Theoretical molecular rheology of branched polymers in simple and complex flows: the pom-pom model

The nonlinear rheological constitutive equation of a class of multiply branched polymers is derived using the tube model. The molecular architecture may be thought of as two q-arm stars connected by a polymeric ''crossbar.'' The dynamics lead to a novel integrodifferential equation which exhibits extreme strain hardening in extension and strain softening in shear. Calculations of flow through a contraction predict that the degree of long-chain branching controls the growth of corner vortices, in agreement with experiments on commercial branched polymers.