Entanglement Transition of Randomly Branched Polymers in the Hyperbranched Class

Abstract

We study the melt rheology of randomly branched polymers in the hyperbranched polymer (HBP) class which are formed by the co-condensation of AB and AB 2 type monomers. Specifically, we study the effect of branch length M x on the entanglement transition in the HBP class. To this end, two series of HBPs were prepared using AB 2 mole fractions of 10% and 1% respectively. This allowed us to vary M x from just below to just above M e, the entanglement molecular weight for linear chains of the same chemistry. For the 10% branched samples ( M x < M e ), we were able to quantitatively model the low and intermediate frequency rheology data using a Rouse model for unentangled chains. For the 1% branched samples ( M x > M e ), there is a clear entanglement plateau for the higher molecular weight samples and we were able to quantitatively model the rheology around the entanglement plateau region using the tube model. Our data demonstrate conclusively that the entanglement transition for randomly branched polymers in the HBP class is controlled by M x and the transition occurs around M x ≈ M e . These conclusions are the same as for randomly branched polymers in the percolation class. We are able to explain these results using either the Colby−Rubinstein model or double reptation model for entanglements if we assume that whole molecules and side branches with Rouse times less than the Rouse time of an entanglement do not contribute to entanglement formation.