Polydispersity and Molecular Weight Distribution of Hyperbranched Graft Copolymers via “Hypergrafting” of AB_<i>m</i> Monomers from Polydisperse Macroinitiator Cores: Theory Meets Synthesis

Abstract

The hypergrafting strategy designates the synthesis of hyperbranched graft copolymers (HGCs) in a grafting-from approach, using ABm monomers, from multifunctional, polydisperse macroinitiator cores by slow monomer addition. Hypergrafting leads to complex polymer topologies with defined molecular weight, degree of branching (DB), and polydispersity (PD). By a generating function formalism, a generally applicable equation for the PD of HGCs (PD = PDf + (m – 1)/f̅) is derived, where PDf is the polydispersity of the core and f̅ its average functionality. In addition, the complete molecular weight distribution function has been calculated for varied m and f̅ as well as for a given distribution of initiator functionalities f. For comparison of the theoretical predictions with experimental results, a series of novel linear polyglycerol-graft-hyperbranched polyglycerol (linPG-g-hbPG) HGCs (Mn = 1000–4000 g mol–1) were synthesized and characterized as a model system. An increase in polydispersity occurred as a consequence of the hypergrafting process, confirming the theoretical predictions of the novel equation. Moreover, the model system allows for the determination of the DB of hbPG prepared by hypergrafting from linear polyglycerol macroinitatiors (DB = 0.59–0.61). The theoretical results presented are key to achieve control over the branch-on-branch topology of hyperbranched blocks in nonconventional polymer architectures, such as linear–hyperbranched block copolymers.