On two intrinsic length scales in polymer physics: Topological constraintsvs. entanglement length

The interplay of topological constraints, excluded-volume interactions, per sistence length and dynamical entanglement length in solutions and melts of linear chains and rin polymers is investigated by means of kinetic Monte C arlo simulations of a three-dimensional lattice model. In unknotted and unc oncatenated rings, topological constraints manifest them selves in the stat ic properties above a typical length scale d(t) similar to 1/rootl phi (phi being the volume fraction, l the mean bond length). Although one might exp ect that the same topological length will play a role in the dynamics of en tangled polymers, we show that this is not the case. Instead, a different i ntrinsic length de, which scales like excluded-volume blob size xi, governs the scaling of the dynamical properties of both linear chains and rings. I n contrast to d(t), d(e) has a strong dependence on the chain stiffness. Th e latter property enables us to study the full crossover scaling in dynamic al properties, up to strongly entangled polymers. In agreement with experim ent the scaling functions of both architectures are found to be very simila r.