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.
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