Abstract
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.