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.

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. [S0031-9007(97)

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