Rheology of randomly branched polymers

The molecular structure of randomly branched polymers is understood using percolation theory. Once the chain length between branch points and the extent of reaction relative to the gel point are specified by synthesis, both the molecular structure and the linear viscoelastic response can be determined using simple models. We demonstrate these ideas using randomly branched polymers with known chain lengths between branch points. Then we exploit this finding to characterize the chain length between branch points for polyethylenes from knowledge of their weight-average molecular weight and zero-shear-rate viscosity.