromolecules in thermodynamic equilibrium display a fixed mass fractal dimension d_{f} under good solvent conditions, regardless of chain topology.  These equilibrium structures accommodate changes in chain topology such as branching c by a decrease in chain tortuosity d_{min}. Symmetric star polymers are used to understand the structure of complex macromolecular topologies. A recently published hybrid Unified scattering function accounts for interarm correlations in symmetric star polymers along with polymer-solvent interaction for chains of arbitrary scaling dimension. Dilute solutions of linear, three-arm and six-arm polyisoprene stars are studied under good solvent conditions in deuterated p-xylene. Reduced chain tortuosity can be viewed as steric straightening of the arms. Steric effects for star topologies are quantified, and it is found that steric straightening of arms is more significant for lower-molecular-weight arms. The observation of constant d_{f} is explained through a modification of Flory-Krigbaum theory for branched polymers.