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.