Polymer branching and first normal stress differences in small-amplitude oscillatory shear flow

General rigid bead-rod theory explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead-rod theory, we relate the normal stress differences of polymeric liquids to the branch position on a backbone branched macromolecule. In this work, we explore the first normal stress differences coefficients of different axisymmetric polymer configurations. When non-dimensionalized with the zero-shear first normal stress difference coefficient, the normal stress differences depend solely on the dimensionless frequency. In this work, in this way, we compare and contrast the normal stress differences of macromolecular chains that are branched. We explore the effects of branch position, length, functionality, spacing, and multiplicity, along a straight chain, in addition to rings and star-shaped macromolecules in small-amplitude oscillatory shear flow.