Applications of commodity polymers are often hindered by their low thermal conductivity. In these systems, going from the standard polymers dictated by weak van der Waals interactions to biocompatible hydrogen bonded smart polymers, the thermal transport coefficient k varies between 0.1 - 0.4 W/Km. Combining all-atom molecular dynamics simulations with some experiments, we study thermal transport and its link to the elastic response of commodity plastics. We find that there exists a maximum attainable stiffness (or sound wave velocity), thus providing an upper bound of k for these solid polymers. The specific chemical structure and the glass transition temperature play no role in controlling k, especially when the microscopic interactions are hydrogen bonding based. Our results are consistent with the minimum thermal conductivity model and existing experiments. The effect of polymer stretching on k is also discussed.
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