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

Abstract

The interplay of topological constraints, excluded-volume interactions, persistence length and dynamical entanglement length in solutions and melts of linear chains and ring polymers is investigated by means of kinetic Monte Carlo simulations of a three-dimensional lattice model. In unknotted and unconcatenated rings, topological constraints manifest themselves in the static properties above a typical length scale dt. ∼ 1/√lφ (φ being the volume fraction, l the mean bond length). Although one might expect that the same topological length will play a role in the dynamics of entangled polymers, we show that this is not the case. Instead, a different intrinsic length de, which scales like excluded-volume blob size ξ, governs the scaling of the dynamical properties of both linear chains and rings. In contrast to dt, de has a strong dependence on the chain stiffness. The latter property enables us to study the full crossover scaling in dynamical properties, up to strongly entangled polymers. In agreement with experiment the scaling functions of both architectures are found to be very similar.