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A series of novel and biocompatible hyperbranched polyglycidol-b-poly(L-lactide) (HBP-b-p(L-lactide)n) (n =10,20,30 and 40) copolymers have been successfully synthesized by anionic ring-opening multi-branching polymerization of glycidol followed by ring-opening polymerization of L-lactide using an ionic liquid,1,3-di-cyclohexyl-benzimidazolium hydrogen carbonate,as a organocatalyst[1].