The equilibrium mechanical properties of a cross-linked gel of telechelic star polymers are studied by rheology and Brownian dynamics simulations. The Brownian dynamics model consists of cores to which Rouse arms are attached. Forces between the cores are obtained from a potential of mean force model developed by Likos and co-workers. Both experimentally and in the simulations, networks were created by attaching sticker groups to the ends of the arms of the polymers, which were next allowed to form bonds among them in a one to one fashion. Simulations were sped up by solving the Rouse dynamics exactly. Moreover, the Rouse model was extended to allow for different frictions on different beads. In order to describe the rheology of the non-cross-linked polymers, it had to be assumed that bead frictions increase with increasing bead number along the arms. This friction model could be transferred to describe the rheology of the network without any adjustments other than an overall increase of the frictions due to the formation of bonds. The slowing down at intermediate times of the network rheologycompared to that of the non-cross-linked polymers is well describedby the model. The percentage of stickers involved in forming inter-starbonds in the system was determined to be 25%, both from simulationsand from an application of the Green–Tobolsky relation to theexperimental plateau value of the shear relaxation modulus. Simulationswith increasing cross-link percentages revealed that on approachingthe gel transition the shear relaxation modulus develops an algebraictail, which gets frozen at a percentage of maximum cross-linking ofabout 11%.
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