Can Polymer Chains Cross Each Other and Still Be Entangled

The effect of chain crossing on polymer entanglement behavior is studied using molecular dynamics simulations of linear hard-sphere chains. The degree of chain crossing is controlled by changing the amplitude of bond vibrations while keeping the average bond length fixed. When the vibration amplitude is small, chain crossing is strictly prohibited, but for larger amplitudes the chains can cross. When chain crossing is strictly prohibited, the apparent scaling of the self-diffusion coefficient, D, and rotational relaxation time, τR, with degree of polymerization, N, is consistent with entangled behavior, and when chains cross freely Rouse dynamics is recovered. There is an intermediate regime, however, when chains are allowed to cross, but crossing events are rare. Under these conditions entanglement behavior is recovered. We therefore conclude that polymer chains can cross and still be entangled for finite length chains. There is no discernible change in the intermolecular static structure factor between ...