Topological contributions to nonlinear elasticity in branched polymers

The dynamics and rheology of entangled polymer fluids are dominated at long times by topological constraints. The topological structure of the molecules themselves is known to control the linear stress relaxation function in a way that agrees well with the ''tube'' model. Here we extend the model to calculate the nonlinear elastic response of highly branched polymers under large shear strains. The nonlinear strain dependence is strongly sensitive to the distribution of free ends in the molecules, in contrast to the linear stress relaxation. Calculations for combs, monodisperse trees, and the classical gelation ensemble are compared to experimental results on the unknown structure of branched polyethylene, and point strongly to a treelike structure.