Theoretical linear and nonlinear rheology of symmetric treelike polymer melts

Molecular calculations for the theological behavior of a melt of multiply b ranched polymers with three levels of branching are presented. Extending th e Doi-Edwards-de Gennes tube model, we consider a relaxation hierarchy wher e the entangled chains relax from the outermost sections toward the center of a branched treelike molecule. Generalizing star-polymer dynamics gives r elaxation times in linear response. By including stretching of segments, pr edictions are made for the stress in nonlinear response. Relative motion be tween tube and polymer chain is included in the orientation dynamics. The n ovel constitutive equation we propose predict characteristic features in th e nonlinear theology. These features arise from coupling of the stretch and orientation in different sections of the molecule. Such coupling and relat ive tube-chain motion are not present in existing molecular theories yet ma y be significant in the theology of multiply branched polymers such as low- density polyethylene. The full tube-model calculation is compared to a "mul timode pom-pom" model of the same architecture, illuminating the approximat ions made in that approach.