We present experiments and theory on the melt dynamics of monodisperse entangled
polymers of H-shaped architecture. Frequency-dependent rheological data on a series of polyisoprene
H-polymers are in good agreement with a tube model theory that combines path-length fluctuation (like
that of star polymer melts) at high frequency, with reptation of the self-entangled “cross-bars” at low
frequencies (like that of linear polymer melts). We account explicitly for mild polydispersity. Nonlinear
step-strain and transient data in shear and extension confirm the presence of a relaxation time not seen
in linear response, corresponding to the curvilinear stretch of the cross-bars. This time is very sensitive
to strain due to the exponential dependence of the branch-point friction constants on the effective dangling
path length. Strain-induced rearrangements of the branch points are confirmed by small-angle neutron
scattering (SANS) on stretched and quenched partially deuterated samples. We develop an extension of
melt-scattering theory to deal with the presence of deformed tube variables to interpret the SANS data.
Molecular calculations for the rheological behavior of a melt of multiply branched polymers with three levels of branching are presented. Extending the Doi-Edwards-de Gennes tube model, we consider a relaxation hierarchy where the entangled chains relax from the outermost sections toward the center of a branched treelike molecule. Generalizing star-polymer dynamics gives relaxation times in linear response. By including stretching of segments, predictions are made for the stress in nonlinear response. Relative motion between tube and polymer chain is included in the orientation dynamics. The novel constitutive equation we propose predicts characteristic features in the nonlinear rheology. These features arise from coupling of the stretch and orientation in different sections of the molecule. Such coupling and relative tube-chain motion are not present in existing molecular theories yet may be significant in the rheology of multiply branched polymers such as low-density polyethylene. The full tubemodel calculation is compared to a "multimode pom-pom" model of the same architecture, illuminating the approximations made in that approach.
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