Onset of Entanglements Revisited. Dynamical Analysis

Abstract

In a series of two papers, we study the onset of entanglements and the transition from Rouse-type to reptation dynamics, in the context of dissipative particle dynamics (DPD) simulations of a coarse-grained polymer melt. A set of monodisperse systems with increasing chain length is examined. We consider both static and dynamic aspects of the problem. Part I, the preceding paper (DOI: 10.1021/ma901131c), presents a topological analysis of our systems. It deals with the continuous transition from unentangled to entangled topology, as chain length increases, at the level of primitive paths (PPs). In part II, this paper, we present the dynamics of our systems, and a comparison between topological and dynamical analysis. We utilize a coarse-grained model of polyethylene, based on the blob (or bead) picture of a polymer chain. The conservative potentials describing bead interactions are derived by a bottom-up approach. Each bead corresponds to 20 carbon atoms. Because of the large coarse-graining level, beads can easily overlap and chain contours can cross each other. We maintain chain uncrossability by introducing a segmental repulsive potential (SRP), adapted to our model. It is demonstrated that suitable parametrization of this potential can reproduce the dynamical transition from Rouse to reptation dynamics. For short chain unentangled systems, we observe a deviation from the pure Rouse behavior, attributed to the presence of chain stiffness, nonbonded interactions, and chain uncrossability, which are not considered by the Rouse model. For long chain systems, global dynamics is typical of reptation. The chain length dependence of viscosity and self-diffusion is described by power laws, with exponents equal to +3.2 and −2.3, respectively. A global and local (Rouse-mode) dynamical analysis, a static topological analysis, and the comparison between them, shows that topological constraints alter polymer dynamics at length scales much shorter than the length scales implied by the reptation model. This is evidenced by a slowing down of Rouse modes, which is maximum at the length scale where the underlying system of interpenetrating PPs appears as a network of topological constraints.